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
Connecting Related Rates and Differential Equations
Brandt, Keith
2012-01-01
This article points out a simple connection between related rates and differential equations. The connection can be used for in-class examples or homework exercises, and it is accessible to students who are familiar with separation of variables.
Directory of Open Access Journals (Sweden)
Ayodele O. Kolawole
Full Text Available Fish hepatic glutathione transferases are connected with the elimination of intracellular pollutants and detoxification of organic micro-pollutants in their aquatic ecosystem. The two-substrate steady state kinetic mechanism of Silver catfish (Synodontis eupterus major hepatic glutathione transferases purified to apparent homogeneity was explored. The enzyme was dimeric enzyme with a monomeric size of 25.6 kDa. Initial-velocity studies and Product inhibition patterns by methyl glutathione and chloride with respect to GSH-CDNB; GSH-ρ-nitrophenylacetate; and GSH-Ethacrynic acid all conforms to a rapid equilibrium sequential random Bi Bi kinetic mechanism rather than steady state sequential random Bi Bi kinetic. α was 2.96 ± 0.35 for the model. The pH profile of Vmax/KM (with saturating 1-chloro-2,4-dinitrobenzene and variable GSH concentrations showed apparent pKa value of 6.88 and 9.86. Inhibition studies as a function of inhibitor concentration show that the enzyme is a homodimer and near neutral GST. The enzyme poorly conjugates 4-hydroxylnonenal and cumene hydroperoxide and may not be involved in oxidative stress protection. The seGST is unique and overwhelmingly shows characteristics similar to those of homodimeric class Pi GSTs, as was indicated by its kinetic mechanism, substrate specificity and inhibition studies. The rate- limiting step, probably the product release, of the reaction is viscosity-dependent and is consequential if macro-viscosogen or micro-viscosogen. Keywords: Silver catfish, Glutathione transferase, Steady-state, Kinetic mechanism, Inhibition
Status of rates and rate equations for thermal leptogenesis
Biondini, S.; Bödeker, D.; Brambilla, N.; Garny, M.; Ghiglieri, J.; Hohenegger, A.; Laine, M.; Mendizabal, S.; Millington, P.; Salvio, A.; Vairo, A.
2018-02-01
In many realizations of leptogenesis, heavy right-handed neutrinos play the main role in the generation of an imbalance between matter and antimatter in the early Universe. Hence, it is relevant to address quantitatively their dynamics in a hot and dense environment by taking into account the various thermal aspects of the problem at hand. The strong washout regime offers an interesting framework to carry out calculations systematically and reduce theoretical uncertainties. Indeed, any matter-antimatter asymmetry generated when the temperature of the hot plasma T exceeds the right-handed neutrino mass scale M is efficiently erased, and one can focus on the temperature window T ≪ M. We review recent progress in the thermal field theoretic derivation of the key ingredients for the leptogenesis mechanism: the right-handed neutrino production rate, the CP asymmetry in the heavy-neutrino decays and the washout rates. The derivation of evolution equations for the heavy-neutrino and lepton-asymmetry number densities, their rigorous formulation and applicability are also discussed.
Quick and Easy Rate Equations for Multistep Reactions
Savage, Phillip E.
2008-01-01
Students rarely see closed-form analytical rate equations derived from underlying chemical mechanisms that contain more than a few steps unless restrictive simplifying assumptions (e.g., existence of a rate-determining step) are made. Yet, work published decades ago allows closed-form analytical rate equations to be written quickly and easily for…
Representing Rate Equations for Enzyme-Catalyzed Reactions
Ault, Addison
2011-01-01
Rate equations for enzyme-catalyzed reactions are derived and presented in a way that makes it easier for the nonspecialist to see how the rate of an enzyme-catalyzed reaction depends upon kinetic constants and concentrations. This is done with distribution equations that show how the rate of the reaction depends upon the relative quantities of…
Studies on Microwave Heated Drying-rate Equations of Foods
呂, 聯通; 久保田, 清; 鈴木, 寛一; 岡崎, 尚; 山下, 洋右
1990-01-01
In order to design various microwave heated drying apparatuses, we must take drying-rate equations which are based on simple drying-rate models. In a previous paper (KUBOTA, et al., 1990), we have studied a convenient microwave heated drying instrument, and studied the simple drying-rate equations of potato and so on by using the simple empirical rate equations that have been reported in previous papers (KUBOTA, 1979-1, 1979-2). In this paper, we studied the microwave drying rate of the const...
Theory of nanolaser devices: Rate equation analysis versus microscopic theory
DEFF Research Database (Denmark)
Lorke, Michael; Skovgård, Troels Suhr; Gregersen, Niels
2013-01-01
A rate equation theory for quantum-dot-based nanolaser devices is developed. We show that these rate equations are capable of reproducing results of a microscopic semiconductor theory, making them an appropriate starting point for complex device simulations of nanolasers. The input...
Equations to Estimate Creatinine Excretion Rate : The CKD Epidemiology Collaboration
Ix, Joachim H.; Wassel, Christina L.; Stevens, Lesley A.; Beck, Gerald J.; Froissart, Marc; Navis, Gerjan; Rodby, Roger; Torres, Vicente E.; Zhang, Yaping (Lucy); Greene, Tom; Levey, Andrew S.
Background and objectives Creatinine excretion rate (CER) indicates timed urine collection accuracy. Although equations to estimate CER exist, their bias and precision are untested and none simultaneously include age, sex, race, and weight. Design, setting, participants, & measurements Participants
Rate equation simulation of temporal characteristics of a pulsed dye ...
Indian Academy of Sciences (India)
-dependent, two-dimensional (in space) rate equation model of a .... fluorescence band of the dye is divided into ten wavelength segments of variable sizes. ... qualitative and reasonably good quantitative agreement with experimental results.
Diffusion equations and the time evolution of foreign exchange rates
Energy Technology Data Exchange (ETDEWEB)
Figueiredo, Annibal; Castro, Marcio T. de [Institute of Physics, Universidade de Brasília, Brasília DF 70910-900 (Brazil); Fonseca, Regina C.B. da [Department of Mathematics, Instituto Federal de Goiás, Goiânia GO 74055-110 (Brazil); Gleria, Iram, E-mail: iram@fis.ufal.br [Institute of Physics, Federal University of Alagoas, Brazil, Maceió AL 57072-900 (Brazil)
2013-10-01
We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers–Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.
Diffusion equations and the time evolution of foreign exchange rates
Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram
2013-10-01
We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.
Diffusion equations and the time evolution of foreign exchange rates
International Nuclear Information System (INIS)
Figueiredo, Annibal; Castro, Marcio T. de; Fonseca, Regina C.B. da; Gleria, Iram
2013-01-01
We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers–Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.
Non-equilibrium reaction rates in chemical kinetic equations
Gorbachev, Yuriy
2018-05-01
Within the recently proposed asymptotic method for solving the Boltzmann equation for chemically reacting gas mixture, the chemical kinetic equations has been derived. Corresponding one-temperature non-equilibrium reaction rates are expressed in terms of specific heat capacities of the species participate in the chemical reactions, bracket integrals connected with the internal energy transfer in inelastic non-reactive collisions and energy transfer coefficients. Reactions of dissociation/recombination of homonuclear and heteronuclear diatomic molecules are considered. It is shown that all reaction rates are the complex functions of the species densities, similarly to the unimolecular reaction rates. For determining the rate coefficients it is recommended to tabulate corresponding bracket integrals, additionally to the equilibrium rate constants. Correlation of the obtained results with the irreversible thermodynamics is established.
Cell membrane temperature rate sensitivity predicted from the Nernst equation.
Barnes, F S
1984-01-01
A hyperpolarized current is predicted from the Nernst equation for conditions of positive temperature derivatives with respect to time. This ion current, coupled with changes in membrane channel conductivities, is expected to contribute to a transient potential shift across the cell membrane for silent cells and to a change in firing rate for pacemaker cells.
ECONOMETRIC APPROACH TO DIFFERENCE EQUATIONS MODELING OF EXCHANGE RATES CHANGES
Directory of Open Access Journals (Sweden)
Josip Arnerić
2010-12-01
Full Text Available Time series models that are commonly used in econometric modeling are autoregressive stochastic linear models (AR and models of moving averages (MA. Mentioned models by their structure are actually stochastic difference equations. Therefore, the objective of this paper is to estimate difference equations containing stochastic (random component. Estimated models of time series will be used to forecast observed data in the future. Namely, solutions of difference equations are closely related to conditions of stationary time series models. Based on the fact that volatility is time varying in high frequency data and that periods of high volatility tend to cluster, the most successful and popular models in modeling time varying volatility are GARCH type models and their variants. However, GARCH models will not be analyzed because the purpose of this research is to predict the value of the exchange rate in the levels within conditional mean equation and to determine whether the observed variable has a stable or explosive time path. Based on the estimated difference equation it will be examined whether Croatia is implementing a stable policy of exchange rates.
Empirical rate equation model and rate calculations of hydrogen generation for Hanford tank waste
International Nuclear Information System (INIS)
HU, T.A.
1999-01-01
Empirical rate equations are derived to estimate hydrogen generation based on chemical reactions, radiolysis of water and organic compounds, and corrosion processes. A comparison of the generation rates observed in the field with the rates calculated for twenty eight tanks shows agreement within a factor of two to three
Rate equation analysis of hydrogen uptake on Si (100) surfaces
International Nuclear Information System (INIS)
Inanaga, S.; Rahman, F.; Khanom, F.; Namiki, A.
2005-01-01
We have studied the uptake process of H on Si (100) surfaces by means of rate equation analysis. Flowers' quasiequilibrium model for adsorption and desorption of H [M. C. Flowers, N. B. H. Jonathan, A. Morris, and S. Wright, Surf. Sci. 396, 227 (1998)] is extended so that in addition to the H abstraction (ABS) and β 2 -channel thermal desorption (TD) the proposed rate equation further includes the adsorption-induced desorption (AID) and β 1 -TD. The validity of the model is tested by the experiments of ABS and AID rates in the reaction system H+D/Si (100). Consequently, we find it can well reproduce the experimental results, validating the proposed model. We find the AID rate curve as a function of surface temperature T s exhibits a clear anti-correlation with the bulk dangling bond density versus T s curve reported in the plasma-enhanced chemical vapor deposition (CVD) for amorphous Si films. The significance of the H chemistry in plasma-enhanced CVD is discussed
Validation of resting metabolic rate prediction equations for teenagers
Directory of Open Access Journals (Sweden)
Paulo Henrique Santos da Fonseca
2007-09-01
Full Text Available The resting metabolic rate (RMR can be defi ned as the minimum rate of energy spent and represents the main component of the energetic outlay. The purpose of this study is to validate equations to predict the resting metabolic rate in teenagers (103 individuals, being 51 girls and 52 boys, with age between 10 and 17 years from Florianópolis – SC – Brazil. It was measured: the body weight, body height, skinfolds and obtained the lean and body fat mass through bioimpedance. The nonproteic RMR was measured by Weir’s equation (1949, utilizing AeroSport TEEM-100 gas analyzer. The studied equations were: Harry and Benedict (1919, Schofi eld (1985, WHO/FAO/UNU (1985, Henry and Rees (1991, Molnár et al. (1998, Tverskaya et al. (1998 and Müller et al. (2004. In order to study the cross-validation of the RMR prediction equations and its standard measure (Weir 1949, the following statistics procedure were calculated: Pearson’s correlation (r ≥ 0.70, the “t” test with the signifi cance level of p0.05 in relation to the standard measure, with exception of the equations suggested for Tverskaya et al. (1998, and the two models of Müller et al (2004. Even though there was not a signifi cant difference, only the models considered for Henry and Rees (1991, and Molnár et al. (1995 had gotten constant error variation under 5%. All the equations analyzed in the study in girls had not reached criterion of correlation values of 0.70 with the indirect calorimetry. Analyzing the prediction equations of RMR in boys, all of them had moderate correlation coeffi cients with the indirect calorimetry, however below 0.70. Only the equation developed for Tverskaya et al. (1998 presented differences (p ABSTRACT0,05 em relação à medida padrão (Weir 1949, com exceção das equações sugeridas por Tverskaya et al. (1998 e os dois modelos de Müller et al (2004. Mesmo não havendo diferença signifi cativa, somente os modelos propostos por Henry e Rees (1991
Validation of estimated glomerular filtration rate equations for Japanese children.
Gotoh, Yoshimitsu; Uemura, Osamu; Ishikura, Kenji; Sakai, Tomoyuki; Hamasaki, Yuko; Araki, Yoshinori; Hamda, Riku; Honda, Masataka
2018-01-25
The gold standard for evaluation of kidney function is renal inulin clearance (Cin). However, the methodology for Cin is complicated and difficult, especially for younger children and/or patients with bladder dysfunction. Therefore, we developed a simple and easier method for obtaining the estimated glomerular filtration rate (eGFR) using equations and values for several biomarkers, i.e., serum creatinine (Cr), serum cystatin C (cystC), serum beta-2 microglobulin (β 2 MG), and creatinine clearance (Ccr). The purpose of the present study was to validate these equations with a new data set. To validate each equation, we used data of 140 patients with CKD with clinical need for Cin, using the measured GFR (mGFR). We compared the results for each eGFR equation with the mGFR using mean error (ME), root mean square error (RMSE), P 30 , and Bland-Altman analysis. The ME of Cr, cystC, β 2 MG, and Ccr based on eGFR was 15.8 ± 13.0, 17.2 ± 16.5, 15.4 ± 14.3, and 10.6 ± 13.0 ml/min/1.73 m 2 , respectively. The RMSE was 29.5, 23.8, 20.9, and 16.7, respectively. The P 30 was 79.4, 71.1, 69.5, and 92.9%, respectively. The Bland-Altman bias analysis showed values of 4.0 ± 18.6, 5.3 ± 16.8, 12.7 ± 17.0, and 2.5 ± 17.2 ml/min/1.73 m 2 , respectively, for these parameters. The bias of each eGFR equation was not large. Therefore, each eGFR equation could be used.
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
Kinematic equations for resolved-rate control of an industrial robot arm
Barker, L. K.
1983-01-01
An operator can use kinematic, resolved-rate equations to dynamically control a robot arm by watching its response to commanded inputs. Known resolved-rate equations for the control of a particular six-degree-of-freedom industrial robot arm and proceeds to simplify the equations for faster computations are derived. Methods for controlling the robot arm in regions which normally cause mathematical singularities in the resolved-rate equations are discussed.
Derivation and application of hydraulic equation for variable-rate ...
African Journals Online (AJOL)
The variable-rate contour-controlled sprinkler (VRCS) for precision irrigation can throw water on a given shaped area and the flow rate is also varied with the throw distance of the sprinkler for the purpose of high uniformity irrigation. Much of past research work were concentrated on the mechanical availability of ...
arXiv Status of rates and rate equations for thermal leptogenesis
Biondini, Simone; Brambilla, Nora; Garny, Mathias; Ghiglieri, Jacopo; Hohenegger, Andreas; Laine, Mikko; Mendizabal, Sebastian; Millington, Peter; Salvio, Alberto; Vairo, Antonio
2018-02-28
In many realizations of leptogenesis, heavy right-handed neutrinos play the main role in the generation of an imbalance between matter and antimatter in the early Universe. Hence, it is relevant to address quantitatively their dynamics in a hot and dense environment by taking into account the various thermal aspects of the problem at hand. The strong washout regime offers an interesting framework to carry out calculations systematically and reduce theoretical uncertainties. Indeed, any matter-antimatter asymmetry generated when the temperature of the hot plasma $T$ exceeds the right-handed neutrino mass scale $M$ is efficiently erased, and one can focus on the temperature window $T \\ll M$. We review recent progresses in the thermal field theoretic derivation of the key ingredients for the leptogenesis mechanism: the right-handed neutrino production rate, the CP asymmetry in the heavy-neutrino decays and the washout rates. The derivation of evolution equations for the heavy-neutrino and lepton-asymmetry number...
Application of a mechanism-based rate equation to black liquor gasification rate data
Energy Technology Data Exchange (ETDEWEB)
Overacker, N.L.; Waag, K.J.; Frederick, W.J. [Oregon State University, OR (United States). Dept. of Chemical Engineering; Whitty, K.J.
1995-09-01
There is growing interest worldwide to develop alternate chemical recovery processes for paper mills which are cheaper, safer, more efficient and more environmentally sound than traditional technology. Pressurized gasification of black liquor is the basis for many proposed schemes and offers the possibility to double the amount of electricity generated per unit of dry black liquor solids. Such technology also has capital, safety and environmental advantages. One of the most important considerations regarding this emerging technology is the kinetics of the gasification reaction. This has been studied empirically at Aabo Akademi University for the pressurized gasification with carbon dioxide and steam. For the purposes of reactor modeling and scale-up, however, a thorough understanding of the mechanism behind the reaction is desirable. This report discusses the applicability of a mechanism-based rate equation to gasification of black liquor. The mechanism considered was developed for alkali-catalyzed gasification of carbon and is tested using black liquor gasification data obtained during simultaneous reaction with H{sub 2}O and CO. Equilibrium considerations and the influence of the water-gas shift reaction are also discussed. The work presented here is a cooperative effort between Aabo Akademi University and Oregon State University. The experimental work and some of the data analysis was performed at Aabo Akademi University. Development of the models and consideration of their applicability was performed primarily at Oregon State University
Rate equations for tracer studies in recirculating reactors
Energy Technology Data Exchange (ETDEWEB)
Happel, J [Columbia Univ., New York (USA). Dept. of Chemical Engineering
1974-10-01
The employment of isotopic tracers is a useful technique for gaining insight into the rate controlling steps of a complex chemical reaction such as is frequently encountered in heterogeneous catalysis. An effective procedure has been to superpose tracer transfer on a reaction which is occurring under steady state conditions. If tracer transfer is employed in this fashion it is often possible to assess the individual step velocities in an assumed reaction mechanism. If transient transfer of tracer is now introduced it is possible in addition to estimate surface concentrations of chemisorbed species. The purpose of the present paper is to present the mathematical relationships involved when transfer of the tracer is not differential in the investigation. For this purpose a simple example is chosen to illustrate the various possibilities involved.
Rate equations for tracer studies in recirculatinng reactors
International Nuclear Information System (INIS)
Happel, J.
1974-01-01
The employment of isotopic tracers is a useful technique for gaining insight into the rate controlling steps of a complex chemical reaction such as is frequently encountered in heterogeneous catalysis. An effective procedure has been to superpose tracer transfer on a reaction which is occurring under steady state conditions. If tracer transfer is employed in this fashion it is often possible to assess the individual step velocities in an assumed reaction mechanism. If transient transfer of tracer is now introduced it is possible in addition to estimate surface concentrations of chemisorbed species. The purpose of the present paper is to present the mathematical relationships involved when transfer of the tracer is not differential in the investigation. For this purpose a simple example is chosen to illustrate the various possibilities involved. (auth.)
Coupled force-balance and particle-occupation rate equations for high-field electron transport
International Nuclear Information System (INIS)
Lei, X. L.
2008-01-01
It is pointed out that in the framework of balance-equation approach, the coupled force-balance and particle-occupation rate equations can be used as a complete set of equations to determine the high-field transport of semiconductors in both strong and weak electron-electron interaction limits. We call to attention that the occupation rate equation conserves the total particle number and maintains the energy balance of the relative electron system, and there is no need to introduce any other term in it. The addition of an energy-drift term in the particle-occupation rate equation [Phys. Rev. B 71, 195205 (2005)] is physically inadequate for the violation of the total particle-number conservation and the energy balance. It may lead to a substantial unphysical increase of the total particle number by the application of a dc electric field
[Estimating glomerular filtration rate in 2012: which adding value for the CKD-EPI equation?].
Delanaye, Pierre; Mariat, Christophe; Moranne, Olivier; Cavalier, Etienne; Flamant, Martin
2012-07-01
Measuring or estimating glomerular filtration rate (GFR) is still considered as the best way to apprehend global renal function. In 2009, the new Chronic Kidney Disease Epidemiology (CKD-EPI) equation has been proposed as a better estimator of GFR than the Modification of Diet in Renal Disease (MDRD) study equation. This new equation is supposed to underestimate GFR to a lesser degree in higher GFR levels. In this review, we will present and deeply discuss the performances of this equation. Based on articles published between 2009 and 2012, this review will underline advantages, notably the better knowledge of chronic kidney disease prevalence, but also limitations of this new equation, especially in some specific populations. We eventually insist on the fact that all these equations are estimations and nephrologists should remain cautious in their interpretation. Copyright © 2012 Association Société de néphrologie. Published by Elsevier SAS. All rights reserved.
International Nuclear Information System (INIS)
Einzel, D.; Woelfle, P.
1978-01-01
The kinetic equation for Bogoliubov quasiparticles for both the A and B phases of superfluid 3 He is derived from the general matrix kinetic equation. A condensed expression for the exact spin-symmetric collision integral is given. The quasiparticle relaxation rate is calculated for the BW state using the s--p approximation for the quasiparticle scattering amplitude. By using the results for the quasiparticle relaxation rate, the mean free path of Bogoliubov quasiparticles is calculated for all temperatures
The specification of cross exchange rate equations used to test Purchasing Power Parity
Hunter, J; Simpson, M
2004-01-01
The Article considers the speciÞcation of models used to test Pur- chasing Power Parity when applied to cross exchange rates. SpeciÞcally, conventional dynamic models used to test stationarity of the real exchange rate are likely to be misspeciÞed, except when the parameters of each ex- change rate equation are the same
Nonlinear fluctuation-induced rate equations for linear birth-death processes
International Nuclear Information System (INIS)
Honkonen, J.
2008-01-01
The Fock-space approach to the solution of master equations for the one-step Markov processes is reconsidered. It is shown that in birth-death processes with an absorbing state at the bottom of the occupation-number spectrum and occupation-number independent annihilation probability occupation-number fluctuations give rise to rate equations drastically different from the polynomial form typical of birth-death processes. The fluctuation-induced rate equations with the characteristic exponential terms are derived for Mikhailov's ecological model and Lanchester's model of modern warfare
Nonlinear fluctuations-induced rate equations for linear birth-death processes
Honkonen, J.
2008-05-01
The Fock-space approach to the solution of master equations for one-step Markov processes is reconsidered. It is shown that in birth-death processes with an absorbing state at the bottom of the occupation-number spectrum and occupation-number independent annihilation probability of occupation-number fluctuations give rise to rate equations drastically different from the polynomial form typical of birth-death processes. The fluctuation-induced rate equations with the characteristic exponential terms are derived for Mikhailov’s ecological model and Lanchester’s model of modern warfare.
Improved decay rates for solutions for a multidimensional generalized Benjamin-Bona-Mahony equation
Said-Houari, Belkacem
2014-01-01
In this paper, we study the decay rates of solutions for the generalized Benjamin-Bona-Mahony equation in multi-dimensional space. For initial data in some L1-weighted spaces, we prove faster decay rates of the solutions. More precisely, using the Fourier transform and the energy method, we show the global existence and the convergence rates of the solutions under the smallness assumption on the initial data and we give better decay rates of the solutions. This result improves early works in J. Differential Equations 158(2) (1999), 314-340 and Nonlinear Anal. 75(7) (2012), 3385-3392. © 2014-IOS Press.
Stochastic substitute for coupled rate equations in the modeling of highly ionized transient plasmas
International Nuclear Information System (INIS)
Eliezer, S.; Falquina, R.; Minguez, E.
1994-01-01
Plasmas produced by intense laser pulses incident on solid targets often do not satisfy the conditions for local thermodynamic equilibrium, and so cannot be modeled by transport equations relying on equations of state. A proper description involves an excessively large number of coupled rate equations connecting many quantum states of numerous species having different degrees of ionization. Here we pursue a recent suggestion to model the plasma by a few dominant states perturbed by a stochastic driving force. The driving force is taken to be a Poisson impulse process, giving a Langevin equation which is equivalent to a Fokker-Planck equation for the probability density governing the distribution of electron density. An approximate solution to the Langevin equation permits calculation of the characteristic relaxation rate. An exact stationary solution to the Fokker-Planck equation is given as a function of the strength of the stochastic driving force. This stationary solution is used, along with a Laplace transform, to convert the Fokker-Planck equation to one of Schroedinger type. We consider using the classical Hamiltonian formalism and the WKB method to obtain the time-dependent solution
Laser Rate Equation Based Filtering for Carrier Recovery in Characterization and Communication
DEFF Research Database (Denmark)
Piels, Molly; Iglesias Olmedo, Miguel; Xue, Weiqi
2015-01-01
We formulate a semiconductor laser rate equationbased approach to carrier recovery in a Bayesian filtering framework. Filter stability and the effect of model inaccuracies (unknown or un-useable rate equation coefficients) are discussed. Two potential application areas are explored: laser...... characterization and carrier recovery in coherent communication. Two rate equation based Bayesian filters, the particle filter and extended Kalman filter, are used in conjunction with a coherent receiver to measure frequency noise spectrum of a photonic crystal cavity laser with less than 20 nW of fiber...
Comment on 'A Forecasting Equation for the Canada-US Dollar Real Exchange Rate'
Kollmann, Robert
1993-01-01
This paper is a comment on the paper 'A Forecasting Equation for the Canada-US Dollar Exchange Rate' (Robert Amano and Simon van Norden, Bank of Canada). The comment was published in: The Exchange Rate and the Economy, Proceedings of 1992 Bank of Canada Conference; Bank of Canada, 1993, Ottawa (ISBN 0-660-15195-2), pp. 266-271.
Validity of predictive equations for basal metabolic rate in Japanese adults.
Miyake, Rieko; Tanaka, Shigeho; Ohkawara, Kazunori; Ishikawa-Takata, Kazuko; Hikihara, Yuki; Taguri, Emiko; Kayashita, Jun; Tabata, Izumi
2011-01-01
Many predictive equations for basal metabolic rate (BMR) based on anthropometric measurements, age, and sex have been developed, mainly for healthy Caucasians. However, it has been reported that many of these equations, used widely, overestimate BMR not only for Asians, but also for Caucasians. The present study examined the accuracy of several predictive equations for BMR in Japanese subjects. In 365 healthy Japanese male and female subjects, aged 18 to 79 y, BMR was measured in the post-absorptive state using a mask and Douglas bag. Six predictive equations were examined. Total error was used as an index of the accuracy of each equation's prediction. Predicted BMR values by Dietary Reference Intakes for Japanese (Japan-DRI), Adjusted Dietary Reference Intakes for Japanese (Adjusted-DRI), and Ganpule equations were not significantly different from the measured BMR in either sex. On the other hand, Harris-Benedict, Schofield, and Food and Agriculture Organization of the United Nations/World Health Organization/United Nations University equations were significantly higher than the measured BMR in both sexes. The prediction error by Japan-DRI, Adjusted-DRI, and Harris-Benedict equations was significantly correlated with body weight in both sexes. Total error using the Ganpule equation was low in both males and females (125 and 99 kcal/d, respectively). In addition, total error using the Adjusted-DRI equation was low in females (95 kcal/d). Thus, the Ganpule equation was the most accurate in predicting BMR in our healthy Japanese subjects, because the difference between the predicted and measured BMR was relatively small, and body weight had no effect on the prediction error.
Directory of Open Access Journals (Sweden)
S. C. Oukouomi Noutchie
2014-01-01
Full Text Available We make use of Laplace transform techniques and the method of characteristics to solve fragmentation equations explicitly. Our result is a breakthrough in the analysis of pure fragmentation equations as this is the first instance where an exact solution is provided for the fragmentation evolution equation with general fragmentation rates. This paper is the key for resolving most of the open problems in fragmentation theory including “shattering” and the sudden appearance of infinitely many particles in some systems with initial finite particles number.
International Nuclear Information System (INIS)
Kenyon, A. J.; Wojdak, M.; Ahmad, I.; Loh, W. H.; Oton, C. J.
2008-01-01
We discuss the use of rate equations to analyze the sensitization of erbium luminescence by silicon nanoclusters. In applying the general form of second-order coupled rate-equations to the Si nanocluster-erbium system, we find that the photoluminescence dynamics cannot be described using a simple rate equation model. Both rise and fall times exhibit a stretched exponential behavior, which we propose arises from a combination of a strongly distance-dependent nanocluster-erbium interaction, along with the finite size distribution and indirect band gap of the silicon nanoclusters. Furthermore, the low fraction of erbium ions that can be excited nonresonantly is a result of the small number of ions coupled to nanoclusters
Rate equation modelling of the optically pumped spin-exchange source
International Nuclear Information System (INIS)
Stenger, J.; Rith, K.
1995-01-01
Sources for spin polarized hydrogen or deuterium, polarized via spin-exchange of a laser optically pumped alkali metal, can be modelled by rate equations. The rate equations for this type of source, operated either with hydrogen or deuterium, are given explicitly with the intention of providing a useful tool for further source optimization and understanding. Laser optical pumping of alkali metal, spin-exchange collisions of hydrogen or deuterium atoms with each other and with alkali metal atoms are included, as well as depolarization due to flow and wall collisions. (orig.)
International Nuclear Information System (INIS)
Gunawan, Indra; Sulistyo, Harry; Rochmad
2001-01-01
The numerical analysis of Hooke Jeeves Methods combined with Runge Kutta Methods is used to determine the exact model of reaction rate equation of pyrrole polymerization. Chemical polymerization of pyrrole was conducted with FeCI 3 / pyrrole solution at concentration ratio of 1.62 mole / mole and 2.18 mole / mole with varrying temperature of 28, 40, 50, and 60 o C. FeCl 3 acts as an oxidation agent to form pyrrole cation that will polymerize. The numerical analysis was done to examine the exact model of reaction rate equation which is derived from reaction equation of initiation, propagation, and termination. From its numerical analysis, it is found that the pyrrole polymerization follows third order of pyrrole cation concentration
A simple algebraic cancer equation: calculating how cancers may arise with normal mutation rates
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Shibata Darryl
2010-01-01
Full Text Available Abstract Background The purpose of this article is to present a relatively easy to understand cancer model where transformation occurs when the first cell, among many at risk within a colon, accumulates a set of driver mutations. The analysis of this model yields a simple algebraic equation, which takes as inputs the number of stem cells, mutation and division rates, and the number of driver mutations, and makes predictions about cancer epidemiology. Methods The equation [p = 1 - (1 - (1 - (1 - udkNm ] calculates the probability of cancer (p and contains five parameters: the number of divisions (d, the number of stem cells (N × m, the number of critical rate-limiting pathway driver mutations (k, and the mutation rate (u. In this model progression to cancer "starts" at conception and mutations accumulate with cell division. Transformation occurs when a critical number of rate-limiting pathway mutations first accumulates within a single stem cell. Results When applied to several colorectal cancer data sets, parameter values consistent with crypt stem cell biology and normal mutation rates were able to match the increase in cancer with aging, and the mutation frequencies found in cancer genomes. The equation can help explain how cancer risks may vary with age, height, germline mutations, and aspirin use. APC mutations may shorten pathways to cancer by effectively increasing the numbers of stem cells at risk. Conclusions The equation illustrates that age-related increases in cancer frequencies may result from relatively normal division and mutation rates. Although this equation does not encompass all of the known complexity of cancer, it may be useful, especially in a teaching setting, to help illustrate relationships between small and large cancer features.
Exponential decay rate of the power spectrum for solutions of the Navier--Stokes equations
International Nuclear Information System (INIS)
Doering, C.R.; Titi, E.S.
1995-01-01
Using a method developed by Foias and Temam [J. Funct. Anal. 87, 359 (1989)], exponential decay of the spatial Fourier power spectrum for solutions of the incompressible Navier--Stokes equations is established and explicit rigorous lower bounds on a small length scale defined by the exponential decay rate are obtained
Rate equation description of quantum noise in nanolasers with few emitters
DEFF Research Database (Denmark)
Mørk, Jesper; Lippi, G. L.
2018-01-01
Rate equations for micro- and nanocavity lasers are formulated which take account of the finite number of emitters, Purcell effects as well as stochastic effects of spontaneous emission quantum noise. Analytical results are derived for the intensity noise and intensity correlation properties, g(2...
DEFF Research Database (Denmark)
Riisgård, Hans Ulrik; Larsen, Poul Scheel; Pleissner, Daniel
2014-01-01
rate (F, l h-1), W (g), and L (mm) as described by the equations: FW = aWb and FL = cLd, respectively. This is done by using available and new experimental laboratory data on M. edulis obtained by members of the same research team using different methods and controlled diets of cultivated algal cells...
Silberg, Judy L.; And Others
1994-01-01
Applied structural equation modeling to twin data to assess impact of genetic and environmental factors on children's behavioral and emotional functioning. Applied models to maternal ratings of behavior of 515 monozygotic and 749 dizygotic twin pairs. Importance of genetic, shared, and specific environmental factors for explaining variation was…
An estimator for the relative entropy rate of path measures for stochastic differential equations
Energy Technology Data Exchange (ETDEWEB)
Opper, Manfred, E-mail: manfred.opper@tu-berlin.de
2017-02-01
We address the problem of estimating the relative entropy rate (RER) for two stochastic processes described by stochastic differential equations. For the case where the drift of one process is known analytically, but one has only observations from the second process, we use a variational bound on the RER to construct an estimator.
Fixation of waste materials in grouts: Part 3, Equation for critical flow rate
International Nuclear Information System (INIS)
Tallent, O.K.; McDaniel, E.W.; Spence, R.D.; Godsey, T.T.; Dodson, K.E.
1986-12-01
Critical flow rate data for grouts prepared from three distinctly different nuclear waste materials have been correlated. The wastes include Oak Ridge National Laboratory (ORNL) low-level waste (LLW) solution, Hanford Facility waste (HFW) solution, and cladding removal waste (CRW) slurry. Data for the three wastes have been correlated with a 0.96 coefficient of correlation by the following equation: log V/sub E/ = 0.289 + 0.707 log μ/sub E/, where V/sub E/ and μ/sub E/ denote critical flow rate in m 3 /min and apparent viscosity in Pa.s, respectively. The equation may be used to estimate critical flow rate for grouts prepared within the compositional range of the investigation. 5 refs., 4 figs., 7 tabs
A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate
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Min Sun
2014-01-01
Full Text Available A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.
International Nuclear Information System (INIS)
Henderson, D.L.
1987-01-01
Time-dependent integral transport equation flux and current kernels for plane and spherical geometry are derived for homogeneous media. Using the multiple collision formalism, isotropic sources that are delta distributions in time are considered for four different problems. The plane geometry flux kernel is applied to a uniformly distributed source within an infinite medium and to a surface source in a semi-infinite medium. The spherical flux kernel is applied to a point source in an infinite medium and to a point source at the origin of a finite sphere. The time-dependent first-flight leakage rates corresponding to the existing steady state first-flight escape probabilities are computed by the Laplace transform technique assuming a delta distribution source in time. The case of a constant source emitting neutrons over a time interval, Δt, for a spatially uniform source is obtained for a slab and a sphere. Time-dependent first-flight leakage rates are also determined for the general two region spherical medium problem for isotropic sources with a delta distribution in time uniformly distributed throughout both the inner and outer regions. The time-dependent collision rates due to the uncollided neutrons are computed for a slab and a sphere using the time-dependent first-flight leakage rates and the time-dependent continuity equation. The case of a constant source emitting neutrons over a time interval, Δt, is also considered
Sabounchi, N S; Rahmandad, H; Ammerman, A
2013-10-01
Basal metabolic rate (BMR) represents the largest component of total energy expenditure and is a major contributor to energy balance. Therefore, accurately estimating BMR is critical for developing rigorous obesity prevention and control strategies. Over the past several decades, numerous BMR formulas have been developed targeted to different population groups. A comprehensive literature search revealed 248 BMR estimation equations developed using diverse ranges of age, gender, race, fat-free mass, fat mass, height, waist-to-hip ratio, body mass index and weight. A subset of 47 studies included enough detail to allow for development of meta-regression equations. Utilizing these studies, meta-equations were developed targeted to 20 specific population groups. This review provides a comprehensive summary of available BMR equations and an estimate of their accuracy. An accompanying online BMR prediction tool (available at http://www.sdl.ise.vt.edu/tutorials.html) was developed to automatically estimate BMR based on the most appropriate equation after user-entry of individual age, race, gender and weight.
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Liu X
2012-10-01
Full Text Available Xun Liu,1,2,* Mu-hua Cheng,3,* Cheng-gang Shi,1 Cheng Wang,1 Cai-lian Cheng,1 Jin-xia Chen,1 Hua Tang,1 Zhu-jiang Chen,1 Zeng-chun Ye,1 Tan-qi Lou11Division of Nephrology, Department of Internal Medicine, The Third Affiliated Hospital of Sun Yet-sun University, Guangzhou, China; 2College of Biology Engineering, South China University of Technology, Guangzhou, China; 3Department of Nuclear Medicine, The Third Affiliated Hospital of Sun Yet-sun University, Guangzhou, China *These authors contributed equally to this paperBackground: Chronic kidney disease (CKD is recognized worldwide as a public health problem, and its prevalence increases as the population ages. However, the applicability of formulas for estimating the glomerular filtration rate (GFR based on serum creatinine (SC levels in elderly Chinese patients with CKD is limited.Materials and methods: Based on values obtained with the technetium-99m diethylenetriaminepentaacetic acid (99mTc-DTPA renal dynamic imaging method, 319 elderly Chinese patients with CKD were enrolled in this study. Serum creatinine was determined by the enzymatic method. The GFR was estimated using the Cockroft–Gault (CG equation, the Modification of Diet in Renal Disease (MDRD equations, the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI equation, the Jelliffe-1973 equation, and the Hull equation.Results: The median of difference ranged from −0.3–4.3 mL/min/1.73 m2. The interquartile range (IQR of differences ranged from 13.9–17.6 mL/min/1.73 m2. Accuracy with a deviation less than 15% ranged from 27.6%–32.9%. Accuracy with a deviation less than 30% ranged from 53.6%–57.7%. Accuracy with a deviation less than 50% ranged from 74.9%–81.5%. None of the equations had accuracy up to the 70% level with a deviation less than 30% from the standard glomerular filtration rate (sGFR. Bland–Altman analysis demonstrated that the mean difference ranged from −3.0–2.4 mL/min/1.73 m2. However, the
Rate equation analysis and non-Hermiticity in coupled semiconductor laser arrays
Gao, Zihe; Johnson, Matthew T.; Choquette, Kent D.
2018-05-01
Optically coupled semiconductor laser arrays are described by coupled rate equations. The coupled mode equations and carrier densities are included in the analysis, which inherently incorporate the carrier-induced nonlinearities including gain saturation and amplitude-phase coupling. We solve the steady-state coupled rate equations and consider the cavity frequency detuning and the individual laser pump rates as the experimentally controlled variables. We show that the carrier-induced nonlinearities play a critical role in the mode control, and we identify gain contrast induced by cavity frequency detuning as a unique mechanism for mode control. Photon-mediated energy transfer between cavities is also discussed. Parity-time symmetry and exceptional points in this system are studied. Unbroken parity-time symmetry can be achieved by judiciously combining cavity detuning and unequal pump rates, while broken symmetry lies on the boundary of the optical locking region. Exceptional points are identified at the intersection between broken symmetry and unbroken parity-time symmetry.
Rate concept and retarded master equations for dissipative tight-binding models
International Nuclear Information System (INIS)
Egger, R.; Mak, C.H.; Weiss, U.
1994-01-01
Employing a ''noninteracting-cluster approximation,'' the dynamics of multistate dissipative tight-binding models has been formulated in terms of a set of generalized retarded master equations. The rates for the various pathways are expressed as power series in the intersite couplings. We apply this to the superexchange mechanism, which is relevant for bacterial photosynthesis and bridged electron transfer systems. This approach provides a general and unified description of both incoherent and coherent transport
Characteristics of quantum dash laser under the rate equation model framework
Khan, Mohammed Zahed Mustafa
2010-09-01
The authors present a numerical model to study the carrier dynamics of InAs/InP quantum dash (QDash) lasers. The model is based on single-state rate equations, which incorporates both, the homogeneous and the inhomogeneous broadening of lasing spectra. The numerical technique also considers the unique features of the QDash gain medium. This model has been applied successfully to analyze the laser spectra of QDash laser. ©2010 IEEE.
Splitting of the rate matrix as a definition of time reversal in master equation systems
International Nuclear Information System (INIS)
Liu Fei; Le, Hong
2012-01-01
Motivated by recent progress in nonequilibrium fluctuation relations, we present a generalized time reversal for stochastic master equation systems with discrete states, which is defined as a splitting of the rate matrix into irreversible and reversible parts. An immediate advantage of this definition is that a variety of fluctuation relations can be attributed to different matrix splittings. Additionally, we find that the accustomed total entropy production formula and conditions of the detailed balance must be modified appropriately to account for the reversible rate part, which was previously ignored. (paper)
Existing creatinine-based equations overestimate glomerular filtration rate in Indians.
Kumar, Vivek; Yadav, Ashok Kumar; Yasuda, Yoshinari; Horio, Masaru; Kumar, Vinod; Sahni, Nancy; Gupta, Krishan L; Matsuo, Seiichi; Kohli, Harbir Singh; Jha, Vivekanand
2018-02-01
Accurate estimation of glomerular filtration rate (GFR) is important for diagnosis and risk stratification in chronic kidney disease and for selection of living donors. Ethnic differences have required correction factors in the originally developed creatinine-based GFR estimation equations for populations around the world. Existing equations have not been validated in the vegetarian Indian population. We examined the performance of creatinine and cystatin-based GFR estimating equations in Indians. GFR was measured by urinary clearance of inulin. Serum creatinine was measured using IDMS-traceable Jaffe's and enzymatic assays, and cystatin C by colloidal gold immunoassay. Dietary protein intake was calculated by measuring urinary nitrogen appearance. Bias, precision and accuracy were calculated for the eGFR equations. A total of 130 participants (63 healthy kidney donors and 67 with CKD) were studied. About 50% were vegetarians, and the remainder ate meat 3.8 times every month. The average creatinine excretion were 14.7 mg/kg/day (95% CI: 13.5 to 15.9 mg/kg/day) and 12.4 mg/kg/day (95% CI: 11.2 to 13.6 mg/kg/day) in males and females, respectively. The average daily protein intake was 46.1 g/day (95% CI: 43.2 to 48.8 g/day). The mean mGFR in the study population was 51.66 ± 31.68 ml/min/1.73m 2 . All creatinine-based eGFR equations overestimated GFR (p < 0.01 for each creatinine based eGFR equation). However, eGFR by CKD-EPI Cys was not significantly different from mGFR (p = 0.38). The CKD-EPI Cys exhibited lowest bias [mean bias: -3.53 ± 14.70 ml/min/1.73m 2 (95% CI: -0.608 to -0.98)] and highest accuracy (P 30 : 74.6%). The GFR in the healthy population was 79.44 ± 20.19 (range: 41.90-134.50) ml/min/1.73m 2 . Existing creatinine-based GFR estimating equations overestimate GFR in Indians. An appropriately powered study is needed to develop either a correction factor or a new equation for accurate assessment of kidney function in the
Montañés Bermúdez, R; Gràcia Garcia, S; Fraga Rodríguez, G M; Escribano Subias, J; Diez de Los Ríos Carrasco, M J; Alonso Melgar, A; García Nieto, V
2014-05-01
The appearance of the K/DOQI guidelines in 2002 on the definition, evaluation and staging of chronic kidney disease (CKD) have led to a major change in how to assess renal function in adults and children. These guidelines, recently updated, recommended that the study of renal function is based, not only on measuring the serum creatinine concentration, but this must be accompanied by the estimation of glomerular filtration rate (GFR) obtained by an equation. However, the implementation of this recommendation in the clinical laboratory reports in the paediatric population has been negligible. Numerous studies have appeared in recent years on the importance of screening and monitoring of patients with CKD, the emergence of new equations for estimating GFR, and advances in clinical laboratories regarding the methods for measuring plasma creatinine and cystatin C, determined by the collaboration between the departments of paediatrics and clinical laboratories to establish recommendations based on the best scientific evidence on the use of equations to estimate GFR in this population. The purpose of this document is to provide recommendations on the evaluation of renal function and the use of equations to estimate GFR in children from birth to 18 years of age. The recipients of these recommendations are paediatricians, nephrologists, clinical biochemistry, clinical analysts, and all health professionals involved in the study and evaluation of renal function in this group of patients. Copyright © 2013 Asociación Española de Pediatría. Published by Elsevier Espana. All rights reserved.
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Appleby JohnAD
2010-01-01
Full Text Available We consider the rate of convergence to equilibrium of Volterra integrodifferential equations with infinite memory. We show that if the kernel of Volterra operator is regularly varying at infinity, and the initial history is regularly varying at minus infinity, then the rate of convergence to the equilibrium is regularly varying at infinity, and the exact pointwise rate of convergence can be determined in terms of the rate of decay of the kernel and the rate of growth of the initial history. The result is considered both for a linear Volterra integrodifferential equation as well as for the delay logistic equation from population biology.
Validation of predictive equations for glomerular filtration rate in the Saudi population
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Al Wakeel Jamal
2009-01-01
Full Text Available Predictive equations provide a rapid method of assessing glomerular filtration rate (GFR. To compare the various predictive equations for the measurement of this parameter in the Saudi population, we measured GFR by the Modification of Diet in Renal Disease (MDRD and Cockcroft-Gault formulas, cystatin C, reciprocal of cystatin C, creatinine clearance, reciprocal of creatinine, and inulin clearance in 32 Saudi subjects with different stages of renal disease. We com-pared GFR measured by inulin clearance and the estimated GFR by the equations. The study included 19 males (59.4% and 13 (40.6% females with a mean age of 42.3 ± 15.2 years and weight of 68.6 ± 17.7 kg. The mean serum creatinine was 199 ± 161 μmol/L. The GFR measured by inulin clearance was 50.9 ± 33.5 mL/min, and the estimated by Cockcroft-Gault and by MDRD equations was 56.3 ± 33.3 and 52.8 ± 32.0 mL/min, respectively. The GFR estimated by MDRD revealed the strongest correlation with the measured inulin clearance (r= 0.976, P= 0.0000 followed by the GFR estimated by Cockcroft-Gault, serum cystatin C, and serum creatinine (r= 0.953, P= 0.0000 (r= 0.787, P= 0.0001 (r= -0.678, P= 0.001, respectively. The reciprocal of cystatin C and serum creatinine revealed a correlation coefficient of 0.826 and 0.93, respectively. Cockroft-Gault for-mula overestimated the GFR by 5.40 ± 10.3 mL/min in comparison to the MDRD formula, which exhibited the best correlation with inulin clearance in different genders, age groups, body mass index, renal transplant recipients, chronic kidney disease stages when compared to other GFR predictive equations.
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Anita Nordenson
2010-09-01
Full Text Available Anita Nordenson2, Anne Marie Grönberg1,2, Lena Hulthén1, Sven Larsson2, Frode Slinde11Department of Clinical Nutrition, Sahlgrenska Academy at University of Gothenburg, Göteborg, Sweden; 2Department of Internal Medicine/Respiratory Medicine and Allergology, Sahlgrenska Academy at University of Gothenburg, SwedenAbstract: Malnutrition is a serious condition in chronic obstructive pulmonary disease (COPD. Successful dietary intervention calls for calculations of resting metabolic rate (RMR. One disease-specific prediction equation for RMR exists based on mainly male patients. To construct a disease-specific equation for RMR based on measurements in underweight or weight-losing women and men with COPD, RMR was measured by indirect calorimetry in 30 women and 11 men with a diagnosis of COPD and body mass index <21 kg/m2. The following variables, possibly influencing RMR were measured: length, weight, middle upper arm circumference, triceps skinfold, body composition by dual energy x-ray absorptiometry and bioelectrical impedance, lung function, and markers of inflammation. Relations between RMR and measured variables were studied using univariate analysis according to Pearson. Gender and variables that were associated with RMR with a P value <0.15 were included in a forward multiple regression analysis. The best-fit multiple regression equation included only fat-free mass (FFM: RMR (kJ/day = 1856 + 76.0 FFM (kg. To conclude, FFM is the dominating factor influencing RMR. The developed equation can be used for prediction of RMR in underweight COPD patients.Keywords: pulmonary disease, chronic obstructive, basal metabolic rate, malnutrition, body composition
Current use of equations for estimating glomerular filtration rate in Spanish laboratories.
Gràcia-Garcia, Sílvia; Montañés-Bermúdez, Rosario; Morales-García, Luis J; Díez-de Los Ríos, M José; Jiménez-García, Juan Á; Macías-Blanco, Carlos; Martínez-López, Rosalina; Ruiz-Altarejos, Joaquín; Ruiz-Martín, Guadalupe; Sanz-Hernández, Sonia; Ventura-Pedret, Salvador
2012-07-17
In 2006 the Spanish Society of Clinical Biochemistry and Molecular Pathology (SEQC) and the Spanish Society of Nephrology (S.E.N.) developed a consensus document in order to facilitate the diagnosis and monitoring of chronic kidney disease with the incorporation of equations for estimating glomerular filtration rate (eGFR) into laboratory reports. The current national prevalence of eGFR reporting and the degree of adherence to these recommendations among clinical laboratories is unknown. We administered a national survey in 2010-11 to Spanish clinical laboratories. The survey was through e-mail or telephone to laboratories that participated in the SEQC’s Programme for External Quality Assurance, included in the National Hospitals Catalogue 2010, including both primary care and private laboratories. A total of 281 laboratories answered to the survey. Of these, 88.2% reported on the eGFR, with 61.9% reporting on the MDRD equation and 31.6% using the MDRD-IDMS equation. A total of 42.5% of laboratories always reported serum creatinine values, and other variables only when specifically requested. Regarding the way results were presented, 46.2% of laboratories reported the exact numerical value only when the filtration rate was below 60mL/min/1.73m2, while 50.6% reported all values regardless. In 56.3% of the cases reporting eGFR, an interpretive commentary of it was enclosed. Although a high percentage of Spanish laboratories have added eGFR in their reports, this metric is not universally used. Moreover, some aspects, such as the equation used and the correct expression of eGFR results, should be improved.
Fernandez-Prado, Raul; Castillo-Rodriguez, Esmeralda; Velez-Arribas, Fernando Javier; Gracia-Iguacel, Carolina; Ortiz, Alberto
2016-12-01
Direct oral anticoagulants (DOACs) may require dose reduction or avoidance when glomerular filtration rate is low. However, glomerular filtration rate is not usually measured in routine clinical practice. Rather, equations that incorporate different variables use serum creatinine to estimate either creatinine clearance in mL/min or glomerular filtration rate in mL/min/1.73 m 2 . The Cockcroft-Gault equation estimates creatinine clearance and incorporates weight into the equation. By contrast, the Modification of Diet in Renal Disease and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations estimate glomerular filtration rate and incorporate ethnicity but not weight. As a result, an individual patient may have very different renal function estimates, depending on the equation used. We now highlight these differences and discuss the impact on routine clinical care for anticoagulation to prevent embolization in atrial fibrillation. Pivotal DOAC clinical trials used creatinine clearance as a criterion for patient enrollment, and dose adjustment and Federal Drug Administration recommendations are based on creatinine clearance. However, clinical biochemistry laboratories provide CKD-EPI glomerular filtration rate estimations, resulting in discrepancies between clinical trial and routine use of the drugs. Copyright © 2016 Elsevier Inc. All rights reserved.
Asymptotics of steady states of a selection–mutation equation for small mutation rate
Calsina, Àngel
2013-12-01
We consider a selection-mutation equation for the density of individuals with respect to a continuous phenotypic evolutionary trait. We assume that the competition term for an individual with a given trait depends on the traits of all the other individuals, therefore giving an infinite-dimensional nonlinearity. Mutations are modelled by means of an integral operator. We prove existence of steady states and show that, when the mutation rate goes to zero, the asymptotic profile of the population is a Cauchy distribution. © Royal Society of Edinburgh 2013.
Asymptotics of steady states of a selection–mutation equation for small mutation rate
Calsina, À ngel; Cuadrado, Sí lvia; Desvillettes, Laurent; Raoul, Gaë l
2013-01-01
We consider a selection-mutation equation for the density of individuals with respect to a continuous phenotypic evolutionary trait. We assume that the competition term for an individual with a given trait depends on the traits of all the other individuals, therefore giving an infinite-dimensional nonlinearity. Mutations are modelled by means of an integral operator. We prove existence of steady states and show that, when the mutation rate goes to zero, the asymptotic profile of the population is a Cauchy distribution. © Royal Society of Edinburgh 2013.
Utility rate equations of group population dynamics in biological and social systems.
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Vyacheslav I Yukalov
Full Text Available We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human composed of several trait groups. The suggested approach is based on the combination of ideas employed in the theory of biological populations, system theory, and utility theory. The evolution equations are defined as utility rate equations, whose parameters are characterized by the utility of each group with respect to the society as a whole and by the mutual utilities of groups with respect to each other. We analyze in detail the cases of two groups (cooperators and defectors and of three groups (cooperators, defectors, and regulators and find that, in a self-organized society, neither defectors nor regulators can overpass the maximal fractions of about [Formula: see text] each. This is in agreement with the data for bee and ant colonies. The classification of societies by their distance from equilibrium is proposed. We apply the formalism to rank the countries according to the introduced metric quantifying their relative stability, which depends on the cost of defectors and regulators as well as their respective population fractions. We find a remarkable concordance with more standard economic ranking based, for instance, on GDP per capita.
Murayama, I; Miyano, A; Sasaki, Y; Hirata, T; Ichijo, T; Satoh, H; Sato, S; Furuhama, K
2013-11-01
This study was performed to clarify whether a formula (Holstein equation) based on a single blood sample and the isotonic, nonionic, iodine contrast medium iodixanol in Holstein dairy cows can apply to the estimation of glomerular filtration rate (GFR) for beef cattle. To verify the application of iodixanol in beef cattle, instead of the standard tracer inulin, both agents were coadministered as a bolus intravenous injection to identical animals at doses of 10 mg of I/kg of BW and 30 mg/kg. Blood was collected 30, 60, 90, and 120 min after the injection, and the GFR was determined by the conventional multisample strategies. The GFR values from iodixanol were well consistent with those from inulin, and no effects of BW, age, or parity on GFR estimates were noted. However, the GFR in cattle weighing less than 300 kg, aged<1 yr old, largely fluctuated, presumably due to the rapid ruminal growth and dynamic changes in renal function at young adult ages. Using clinically healthy cattle and those with renal failure, the GFR values estimated from the Holstein equation were in good agreement with those by the multisample method using iodixanol (r=0.89, P=0.01). The results indicate that the simplified Holstein equation using iodixanol can be used for estimating the GFR of beef cattle in the same dose regimen as Holstein dairy cows, and provides a practical and ethical alternative.
Utility Rate Equations of Group Population Dynamics in Biological and Social Systems
Yukalov, Vyacheslav I.; Yukalova, Elizaveta P.; Sornette, Didier
2013-01-01
We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human) composed of several trait groups. The suggested approach is based on the combination of ideas employed in the theory of biological populations, system theory, and utility theory. The evolution equations are defined as utility rate equations, whose parameters are characterized by the utility of each group with respect to the society as a whole and by the mutual utilities of groups with respect to each other. We analyze in detail the cases of two groups (cooperators and defectors) and of three groups (cooperators, defectors, and regulators) and find that, in a self-organized society, neither defectors nor regulators can overpass the maximal fractions of about each. This is in agreement with the data for bee and ant colonies. The classification of societies by their distance from equilibrium is proposed. We apply the formalism to rank the countries according to the introduced metric quantifying their relative stability, which depends on the cost of defectors and regulators as well as their respective population fractions. We find a remarkable concordance with more standard economic ranking based, for instance, on GDP per capita. PMID:24386163
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L. Gheibi
2008-04-01
Full Text Available Background and aims Musculoskeletal Disorders are prevalent in construction workers in comparison to other working groups. These workers in damming construction worked at awkward postures for long times, so ergonomic assessment of jobs was important. Methods This is a descriptive-analytical cross sectional study that conducted in 2008 on a random sample of workers of damming construction in Takab city (110 men who were assessed by Nordic Musculoskeletal questionnaire and digital indicator for heart measurement. To estimate Vo2max consumption Fox equation was used and data were analyzed by SPSS software. Results The average of total time of worked was 36.6 86.8 months. Results showed that the most prevalent (%55.5 MSDs was low back pain which was positively related with type of job, the number of standing and sitting posotions at work, total time of work, age, smoking, level of education, weight,Vo2max that estimated by Fox Equation, and heart rate at working (P<0.05. Conclusion The results of this study reveal that prevalence rate of musculoskeletal disorders are high among damming construction workers, and heart rate and Vo2max consumption increases with increase in work load. Therefore, optimal physiological conditions should be considered and physical capacity be measured. Prior to employment of workers approperiate corrections are warranted
Directory of Open Access Journals (Sweden)
Yoshimoto Akifumi
2015-01-01
Full Text Available These days, polymer foams, such as polyurethane foam and polystyrene foam, are used in various situations as a thermal insulator or shock absorber. In general, however, their strength is insufficient in high temperature environments because of their low glass transition temperature. Polyimide is a polymer which has a higher glass transition temperature and high strength. Its mechanical properties do not vary greatly, even in low temperature environments. Therefore, polyimide foam is expected to be used in the aerospace industry. Thus, the constitutive equation of polyimide foam that can be applied across a wide range of strain rates and ambient temperature is very useful. In this study, a series of compression tests at various strain rates, from 10−3 to 103 s−1 were carried out in order to examine the effect of strain rate on the compressive properties of polyimide foam. The flow stress of polyimide foam increased rapidly at dynamic strain rates. The effect of ambient temperature on the properties of polyimide foam was also investigated at temperature from − 190 °C to 270°∘C. The flow stress decreased with increasing temperature.
Lainscsek, C; Rowat, P; Schettino, L; Lee, D; Song, D; Letellier, C; Poizner, H
2012-03-01
Parkinson's disease is a degenerative condition whose severity is assessed by clinical observations of motor behaviors. These are performed by a neurological specialist through subjective ratings of a variety of movements including 10-s bouts of repetitive finger-tapping movements. We present here an algorithmic rating of these movements which may be beneficial for uniformly assessing the progression of the disease. Finger-tapping movements were digitally recorded from Parkinson's patients and controls, obtaining one time series for every 10 s bout. A nonlinear delay differential equation, whose structure was selected using a genetic algorithm, was fitted to each time series and its coefficients were used as a six-dimensional numerical descriptor. The algorithm was applied to time-series from two different groups of Parkinson's patients and controls. The algorithmic scores compared favorably with the unified Parkinson's disease rating scale scores, at least when the latter adequately matched with ratings from the Hoehn and Yahr scale. Moreover, when the two sets of mean scores for all patients are compared, there is a strong (r = 0.785) and significant (p<0.0015) correlation between them.
Directory of Open Access Journals (Sweden)
Totok R. Biyanto
2016-06-01
Full Text Available Safety Instrumented Function (SIF is implemented on the system to prevent hazard in process industry. In general, most of SIF implementation in process industry works in low demand condition. Safety valuation of SIF that works in low demand can be solved by using quantitative method. The quantitative method is a simplified exponential equation form of MacLaurin series, which can be called simplified equation. Simplified equation used in high demand condition will generate a higher Safety Integrity Level (SIL and it will affect the higher safety cost. Therefore, the value of low or high demand rate limit should be determined to prevent it. The result of this research is a first order equation that can fix the error of SIL, which arises from the usage of simplified equation, without looking the demand rate limit for low and high demand. This equation is applied for SIL determination on SIF with 1oo1 vote. The new equation from this research is λ = 0.9428 λMC + 1.062E−04 H/P, with 5% average of error, where λMC is a value of λ from the simplified equation, Hazardous event frequency (H is a probabilistic frequency of hazard event and P is Probability of Failure on Demand (PFD in Independent Protection Layers (IPLs. The equation generated from this research could correct SIL of SIF in various H and P. Therefore, SIL design problem could be solved and it provides an appropriate SIL.
Goličnik, Marko
2011-01-01
The Michaelis-Menten rate equation can be found in most general biochemistry textbooks, where the time derivative of the substrate is a hyperbolic function of two kinetic parameters (the limiting rate V, and the Michaelis constant K(M) ) and the amount of substrate. However, fundamental concepts of enzyme kinetics can be difficult to understand fully, or can even be misunderstood, by students when based only on the differential form of the Michaelis-Menten equation, and the variety of methods available to calculate the kinetic constants from rate versus substrate concentration "textbook data." Consequently, enzyme kinetics can be confusing if an analytical solution of the Michaelis-Menten equation is not available. Therefore, the still rarely known exact solution to the Michaelis-Menten equation is presented here through the explicit closed-form equation in terms of the Lambert W(x) function. Unfortunately, as the W(x) is not available in standard curve-fitting computer programs, the practical use of this direct solution is limited for most life-science students. Thus, the purpose of this article is to provide analytical approximations to the equation for modeling Michaelis-Menten kinetics. The elementary and explicit nature of these approximations can provide students with direct and simple estimations of kinetic parameters from raw experimental time-course data. The Michaelis-Menten kinetics studied in the latter context can provide an ideal alternative to the 100-year-old problems of data transformation, graphical visualization, and data analysis of enzyme-catalyzed reactions. Hence, the content of the course presented here could gradually become an important component of the modern biochemistry curriculum in the 21st century. Copyright © 2011 Wiley Periodicals, Inc.
Effect of creatinine assay calibration on glomerular filtration rate prediction by MDRD equation
Directory of Open Access Journals (Sweden)
Débora Spessatto
2009-01-01
Full Text Available Background: The evaluation of renal function should be performed with glomerular filtration rate (GFR estimation employing the Modification of Diet in Renal Disease (MDRD study equation, which includes age, gender, ethnicity and serum creatinine. However, creatinine methods require traceability with standardized methods. Objective: To analyse the impact of creatinine calibration on MDRD calculated GFR. Methods: 140 samples of plasma with creatinine values <2,0 mg/dl were analysed by Jaffé’s reaction with Creatinina Modular P (Roche ®; method A; reference and Creatinina Advia 1650 (Bayer ®; method B; non-standardized. The results with the different methods were compared and aligned with standardized method through a conversion formula. MDRD GFR was estimated. Results: Values were higher for method B (1.03 ± 0.29 vs. 0.86 ± 0.32 mg/dl, P<0.001. This difference declined when methods were aligned with the equation y=1.07x -0.249, and the aligned values were 0,9 ± 0,31 mg/dl. Non-traceable creatinine methods misclassificaed chronic kidney disease in 10% more (false positive. This disagreement disappeared after the regression alignment. Conclusion: Creatinine method calibration has a large impact over the final results of serum creatinine and GFR. The alignment of the non-standardized results through conversion formulas is a reasonable alternative to harmonize serum creatinine results while waiting for the full implementation of international standardization programs.
Rate equations modeling for hydrogen inventory studies during a real tokamak material thermal cycle
Energy Technology Data Exchange (ETDEWEB)
Bonnin, X., E-mail: xavier.bonnin@iter.org [LSPM-CNRS, Université Paris 13, Sorbonne Paris Cité, 99 avenue Jean-Baptiste Clément, F-93430 Villetaneuse (France); Hodille, E. [IRFM, CEA-Cadarache, F-13108 St-Paul-Lez-Durance (France); Ning, N. [LSPM-CNRS, Université Paris 13, Sorbonne Paris Cité, 99 avenue Jean-Baptiste Clément, F-93430 Villetaneuse (France); Sang, C. [School of Physics and Optoelectronics Technology, Dalian University of Technology, Dalian 116024 (China); Grisolia, Ch. [IRFM, CEA-Cadarache, F-13108 St-Paul-Lez-Durance (France)
2015-08-15
Prediction and control of tritium inventory in plasma-facing components (PFCs) is a critical nuclear safety issue for ITER and future fusion devices. This goal can be achieved through rate equations models as presented here. We calibrate our models with thermal desorption spectrometry results to obtain a validated set of material parameters relevant to hydrogen inventory processes in bulk tungsten. The best fits are obtained with two intrinsic trap types, deep and shallow, and an extrinsic trap created by plasma irradiation and plastic deformation of the tungsten matrix associated with blister formation. We then consider a realistic cycle of plasma discharges consisting of 400 s of plasma exposure followed by a resting period of 1000 s, repeating for several hours. This cycle is then closed by a long “overnight” period, thus providing an estimate of the amount of tritium retained in the PFCs after a full day of standard operation.
Ito, Kazufumi
1987-01-01
The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.
John A. D. Appleby
2010-01-01
We consider the rate of convergence to equilibrium of Volterra integrodifferential equations with infinite memory. We show that if the kernel of Volterra operator is regularly varying at infinity, and the initial history is regularly varying at minus infinity, then the rate of convergence to the equilibrium is regularly varying at infinity, and the exact pointwise rate of convergence can be determined in terms of the rate of decay of the kernel and the rate of growth of the initial history. ...
Xie, Peng; Huang, Jian-Min; Li, Ying; Liu, Huai-Jun; Qu, Yan
2017-06-01
To investigate the application of the new modified Chronic Kidney Disease Epidemiology Collaboration (mCKD-EPI) equation developed by Liu for the measurement of glomerular filtration rate (GFR) in Chinese patients with chronic kidney disease (CKD) and to evaluate whether this modified form is more accurate than the original one in clinical practice. GFR was determined simultaneously by 3 methods: (a) 99m Tc-diethylene triamine pentaacetic acid ( 99m Tc-DTPA) dual plasma sample clearance method (mGFR), which was used as the reference standard; (b) CKD-EPI equation (eGFRckdepi); (c) modified CKD-EPI equation (eGFRmodified). Concordance correlation and Passing-Bablok regression were used to compare the validity of eGFRckdepi and eGFRmodified. Bias, precision and accuracy were compared to identify which equation showed the better performance in determining GFR. A total of 170 patients were enrolled. Both eGFRckdepi and eGFRmodified correlated well with mGFR (concordance correlation coefficient 0.90 and 0.74, respectively) and the Passing-Bablok regression equation of eGFRckdepi and eGFRmodified against mGFR was mGFR = 0.37 + 1.04 eGFRckdepi and -49.25 + 1.74 eGFRmodified, respectively. In terms of bias, precision and 30 % accuracy, eGFRmodified showed a worse performance compared to eGFRckdepi, in the whole cohort. The new modified CKD-EPI equation cannot replace the original CKD-EPI equation in determining GFR in Chinese patients with CKD.
Barker, L. K.; Houck, J. A.; Carzoo, S. W.
1984-01-01
An operator commands a robot hand to move in a certain direction relative to its own axis system by specifying a velocity in that direction. This velocity command is then resolved into individual joint rotational velocities in the robot arm to effect the motion. However, the usual resolved-rate equations become singular when the robot arm is straightened. To overcome this elbow joint singularity, equations were developed which allow continued translational control of the robot hand even though the robot arm is (or is nearly) fully extended. A feature of the equations near full arm extension is that an operator simply extends and retracts the robot arm to reverse the direction of the elbow bend (difficult maneuver for the usual resolved-rate equations). Results show successful movement of a graphically simulated robot arm.
Mazaheri, Mehrdad; Theuns, Peter
2009-01-01
The current study evaluates three hypothesized models on subjective well-being, comprising life domain ratings (LDR), overall satisfaction with life (OSWL), and overall dissatisfaction with life (ODWL), using structural equation modeling (SEM). A sample of 1,310 volunteering students, randomly assigned to six conditions, rated their overall life…
International Nuclear Information System (INIS)
Winkler, E.
1991-01-01
The general theory of inhomogeneous compartments with age-dependent elimination rates is illustrated by examples. Mathematically, it turns out that models consisting of partial differential equations include ordinary, delayed and integro-differential equations, a general fact which is treated here in the context of linear tracer kinetics. The examples include standard compartments as a degenerate case, systems of standard compartments (compartment blocks), models resulting in special residence time distributions, models with pipes, and systems with heterogeneous particles. (orig./BBR) [de
Hodille, E. A.; Bernard, E.; Markelj, S.; Mougenot, J.; Becquart, C. S.; Bisson, R.; Grisolia, C.
2017-12-01
Based on macroscopic rate equation simulations of tritium migration in an actively cooled tungsten (W) plasma facing component (PFC) using the code MHIMS (migration of hydrogen isotopes in metals), an estimation has been made of the tritium retention in ITER W divertor target during a non-uniform exponential distribution of particle fluxes. Two grades of materials are considered to be exposed to tritium ions: an undamaged W and a damaged W exposed to fast fusion neutrons. Due to strong temperature gradient in the PFC, Soret effect’s impacts on tritium retention is also evaluated for both cases. Thanks to the simulation, the evolutions of the tritium retention and the tritium migration depth are obtained as a function of the implanted flux and the number of cycles. From these evolutions, extrapolation laws are built to estimate the number of cycles needed for tritium to permeate from the implantation zone to the cooled surface and to quantify the corresponding retention of tritium throughout the W PFC.
How Hot Precursor Modify Island Nucleation: A Rate-Equation Model
Morales-Cifuentes, Josue; Einstein, T. L.; Pimpinelli, Alberto
2015-03-01
We describe the analysis, based on rate equations, of the hot precursor model mentioned in the previous talk. Two key parameters are the competing times of ballistic monomers decaying into thermalized monomers vs. being captured by an island, which naturally define a ``thermalization'' scale for the system. We interpret the energies and dimmensionless parameters used in the model, and provide both an implicit analytic solution and a convenient asymptotic approximation. Further analysis reveals novel scaling regimes and nonmonotonic crossovers between them. To test our model, we applied it to experiments on parahexaphenyl (6P) on sputtered mica. With the resulting parameters, the curves derived from our analytic treatment account very well for the data at the 4 different temperatures. The fit shows that the high-flux regime corresponds not to ALA (attachment-limited aggregation) or HMA (hot monomer aggregation) but rather to an intermediate scaling regime related to DLA (diffusion-limited aggregation). We hope this work stimulates further experimental investigations. Work at UMD supported by NSF CHE 13-05892.
Rate equation modelling of erbium luminescence dynamics in erbium-doped silicon-rich-silicon-oxide
Energy Technology Data Exchange (ETDEWEB)
Shah, Miraj, E-mail: m.shah@ee.ucl.ac.uk [Department of Electronic and Electrical Engineering, UCL, Torrington Place, London WC1E 7JE (United Kingdom); Wojdak, Maciej; Kenyon, Anthony J. [Department of Electronic and Electrical Engineering, UCL, Torrington Place, London WC1E 7JE (United Kingdom); Halsall, Matthew P.; Li, Hang; Crowe, Iain F. [Photon Science Institute and School of Electrical and Electronic Engineering, University of Manchester, Sackville St Building, Manchester M13 9PL (United Kingdom)
2012-12-15
Erbium doped silicon-rich silica offers broad band and very efficient excitation of erbium photoluminescence (PL) due to a sensitization effect attributed to silicon nanocrystals (Si-nc), which grow during thermal treatment. PL decay lifetime measurements of sensitised Er{sup 3+} ions are usually reported to be stretched or multi exponential, very different to those that are directly excited, which usually show a single exponential decay component. In this paper, we report on SiO{sub 2} thin films doped with Si-nc's and erbium. Time resolved PL measurements reveal two distinct 1.54 {mu}m Er decay components; a fast microsecond component, and a relatively long lifetime component (10 ms). We also study the structural properties of these samples through TEM measurements, and reveal the formation of Er clusters. We propose that these Er clusters are responsible for the fast {mu}s decay component, and we develop rate equation models that reproduce the experimental transient observations, and can explain some of the reported transient behaviour in previously published literature.
Xiao, Guizhen; Xie, Qiuyou; He, Yanbin; Wang, Ziwen; Chen, Yan; Jiang, Mengliu; Ni, Xiaoxiao; Wang, Qinxian; Murong, Min; Guo, Yequn; Qiu, Xiaowen; Yu, Ronghao
2017-10-01
Accurately predicting the basal metabolic rate (BMR) of patients in a vegetative state (VS) or minimally conscious state (MCS) is critical to proper nutritional therapy, but commonly used equations have not been shown to be accurate. Therefore, we compared the BMR measured by indirect calorimetry (IC) to BMR values estimated using common predictive equations in VS and MCS patients. Body composition variables were measured using the bioelectric impedance analysis (BIA) technique. BMR was measured by IC in 82 patients (64 men and 18 women) with VS or MCS. Patients were classified by body mass index as underweight (BMR was estimated for each group using the Harris-Benedict (H-B), Schofield, or Cunningham equations and compared to the measured BMR using Bland-Altman analyses. For the underweight group, there was a significant difference between the measured BMR values and the estimated BMR values calculated using the H-B, Schofield, and Cunningham equations (p BMR values estimated using the H-B and Cunningham equations were different significantly from the measured BMR (p BMR in the normal-weight group. The Schofield equation showed the best concordance (only 41.5%) with the BMR values measured by IC. None of the commonly used equations to estimate BMR were suitable for the VS or MCS populations. Indirect calorimetry is the preferred way to avoid either over or underestimate of BMR values. Copyright © 2016. Published by Elsevier Ltd.
Lewis, Teresa V; Harrison, Donald L; Gildon, Brooke L; Carter, Sandra M; Turman, Martin A
2016-06-01
To determine if significant correlations exist between glomerular filtration rate (GFR) prediction equation values, derived by using the original Schwartz equation and the Chronic Kidney Disease in Children (CKiD) bedside equation with a 24-hour urine creatinine clearance (Clcr ) value normalized to a body surface area of 1.73 m(2) in overweight and obese children. Prospective analysis (20 patients) and retrospective analysis (43 patients). Pediatric inpatient ward and pediatric nephrology clinic at a comprehensive academic medical center. Sixty-three pediatric patients (aged 5-17 years), of whom 27 were overweight (body mass index [BMI] at the 85th percentile or higher) and 36 were not overweight (BMI lower than the 85th percentile [controls]) between 2007 and 2012. Data from the overweight patients were compared with nonoverweight controls. GFR values were calculated by using the original Schwartz equation and the CKiD bedside equation. Each patient's 24-hour urine Clcr value normalized to a body surface area of 1.73 m(2) served as the index value. A Pearson correlation coefficient model was used to determine association between the 24-hour urine Clcr value (index value) with the Schwartz and CKiD GFR estimations. Significant correlation was found to exist between the Schwartz and CKiD bedside GFR estimations relative to the 24-hour urine Clcr in the control subjects (r = 0.85, poverweight subjects (r = 0.86, poverweight children with a kidney disorder. The CKiD bedside GFR estimations were not significantly different compared with 24-hour urine Clcr values for the overweight group with kidney disorder (p=0.85). The Schwartz and CKiD bedside estimations of GFR correlated with 24-hour urine Clcr values in both overweight and nonoverweight children. Compared with the Schwartz equation, which tended to overestimate renal function, the CKiD bedside equation appeared to approximate 24-hour urine Clcr more closely in overweight children with kidney disorder. © 2016
Gaeuman, David; Andrews, E.D.; Krause, Andreas; Smith, Wes
2009-01-01
Bed load samples from four locations in the Trinity River of northern California are analyzed to evaluate the performance of the Wilcock‐Crowe bed load transport equations for predicting fractional bed load transport rates. Bed surface particles become smaller and the fraction of sand on the bed increases with distance downstream from Lewiston Dam. The dimensionless reference shear stress for the mean bed particle size (τ*rm) is largest near the dam, but varies relatively little between the more downstream locations. The relation between τ*rm and the reference shear stresses for other size fractions is constant across all locations. Total bed load transport rates predicted with the Wilcock‐Crowe equations are within a factor of 2 of sampled transport rates for 68% of all samples. The Wilcock‐Crowe equations nonetheless consistently under‐predict the transport of particles larger than 128 mm, frequently by more than an order of magnitude. Accurate prediction of the transport rates of the largest particles is important for models in which the evolution of the surface grain size distribution determines subsequent bed load transport rates. Values of τ*rm estimated from bed load samples are up to 50% larger than those predicted with the Wilcock‐Crowe equations, and sampled bed load transport approximates equal mobility across a wider range of grain sizes than is implied by the equations. Modifications to the Wilcock‐Crowe equation for determining τ*rm and the hiding function used to scale τ*rm to other grain size fractions are proposed to achieve the best fit to observed bed load transport in the Trinity River.
DEFF Research Database (Denmark)
method allows us to develop a new expression for the growth rate. The method is based on the stochastic continuous-discrete time state-space model, with a continuous-time state equation (a stochastic differential equation, SDE) combined with a discrete-time measurement equation. In our study the SDE...... described by Kristensen et. al [2]. The resulting time series allows us graphically to inspect the functional dependence of the growth rate on the substrate content. From the method described above we find three new plausible expressions for μ(S). Therefore we apply the likelihood-ratio test to compare...... for the Monod expression. Thus, the method was applied to successfully determine a significant better expression for the substrate dependent growth expression, and we find the method generally applicable for model development. References [1] Kristensen NR, Madsen H, Jørgensen, SB (2004) A method for systematic...
DEFF Research Database (Denmark)
Orskov, Bjarne; Borresen, Malene L; Feldt-Rasmussen, Bo
2010-01-01
(CKD-EPI) equation, the Cockcroft-Gault equation adjusted for body surface area and the MDRD equation with cystatin C. Performance was evaluated by mean bias, precision and accuracy. RESULTS: The MDRD equation with cystatin C had 97% of GFR estimates within 30% of measured GFR (accuracy). Both the CKD-EPI....... The CKD-EPI or the Cockcroft-Gault equations showed better performance compared to the 4-variable MDRD equation....
Directory of Open Access Journals (Sweden)
Danielle Ribeiro de Souza
2015-04-01
Full Text Available The purpose of the present study was to identify energy intake (EI underreporting and to estimate the impact of using a population specific equation for the basal metabolic rate (BMR in a probability sample of adults from Niterói, Rio de Janeiro State, Brazil. A sample of 1,726 subjects participated in the study. EI was assessed by a 24-hour dietary recall and EI/BMR was computed with BMR estimated using internationally recommended equations as well as specific equations developed for the adult population of Niterói. Mean EI was 1,570.9 and 2,188.8kcal.day-1 for women and men, respectively. EI decreased with increasing age in both men and women. BMR estimated by the Brazilian equation was significantly lower than the values estimated by the international equation for all age, sex and nutritional status groups. In general, EI underreporting was found in at least 50% of the population, higher in women, and increased with increasing age and body mass index (BMI. The results of the present study confirm that EI is underreported, even when BMR is estimated using population-specific equations.
Farjas, Jordi; Roura, Pere
2008-01-01
Avrami's model describes the kinetics of phase transformation under the assumption of spatially random nucleation. In this paper we provide a quasi-exact analytical solution of Avrami's model when the transformation takes place under continuous heating. This solution has been obtained with different activation energies for both nucleation and growth rates. The relation obtained is also a solution of the so-called Kolmogorov-Johnson-Mehl-Avrami transformation rate equation. The corresponding n...
International Nuclear Information System (INIS)
Winkler, E.
1991-01-01
Mathematical models in tracer kinetics are usually based on ordinary differential equations which correspond to a system of kinetically homogeneous compartments (standard compartments). A generalization is possible by the admission of inhomogeneities in the behaviour of the elements belonging to a compartment. The important special case of the age-dependence of elimination rates is treated in its deterministic version. It leads to partial different equations (i.e., systems with distributed coefficients) with the 'age' or the 'residence time' of an element of the compartment as a variable additional to 'time'. The basic equations for one generalized compartment and for systems of such compartments are given together with their general solutions. (orig.) [de
Faye, Grégory; Rankin, James; Chossat, Pascal
2013-05-01
The existence of spatially localized solutions in neural networks is an important topic in neuroscience as these solutions are considered to characterize working (short-term) memory. We work with an unbounded neural network represented by the neural field equation with smooth firing rate function and a wizard hat spatial connectivity. Noting that stationary solutions of our neural field equation are equivalent to homoclinic orbits in a related fourth order ordinary differential equation, we apply normal form theory for a reversible Hopf bifurcation to prove the existence of localized solutions; further, we present results concerning their stability. Numerical continuation is used to compute branches of localized solution that exhibit snaking-type behaviour. We describe in terms of three parameters the exact regions for which localized solutions persist.
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
International Nuclear Information System (INIS)
Chandra, V.K.; Chandra, B.P.; Tiwari, M.; Baghel, R.N.; Ramrakhiani, M.
2012-01-01
When a voltage pulse is applied under forward biased condition to a spin-coated bilayer organic light-emitting diode (OLED), then initially the electroluminescence (EL) intensity appearing after a delay time, increases with time and later on it attains a saturation value. At the end of the voltage pulse, the EL intensity decreases with time, attains a minimum intensity and then it again increases with time, attains a peak value and later on it decreases with time. For the OLEDs, in which the lifetime of trapped carriers is less than the decay time of the EL occurring prior to the onset of overshoot, the EL overshoot begins just after the end of voltage pulse. The overshoot in spin-coated bilayer OLEDs is caused by the presence of an interfacial layer of finite thickness between hole and electron transporting layers in which both transport molecules coexist, whereby the interfacial energy barrier impedes both hole and electron passage. When a voltage pulse is applied to a bilayer OLED, positive and negative space charges are established at the opposite faces of the interfacial layer. Subsequently, the charge recombination occurs with the incoming flux of injected carriers of opposite polarity. When the voltage is turned off, the interfacial charges recombine under the action of their mutual electric field. Thus, after switching off the external voltage the electrons stored in the interface next to the anode cell compartment experience an electric field directed from cathode to anode, and therefore, the electrons move towards the cathode, that is, towards the positive space charge, whereby electron–hole recombination gives rise to luminescence. The EL prior to onset of overshoot is caused by the movement of electrons in the electron transporting states, however, the EL in the overshoot region is caused by the movement of detrapped electrons. On the basis of the rate equations for the detrapping and recombination of charge carriers accumulated at the interface
Hao, Tian
2015-02-28
The tap density of a granular powder is often linked to the flowability via the Carr index that measures how tight a powder can be packed, under an assumption that more easily packed powders usually flow poorly. Understanding how particles are packed is important for revealing why a powder flows better than others. There are two types of empirical equations that were proposed to fit the experimental data of packing fractions vs. numbers of taps in the literature: the inverse logarithmic and the stretched exponential. Using the rate process theory and the free volume concept under the assumption that particles will obey similar thermodynamic laws during the tapping process if the "granular temperature" is defined in a different way, we obtain the tap density equations, and they are reducible to the two empirical equations currently widely used in literature. Our equations could potentially fit experimental data better with an additional adjustable parameter. The tapping amplitude and frequency, the weight of the granular materials, and the environmental temperature are grouped into this parameter that weighs the pace of the packing process. The current results, in conjunction with our previous findings, may imply that both "dry" (granular) and "wet" (colloidal and polymeric) particle systems are governed by the same physical mechanisms in term of the role of the free volume and how particles behave (a rate controlled process).
International Nuclear Information System (INIS)
Takiyama, K.; Watanabe, M.; Oda, T.
1998-01-01
Possibility of applying polarized laser-induced fluorescence (LIF) spectroscopy for measuring the electric field in a plasma with a large collisional depolarization has been investigated. A rate equation model including the depolarization process was employed to analyze the time evolution of LIF polarization components. The polarized LIF pulse shapes observed in the sheath of a He glow discharge plasma were successfully reproduced, and the electric field distribution was obtained with high accuracy. (author)
Determinants of the ZAR/USD exchange rate and policy implications: A simultaneous-equation model
Directory of Open Access Journals (Sweden)
Yu Hsing
2016-12-01
Full Text Available This paper examines the determinants of the South African rand/US dollar (ZAR/USD exchange rate based on demand and supply analysis. Applying the EGARCH method, the paper finds that the ZAR/USD exchange rate is positively associated with the South African government bond yield, US real GDP, the US stock price and the South African inflation rate and negatively influenced by the 10-year US government bond yield, South African real GDP, the South African stock price, and the US inflation rate. The adoption of a free floating exchange rate regime has reduced the value of the rand vs. the US dollar.
Evolution of a Network of Vortex Loops in He-II: Exact Solution of the Rate Equation
International Nuclear Information System (INIS)
Nemirovskii, Sergey K.
2006-01-01
The evolution of a network of vortex loops in He-II due to the fusion and breakdown of vortex loops is studied. We perform investigation on the base of the ''rate equation'' for the distribution function n(l) of number of loops of length l. By use of the special ansatz we have found the exact powerlike solution of the rate equation in a stationary case. That solution is the famous equilibrium distribution n(l)∝l -5/2 obtained earlier from thermodynamic arguments. Our result, however, is not equilibrium; it describes the state with two mutual fluxes of the length (or energy) in l space. Analyzing this solution we drew several results on the structure and dynamics of the vortex tangle in the superfluid turbulent helium. In particular, we obtained that the mean radius of the curvature is of the order of interline space and that the decay of the vortex tangle obeys the Vinen equation. We also evaluated the full rate of reconnection
Evolution of a network of vortex loops in He-II: exact solution of the rate equation.
Nemirovskii, Sergey K
2006-01-13
The evolution of a network of vortex loops in He-II due to the fusion and breakdown of vortex loops is studied. We perform investigation on the base of the "rate equation" for the distribution function n(l) of number of loops of length l. By use of the special ansatz we have found the exact power-like solution of the rate equation in a stationary case. That solution is the famous equilibrium distribution n(l) proportional l(-5/2) obtained earlier from thermodynamic arguments. Our result, however, is not equilibrium; it describes the state with two mutual fluxes of the length (or energy) in l space. Analyzing this solution we drew several results on the structure and dynamics of the vortex tangle in the superfluid turbulent helium. In particular, we obtained that the mean radius of the curvature is of the order of interline space and that the decay of the vortex tangle obeys the Vinen equation. We also evaluated the full rate of reconnection.
Energy Technology Data Exchange (ETDEWEB)
Chandra, V.K. [Department of Electrical and Electronics Engineering, Chhatrapati Shivaji Institute of Technology, Shivaji Nagar, Kolihapuri, Durg 491001 (C.G.) (India); Chandra, B.P., E-mail: bpchandra4@yahoo.co.in [Department of Applied Physics, Ashoka Institute of Technology and Management, Rajnandgaon 491441 (C.G.) (India); Tiwari, M. [Department of Postgraduate Studies and Research in Physics and Electronics, Rani Durgavati University, Jabalpur 482001 (M.P.) (India); Baghel, R.N. [School of Studies in Physics and Astrophysics, Pt. Ravishankar Shukla University, Raipur 492010 (C.G.) (India); Ramrakhiani, M. [Department of Postgraduate Studies and Research in Physics and Electronics, Rani Durgavati University, Jabalpur 482001 (M.P.) (India)
2012-06-15
When a voltage pulse is applied under forward biased condition to a spin-coated bilayer organic light-emitting diode (OLED), then initially the electroluminescence (EL) intensity appearing after a delay time, increases with time and later on it attains a saturation value. At the end of the voltage pulse, the EL intensity decreases with time, attains a minimum intensity and then it again increases with time, attains a peak value and later on it decreases with time. For the OLEDs, in which the lifetime of trapped carriers is less than the decay time of the EL occurring prior to the onset of overshoot, the EL overshoot begins just after the end of voltage pulse. The overshoot in spin-coated bilayer OLEDs is caused by the presence of an interfacial layer of finite thickness between hole and electron transporting layers in which both transport molecules coexist, whereby the interfacial energy barrier impedes both hole and electron passage. When a voltage pulse is applied to a bilayer OLED, positive and negative space charges are established at the opposite faces of the interfacial layer. Subsequently, the charge recombination occurs with the incoming flux of injected carriers of opposite polarity. When the voltage is turned off, the interfacial charges recombine under the action of their mutual electric field. Thus, after switching off the external voltage the electrons stored in the interface next to the anode cell compartment experience an electric field directed from cathode to anode, and therefore, the electrons move towards the cathode, that is, towards the positive space charge, whereby electron-hole recombination gives rise to luminescence. The EL prior to onset of overshoot is caused by the movement of electrons in the electron transporting states, however, the EL in the overshoot region is caused by the movement of detrapped electrons. On the basis of the rate equations for the detrapping and recombination of charge carriers accumulated at the interface
Improved decay rates for solutions for a multidimensional generalized Benjamin-Bona-Mahony equation
Said-Houari, Belkacem
2014-01-01
the Fourier transform and the energy method, we show the global existence and the convergence rates of the solutions under the smallness assumption on the initial data and we give better decay rates of the solutions. This result improves early works in J
Gerencsér, Máté; Jentzen, Arnulf; Salimova, Diyora
2017-11-01
In a recent article (Jentzen et al. 2016 Commun. Math. Sci. 14 , 1477-1500 (doi:10.4310/CMS.2016.v14.n6.a1)), it has been established that, for every arbitrarily slow convergence speed and every natural number d ∈{4,5,…}, there exist d -dimensional stochastic differential equations with infinitely often differentiable and globally bounded coefficients such that no approximation method based on finitely many observations of the driving Brownian motion can converge in absolute mean to the solution faster than the given speed of convergence. In this paper, we strengthen the above result by proving that this slow convergence phenomenon also arises in two ( d =2) and three ( d =3) space dimensions.
Grima, R
2010-07-21
Chemical master equations provide a mathematical description of stochastic reaction kinetics in well-mixed conditions. They are a valid description over length scales that are larger than the reactive mean free path and thus describe kinetics in compartments of mesoscopic and macroscopic dimensions. The trajectories of the stochastic chemical processes described by the master equation can be ensemble-averaged to obtain the average number density of chemical species, i.e., the true concentration, at any spatial scale of interest. For macroscopic volumes, the true concentration is very well approximated by the solution of the corresponding deterministic and macroscopic rate equations, i.e., the macroscopic concentration. However, this equivalence breaks down for mesoscopic volumes. These deviations are particularly significant for open systems and cannot be calculated via the Fokker-Planck or linear-noise approximations of the master equation. We utilize the system-size expansion including terms of the order of Omega(-1/2) to derive a set of differential equations whose solution approximates the true concentration as given by the master equation. These equations are valid in any open or closed chemical reaction network and at both the mesoscopic and macroscopic scales. In the limit of large volumes, the effective mesoscopic rate equations become precisely equal to the conventional macroscopic rate equations. We compare the three formalisms of effective mesoscopic rate equations, conventional rate equations, and chemical master equations by applying them to several biochemical reaction systems (homodimeric and heterodimeric protein-protein interactions, series of sequential enzyme reactions, and positive feedback loops) in nonequilibrium steady-state conditions. In all cases, we find that the effective mesoscopic rate equations can predict very well the true concentration of a chemical species. This provides a useful method by which one can quickly determine the
High strain rates spallation phenomena with relation to the equation of state
International Nuclear Information System (INIS)
Dekel, E.
1997-11-01
Theoretical spall strength, defined as the stress needed to separate a material along a plane surface instantaneously, is one order of magnitude larger then the measured spell strength at strain rates up to 10 6 s -1 . The discrepancy is explained by material initial flaws and cavities which grow and coalesce under stress and weaken the material. Measurements of spall strength of materials shocked by a high power laser shows a rapid increase in the spall strength with the strain rate at strain rates of about 10 7 s -1 . This indicates that the initial flaws does not have time to coalesce and the interatomic forces become dominant. In order to break the material more cavities must be created. This cavities are characterized by the interatomic forces and are created statistically: material under tensile stress is in a metastable condition and due to thermal fluctuations cavities are formed. Cavities larger than a certain critical size grow due to the stress. They grow until the material disintegrates at the spall plane. The theoretical results predict the increase in spall strength at high strain rates, as observed experimentally. (authors)
International Nuclear Information System (INIS)
Webb, J F; Yong, K S C; Haldar, M K
2015-01-01
Using results that come out of a simplified rate equation model, the suppression of residual amplitude modulation in injection locked quantum cascade lasers with the master laser modulated by its drive current is investigated. Quasi-static and dynamic expressions for intensity modulation are used. The suppression peaks at a specific value of the injection ratio for a given detuning and linewidth enhancement factor. The intensity modulation suppression remains constant over a range of frequencies. The effects of injection ratio, detuning, coupling efficiency and linewidth enhancement factor are considered. (paper)
Nikolaidis, Pantelis T.; Rosemann, Thomas; Knechtle, Beat
2018-01-01
Age-based prediction equations of maximal heart rate (HRmax), such as the popular formulas Fox's 220-age, or Tanaka's 208-0.7 × age, have been widely used in various populations. Surprisingly, so far these equations have not been validated in marathon runners, despite the importance of the role of HRmax for training purposes in endurance running. The aim of the present study was to examine the validity of Fox and Tanaka equations in a large sample of women and men recreational marathon runners. Participants (n = 180, age 43.2 ± 8.5 years, VO2max 46.8 mL/min/kg, finishers in at least one marathon during the last year) performed a graded exercise test on a treadmill, where HRmax was measured. Measured HRmax correlated largely with age in the total sample (r = −0.50, p marathon runners. In addition, exercise physiologists and sport scientists should consider the observed differences among various assessment methods when performing exercise testing or prescribing training program relying on HR. PMID:29599724
Nikolaidis, Pantelis T; Rosemann, Thomas; Knechtle, Beat
2018-01-01
Age-based prediction equations of maximal heart rate (HR max ), such as the popular formulas Fox's 220-age, or Tanaka's 208-0.7 × age, have been widely used in various populations. Surprisingly, so far these equations have not been validated in marathon runners, despite the importance of the role of HR max for training purposes in endurance running. The aim of the present study was to examine the validity of Fox and Tanaka equations in a large sample of women and men recreational marathon runners. Participants ( n = 180, age 43.2 ± 8.5 years, VO 2max 46.8 mL/min/kg, finishers in at least one marathon during the last year) performed a graded exercise test on a treadmill, where HR max was measured. Measured HR max correlated largely with age in the total sample ( r = -0.50, p marathon runners. In addition, exercise physiologists and sport scientists should consider the observed differences among various assessment methods when performing exercise testing or prescribing training program relying on HR.
Macroscopic rate equation modeling of trapping/detrapping of hydrogen isotopes in tungsten materials
Energy Technology Data Exchange (ETDEWEB)
Hodille, E.A., E-mail: etienne.hodille@cea.fr [CEA, IRFM, F-13108 Saint Paul lez Durance (France); Bonnin, X. [LSPM-CNRS, Université Paris 13, Sorbonne Paris Cité, F-93430 Villetaneuse (France); Bisson, R.; Angot, T. [Aix-Marseille Université, PIIM, CNRS, UMR 7345, 13397 Marseille (France); Becquart, C.S. [Université Lille I, UMET, UMR 8207, 59655 Villeneuve d’Ascq cédex France (France); Layet, J.M. [Aix-Marseille Université, PIIM, CNRS, UMR 7345, 13397 Marseille (France); Grisolia, C. [CEA, IRFM, F-13108 Saint Paul lez Durance (France)
2015-12-15
Relevant parameters for trapping of Hydrogen Isotopes (HIs) in polycrystalline tungsten are determined with the MHIMS code (Migration of Hydrogen Isotopes in MaterialS) which is used to reproduce Thermal Desorption Spectrometry experiments. Three types of traps are found: two intrinsic traps (detrapping energy of 0.87 eV and 1.00 eV) and one extrinsic trap created by ion irradiation (detrapping energy of 1.50 eV). Then MHIMS is used to simulate HIs retention at different fluences and different implantation temperatures. Simulation results agree well with experimental data. It is shown that at 300 K the retention is limited by diffusion in the bulk. For implantation temperatures above 500 K, the retention is limited by trap creation processes. Above 600 K, the retention drops by two orders of magnitude as compared to the retention at 300 K. With the determined detrapping energies, HIs outgassing at room temperature is predicted. After ions implantation at 300 K, 45% of the initial retention is lost to vacuum in 300 000 s while during this time the remaining trapped HIs diffuse twice as deep into the bulk. - Highlights: • Code development to solve numerically the model equations of diffusion and trapping of hydrogen in metals. • Parametrization of the model trapping parameters (detrapping energies and density): fitting of experimental TDS spectrum. • Confrontation model/experiment: evolution of retention with fluence and implantation temperature. • Investigation of period of rest between implantation and TDS on retention and depth profile.
Studies on rate equations for defects in irradiated solids using the local analysis method
International Nuclear Information System (INIS)
Carvalho e Camargo, M.U. de.
1983-10-01
The void formation and swelling phenomenon in material for nuclear reactors structures, mainly for fast reactors, has been studied by several authors. A simple calculation covering the basic instance of radiation damage in irradiated solid solution, using the local analysis in rate theory is presented here. A simple description of pratical and fundamental interest for the complex problem of solid solution under irradiation is given. (Author) [pt
Agoons, D D; Balti, E V; Kaze, F F; Azabji-Kenfack, M; Ashuntantang, G; Kengne, A P; Sobngwi, E; Mbanya, J C
2016-09-01
We evaluated the performance of the Modification of Diet in Renal Disease (MDRD), Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) and Cockcroft-Gault (CG) equations against creatinine clearance (CrCl) to estimate glomerular filtration rate (GFR) in 51 patients with Type 2 diabetes. The CrCl value was obtained from the average of two consecutive 24-h urine samples. Results were adjusted for body surface area using the Dubois formula. Serum creatinine was measured using the kinetic Jaffe method and was calibrated to standardized levels. Bland-Altman analysis and kappa statistic were used to examine agreement between measured and estimated GFR. Estimates of GFR from the CrCl, MDRD, CKD-EPI and CG equations were similar (overall P = 0.298), and MDRD (r = 0.58; 95% CI: 0.36-0.74), CKD-EPI (r = 0.55; 95% CI: 0.33-0.72) and CG (r = 0.61; 95% CI: 0.39-0.75) showed modest correlation with CrCl (all P fair-to-moderate agreement with CrCl (kappa: 0.38-0.51). The c-statistic for all three equations ranged between 0.75 and 0.77 with no significant difference (P = 0.639 for c-statistic comparison). The MDRD equation seems to have a modest advantage over CKD-EPI and CG in estimating GFR and detecting impaired renal function in sub-Saharan African patients with Type 2 diabetes. The overall relatively modest correlation with CrCl, however, suggests the need for context-specific estimators of GFR or context adaptation of existing estimators. © 2015 Diabetes UK.
How "Hot Precursors" Modify Island Nucleation: A Rate-Equation Model
Morales-Cifuentes, Josue R.; Einstein, T. L.; Pimpinelli, A.
2014-12-01
We propose a novel island nucleation and growth model explicitly including transient (ballistic) mobility of the monomers deposited at rate F , assumed to be in a hot precursor state before thermalizing. In limiting regimes, corresponding to fast (diffusive) and slow (ballistic) thermalization, the island density N obeys scaling N ∝Fα . In between is found a rich, complex behavior, with various distinctive scaling regimes, characterized by effective exponents αeff and activation energies that we compute exactly. Application to N (F ,T ) of recent organic-molecule deposition experiments yields an excellent fit.
International Nuclear Information System (INIS)
Choi, Ho June; Koo, In Sun
2012-01-01
The specific rates of sovolysis of 4-methylthiophene-2-carbonyl chloride (1) have been determined in 26 pure and binary solvents at 25.0 .deg. C. Product selectivities are reported for solvolyses of 1 in aqueous ethanol and methanol binary mixtures. Comparison of the specific rates of solvolyses of 1 with those for p-methoxybenzoyl chloride (2) in terms of linear free energy relationships (LFER) are helpful in mechanistic considerations, as is also treatment in terms of the extended Grunwald-Winstein equation. It is proposed that the solvolyses of 1 in binary aqueous solvent mixtures proceed through an S N 1 and/or ionization (I) pathway rather than through an associative S N 2 and/or addition-elimination (A-E) pathway
Fukuda, Makoto; Yoshimura, Kengo; Namekawa, Koki; Sakai, Kiyotaka
2017-06-01
The objective of the present study is to evaluate the effect of filtration coefficient and internal filtration on dialysis fluid flow and mass transfer coefficient in dialyzers using dimensionless mass transfer correlation equations. Aqueous solution of vitamin B 12 clearances were obtained for REXEED-15L as a low flux dialyzer, and APS-15EA and APS-15UA as high flux dialyzers. All the other design specifications were identical for these dialyzers except for filtration coefficient. The overall mass transfer coefficient was calculated, moreover, the exponents of Reynolds number (Re) and film mass transfer coefficient of the dialysis-side fluid (k D ) for each flow rate were derived from the Wilson plot and dimensionless correlation equation. The exponents of Re were 0.4 for the low flux dialyzer whereas 0.5 for the high flux dialyzers. Dialysis fluid of the low flux dialyzer was close to laminar flow because of its low filtration coefficient. On the other hand, dialysis fluid of the high flux dialyzers was assumed to be orthogonal flow. Higher filtration coefficient was associated with higher k D influenced by mass transfer rate through diffusion and internal filtration. Higher filtration coefficient of dialyzers and internal filtration affect orthogonal flow of dialysis fluid.
Directory of Open Access Journals (Sweden)
Luceta McRoy
2017-02-01
Full Text Available Background: Asthma is one of the leading causes of emergency department visits and school absenteeism among school-aged children in the United States, but there is significant local-area variation in emergency department visit rates, as well as significant differences across racial-ethnic groups. Analysis: We first calculated emergency department (ED visit rates among Medicaid-enrolled children age 5–12 with asthma using a multi-state dataset. We then performed exploratory factor analysis using over 226 variables to assess whether they clustered around three county-level conceptual factors (socioeconomic status, healthcare capacity, and air quality thought to be associated with variation in asthma ED visit rates. Measured variables (including ED visit rate as the outcome of interest were then standardized and tested in a simple conceptual model through confirmatory factor analysis. Results: County-level (contextual variables did cluster around factors declared a priori in the conceptual model. Structural equation models connecting the ED visit rates to socioeconomic status, air quality, and healthcare system professional capacity factors (consistent with our conceptual framework converged on a solution and achieved a reasonable goodness of fit on confirmatory factor analysis. Conclusion: Confirmatory factor analysis offers an approach for quantitatively testing conceptual models of local-area variation and racial disparities in asthma-related emergency department use.
Directory of Open Access Journals (Sweden)
Alaleh Gheissari
2014-01-01
Full Text Available To determine the performance of the updated Schwartz, combined Schwartz and Grubb glomerular filtration rate (GFR equations in a relatively large number of healthy children with no known renal disease, we studied 712 students aged between seven and 18 years from the Isfahan province of Iran by random cluster sampling between 2009 and 2010. Blood investigations included blood urea nitrogen, creatinine and cystatin C. For each participant, GFR was calculated based on the three equations. We used Bland-Altman plots and weighted kappa statistics to compare the performance of the study equations. The mean age of the children was 12.2 ± 2.4 years. A high concordance in estimating GFR (mean difference: 0 ± 12.7 mL/min/1.73 m 2 and a very good agreement in defining chronic kidney disease (CKD and non-CKD individuals (weighted kappa: 0.85; 95% confidence intervals: 0.69-1 were observed between the updated Schwartz and the combined Schwartz equations. Poor agreement was observed between the Grubb equation and two Schwartz equations in estimating GFR and defining CKD. There was no systematic deviation between the updated Schwartz and the combined Schwartz equations in children with normal renal function. The Grubb equation was highly inconsistent with both Schwartz equations in this population. We conclude that the updated Schwartz equation is simpler and more accessible than the combined Schwartz equation in daily clinical practice and CKD screening programs.
Oki, Kensuke; Ma, Bei; Ishitani, Yoshihiro
2017-11-01
Population distributions and transition fluxes of the A exciton in bulk GaN are theoretically analyzed using rate equations of states of the principal quantum number n up to 5 and the continuum. These rate equations consist of the terms of radiative, electron-collisional, and phononic processes. The dependence of the rate coefficients on temperature is revealed on the basis of the collisional-radiative model of hydrogen plasma for the electron-collisional processes and theoretical formulation using Fermi's "golden rule" for the phononic processes. The respective effects of the variations in electron, exciton, and lattice temperatures are exhibited. This analysis is a base of the discussion on nonthermal equilibrium states of carrier-exciton-phonon dynamics. It is found that the exciton dissociation is enhanced even below 150 K mainly by the increase in the lattice temperature. When the thermal-equilibrium temperature increases, the population fluxes between the states of n >1 and the continuum become more dominant. Below 20 K, the severe deviation from the Saha-Boltzmann distribution occurs owing to the interband excitation flux being higher than the excitation flux from the 1 S state. The population decay time of the 1 S state at 300 K is more than ten times longer than the recombination lifetime of excitons with kinetic energy but without the upper levels (n >1 and the continuum). This phenomenon is caused by a shift of population distribution to the upper levels. This phonon-exciton-radiation model gives insights into the limitations of conventional analyses such as the ABC model, the Arrhenius plot, the two-level model (n =1 and the continuum), and the neglect of the upper levels.
Caselli, Paola; Stantcheva, Tatiana; Shalabiea, Osama; Shematovich, Valery I.; Herbst, Eric
2002-10-01
The formation of singly and doubly deuterated isotopomers of formaldehyde and of singly, doubly, and multiply deuterated isotopomers of methanol on interstellar grain surfaces has been studied with a semi-empirical modified rate approach and a Monte Carlo method in the temperature range 10- 20 K. Agreement between the results of the two methods is satisfactory for all major and many minor species throughout this range. If gas-phase fractionation can produce a high abundance of atomic deuterium, which then accretes onto grain surfaces, diffusive surface chemistry can produce large abundances of deuterated species, especially at low temperatures and high gas densities. Warming temperatures will then permit these surface species to evaporate into the gas, where they will remain abundant for a considerable period. We calculate that the doubly deuterated molecules CHD 2OH and CH 2DOD are particularly abundant and should be searched for in the gas phase of protostellar sources. For example, at 10 K and high density, these species can achieve up to 10-20% of the abundance of methanol.
International Nuclear Information System (INIS)
Dong, B; Ding, G H; Lei, X L
2015-01-01
A general theoretical formulation for the effect of a strong on-site Coulomb interaction on the time-dependent electron transport through a quantum dot under the influence of arbitrary time-varying bias voltages and/or external fields is presented, based on slave bosons and the Keldysh nonequilibrium Green's function (GF) techniques. To avoid the difficulties of computing double-time GFs, we generalize the propagation scheme recently developed by Croy and Saalmann to combine the auxiliary-mode expansion with the celebrated Lacroix's decoupling approximation in dealing with the second-order correlated GFs and then establish a closed set of coupled equations of motion, called second-order quantum rate equations (SOQREs), for an exact description of transient dynamics of electron correlated tunneling. We verify that the stationary solution of our SOQREs is able to correctly describe the Kondo effect on a qualitative level. Moreover, a comparison with other methods, such as the second-order von Neumann approach and Hubbard-I approximation, is performed. As illustrations, we investigate the transient current behaviors in response to a step voltage pulse and a harmonic driving voltage, and linear admittance as well, in the cotunneling regime. (paper)
Energy Technology Data Exchange (ETDEWEB)
Domanskyi, Sergii; Schilling, Joshua E.; Privman, Vladimir, E-mail: privman@clarkson.edu [Department of Physics, Clarkson University, Potsdam, New York 13676 (United States); Gorshkov, Vyacheslav [National Technical University of Ukraine — KPI, Kiev 03056 (Ukraine); Libert, Sergiy, E-mail: libert@cornell.edu [Department of Biomedical Sciences, Cornell University, Ithaca, New York 14853 (United States)
2016-09-07
We develop a theoretical approach that uses physiochemical kinetics modelling to describe cell population dynamics upon progression of viral infection in cell culture, which results in cell apoptosis (programmed cell death) and necrosis (direct cell death). Several model parameters necessary for computer simulation were determined by reviewing and analyzing available published experimental data. By comparing experimental data to computer modelling results, we identify the parameters that are the most sensitive to the measured system properties and allow for the best data fitting. Our model allows extraction of parameters from experimental data and also has predictive power. Using the model we describe interesting time-dependent quantities that were not directly measured in the experiment and identify correlations among the fitted parameter values. Numerical simulation of viral infection progression is done by a rate-equation approach resulting in a system of “stiff” equations, which are solved by using a novel variant of the stochastic ensemble modelling approach. The latter was originally developed for coupled chemical reactions.
Hao, Tian; Xu, Yuanze; Hao, Ting
2018-04-01
The Eyring's rate process theory and free volume concept are employed to treat protons (or other particles) transporting through a 2D (two dimensional) crystal like graphene and hexagonal boron nitride. The protons are assumed to be activated first in order to participate conduction and the conduction rate is dependent on how much free volume available in the system. The obtained proton conductivity equations show that only the number of conduction protons, proton size and packing structure, and the energy barrier associated with 2D crystals are critical; the quantization conductance is unexpectedly predicted with a simple Arrhenius type temperature dependence. The predictions agree well with experimental observations and clear out many puzzles like much smaller energy barrier determined from experiments than from the density function calculations and isotope separation rate independent of the energy barrier of 2D crystals, etc. Our work may deepen our understandings on how protons transport through a membrane and has direct implications on hydrogen related technology and proton involved bioprocesses.
Directory of Open Access Journals (Sweden)
Ramzi Othman
2015-01-01
Full Text Available In several industrial applications, metallic structures are facing impact loads. Therefore, there is an important need for developing constitutive equations which take into account the strain rate sensitivity of their mechanical properties. The Johnson-Cook equation was widely used to model the strain rate sensitivity of metals. However, it implies that the yield and flow stresses are linearly increasing in terms of the logarithm of strain rate. This is only true up to a threshold strain rate. In this work, a three-constant constitutive equation, assuming an apparent activation volume which decreases as the strain rate increases, is applied here for some metals. It is shown that this equation fits well the experimental yield and flow stresses for a very wide range of strain rates, including quasi-static, high, and very high strain rates (from 10−5 to 5 × 104 s−1. This is the first time that a constitutive equation is showed to be able to fit the yield stress over a so large strain rate range while using only three material constants.
Directory of Open Access Journals (Sweden)
Pantelis T. Nikolaidis
2018-03-01
Full Text Available Age-based prediction equations of maximal heart rate (HRmax, such as the popular formulas Fox's 220-age, or Tanaka's 208-0.7 × age, have been widely used in various populations. Surprisingly, so far these equations have not been validated in marathon runners, despite the importance of the role of HRmax for training purposes in endurance running. The aim of the present study was to examine the validity of Fox and Tanaka equations in a large sample of women and men recreational marathon runners. Participants (n = 180, age 43.2 ± 8.5 years, VO2max 46.8 mL/min/kg, finishers in at least one marathon during the last year performed a graded exercise test on a treadmill, where HRmax was measured. Measured HRmax correlated largely with age in the total sample (r = −0.50, p < 0.001, women (r = −0.60, p < 0.001 and men (r = −0.53, p < 0.001. In women, a large main effect of method on HRmax (p = 0.001, η2 = 0.294 was shown with measured HRmax lower than Fox-HRmax (−4.8 bpm; −8.4, −1.3 and Tanaka-HRmax (−4.9 bpm; −8.1, −1.8. In men, a moderate effect of assessment method on HRmax was found (p = 0.001, η2 = 0.066 with measured HRmax higher than Fox-HRmax (+2.8; 1.0, 4.6, Tanaka-HRmax higher than Fox-HRmax (+1.2; 0.7, 1.7. Based on these findings, it was concluded that Fox and Tanaka' formulas overestimated HRmax by ~5 bpm in women, whereas Fox underestimated HRmax in men by ~3 bpm. Thus, we recommend the further use of Tanaka's formula in men marathon runners. In addition, exercise physiologists and sport scientists should consider the observed differences among various assessment methods when performing exercise testing or prescribing training program relying on HR.
Mortensen, Stig B; Klim, Søren; Dammann, Bernd; Kristensen, Niels R; Madsen, Henrik; Overgaard, Rune V
2007-10-01
The non-linear mixed-effects model based on stochastic differential equations (SDEs) provides an attractive residual error model, that is able to handle serially correlated residuals typically arising from structural mis-specification of the true underlying model. The use of SDEs also opens up for new tools for model development and easily allows for tracking of unknown inputs and parameters over time. An algorithm for maximum likelihood estimation of the model has earlier been proposed, and the present paper presents the first general implementation of this algorithm. The implementation is done in Matlab and also demonstrates the use of parallel computing for improved estimation times. The use of the implementation is illustrated by two examples of application which focus on the ability of the model to estimate unknown inputs facilitated by the extension to SDEs. The first application is a deconvolution-type estimation of the insulin secretion rate based on a linear two-compartment model for C-peptide measurements. In the second application the model is extended to also give an estimate of the time varying liver extraction based on both C-peptide and insulin measurements.
Fach, S; Sitzenfrei, R; Rauch, W
2009-01-01
It is state of the art to evaluate and optimise sewer systems with urban drainage models. Since spill flow data is essential in the calibration process of conceptual models it is important to enhance the quality of such data. A wide spread approach is to calculate the spill flow volume by using standard weir equations together with measured water levels. However, these equations are only applicable to combined sewer overflow (CSO) structures, whose weir constructions correspond with the standard weir layout. The objective of this work is to outline an alternative approach to obtain spill flow discharge data based on measurements with a sonic depth finder. The idea is to determine the relation between water level and rate of spill flow by running a detailed 3D computational fluid dynamics (CFD) model. Two real world CSO structures have been chosen due to their complex structure, especially with respect to the weir construction. In a first step the simulation results were analysed to identify flow conditions for discrete steady states. It will be shown that the flow conditions in the CSO structure change after the spill flow pipe acts as a controlled outflow and therefore the spill flow discharge cannot be described with a standard weir equation. In a second step the CFD results will be used to derive rating curves which can be easily applied in everyday practice. Therefore the rating curves are developed on basis of the standard weir equation and the equation for orifice-type outlets. Because the intersection of both equations is not known, the coefficients of discharge are regressed from CFD simulation results. Furthermore, the regression of the CFD simulation results are compared with the one of the standard weir equation by using historic water levels and hydrographs generated with a hydrodynamic model. The uncertainties resulting of the wide spread use of the standard weir equation are demonstrated.
Yamaguchi, Tsuyoshi; Higashihara, Eiji; Okegawa, Takatsugu; Miyazaki, Isao; Nutahara, Kikuo
2018-05-22
The reliability of various equations for estimating the GFR in ADPKD patients and the influence of tolvaptan on the resulting estimates have not been examined when GFR is calculated on the basis of inulin clearance. We obtained baseline and on-tolvaptan measured GFRs (mGFRs), calculated on the basis of inulin clearance, in 114 ADPKD, and these mGFRs were compared with eGFRs calculated according to four basic equations: the MDRD, CKD-EPI, and JSN-CKDI equations and the Cockcroft-Gault formula, as well as the influence of tolvaptan and of inclusion of cystatin C on accuracy of the results. Accuracy of each of the seven total equations was evaluated on the basis of the percentage of eGFR values within mGFR ± 30% (P 30 ). mGFRs were distributed throughout CKD stages 1-5. Regardless of the CKD stage, P 30 s of the MDRD, CKD-EPI, and JSN-CKDI equations did not differ significantly between baseline values and on-tolvaptan values. In CKD 1-2 patients, P 30 of the CKD-EPI equation was 100.0%, whether or not the patient was on-tolvaptan. In CKD 3-5 patients, P 30 s of the MDRD, CKD-EPI, and JSN-CKDI equations were similar. For all four equations, regression coefficients and intercepts did not differ significantly between baseline and on-tolvaptan values, but accuracy of the Cockcroft-Gault formula was inferior to that of the other three equations. Incorporation of serum cystatin C reduced accuracy. The CKD-EPI equation is most reliable, regardless of the severity of CKD. Tolvaptain intake has minimal influence and cystatin C incorporation does not improve accuracy.
Dowling, Thomas C; Wang, En-Shih; Ferrucci, Luigi; Sorkin, John D
2013-09-01
To evaluate the performance of kidney function estimation equations and to determine the frequency of drug dose discordance in an older population. Cross-sectional analysis of data from community-dwelling volunteers randomly selected from the Baltimore Longitudinal Study of Aging from January 1, 2005, to December 31, 2010. A total of 269 men and women with a mean ± SD age of 81 ± 6 years, mean serum creatinine concentration (Scr ) of 1.1 ± 0.4 mg/dl, and mean 24-hour measured creatinine clearance (mClcr ) of 53 ± 13 ml/minute. Kidney function was estimated by using the following equations: Cockcroft-Gault (CG), Modification of Diet in Renal Disease (MDRD), and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI). The performance of each equation was assessed by measuring bias and precision relative to mClcr . Dose calculation errors (discordance) were determined for 10 drugs requiring renal dosage adjustments to avoid toxicity when compared with the dosages approved by the Food and Drug Administration. The CG equation was the least biased estimate of mClcr . The MDRD and CKD-EPI equations were significantly positively biased compared with CG (mean ± SD 34 ± 20% and 22 ± 15%, respectively, prenal impairment. Thus equations estimating glomerular filtration rate should not be substituted in place of the CG equation in older adults for the purpose of renal dosage adjustments. In addition, the common practice of rounding or replacing low Scr values with an arbitrary value of 1.0 mg/dl for use in the CG equation should be avoided. Additional studies that evaluate alternative eGFR equations in the older populations that incorporate pharmacokinetic and pharmacodynamic outcomes measures are needed. © 2013 Pharmacotherapy Publications, Inc.
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Liu X
2013-10-01
Full Text Available Xun Liu,1,2,* Huijuan Ma,1,* Hui Huang,3 Cheng Wang,1 Hua Tang,1 Ming Li,1 Yanni Wang,1 Tanqi Lou1 1Division of Nephrology, Department of Internal Medicine, The Third Affiliated Hospital of Sun Yat-sen University, 2College of Biology Engineering, South China University of Technology, 3Department of Cardiology, Sun Yat-sen Memorial Hospital of Sun Yat-sen University, Guangzhou, People's Republic of China*These authors contributed equally to the paperBackground: We aimed to evaluate the performance of the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI creatinine–cystatin C equation in a cohort of elderly Chinese participants.Materials and methods: Glomerular filtration rate (GFR was measured in 431 elderly Chinese participants by the technetium-99m diethylene-triamine-penta-acetic acid (99mTc-DTPA renal dynamic imaging method, and was calibrated equally to the dual plasma sample 99mTc-DTPA-GFR. Performance of the CKD-EPI creatinine–cystatin C equation was compared with the Cockroft–Gault equation, the re-expressed 4-variable Modification of Diet in Renal Disease (MDRD equation, and the CKD-EPI creatinine equation.Results: Although the bias of the CKD-EPI creatinine–cystatin C equation was greater than with the other equations (median difference, 5.7 mL/minute/1.73 m2 versus a range from 0.4–2.5 mL/minute/1.73 m2; P<0.001 for all, the precision was improved with the CKD-EPI creatinine–cystatin C equation (interquartile range for the difference, 19.5 mL/minute/1.73 m2 versus a range from 23.0–23.6 mL/minute/1.73 m2; P<0.001 for all comparisons, leading to slight improvement in accuracy (median absolute difference, 10.5 mL/minute/1.73 m2 versus 12.2 and 11.4 mL/minute/1.73 m2 for the Cockcroft–Gault equation and the re-expressed 4-variable MDRD equation, P=0.04 for both; 11.6 mL/minute/1.73 m2 for the CKD-EPI creatinine equation, P=0.11, as the optimal scores of performance (6.0 versus a range from 1.0–2.0 for the other
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Winckler, N., E-mail: n.winckler@gsi.de [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Rybalchenko, A. [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Shevelko, V.P. [P.N. Lebedev Physical Institute, 119991 Moscow (Russian Federation); Al-Turany, M. [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); CERN, European Organization for Nuclear Research, 1211 Geneve 23 (Switzerland); Kollegger, T. [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Stöhlker, Th. [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Helmholtz-Institute Jena, D-07743 Jena (Germany); Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität, D-07743 Jena (Germany)
2017-02-01
A detailed description of a recently developed BREIT computer code (Balance Rate Equations of Ion Transportation) for calculating charge-state fractions of ion beams passing through matter is presented. The code is based on the analytical solutions of the differential balance equations for the charge-state fractions as a function of the target thickness and can be used for calculating the ion evolutions in gaseous, solid and plasma targets. The BREIT code is available on-line and requires the charge-changing cross sections and initial conditions in the input file. The eigenvalue decomposition method, applied to obtain the analytical solutions of the rate equations, is described in the paper. Calculations of non-equilibrium and equilibrium charge-state fractions, performed by the BREIT code, are compared with experimental data and results of other codes for ion beams in gaseous and solid targets. Ability and limitations of the BREIT code are discussed in detail.
Winckler, N; Shevelko, V P; Al-Turany, M; Kollegger, T; Stöhlker, Th
2017-01-01
A detailed description of a recently developed BREIT computer code (Balance Rate Equations of Ion Transportation) for calculating charge-state fractions of ion beams passing through matter is presented. The code is based on the analytical solutions of the differential balance equations for the charge-state fractions as a function of the target thickness and can be used for calculating the ion evolutions in gaseous, solid and plasma targets. The BREIT code is available on-line and requires the charge-changing cross sections and initial conditions in the input file. The eigenvalue decomposition method, applied to obtain the analytical solutions of the rate equations, is described in the paper. Calculations of non-equilibrium and equilibrium charge-state fractions, performed by the BREIT code, are compared with experimental data and results of other codes for ion beams in gaseous and solid targets. Ability and limitations of the BREIT code are discussed in detail.
Anderson, Josephine L C; Gruppen, Eke G; van Tienhoven-Wind, Lynnda; Eisenga, Michele F; de Vries, Hanne; Gansevoort, Ron T; Bakker, Stephan J L; Dullaart, Robin P F
BACKGROUND: Effects of variations in thyroid function within the euthyroid range on renal function are unclear. Cystatin C-based equations to estimate glomerular filtration rate (GFR) are currently advocated for mortality and renal risk prediction. However, the applicability of cystatin C-based
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Luiz Lannes Loureiro
Full Text Available The accurate estimative of energy needs is crucial for an optimal physical performance among athletes and the basal metabolic rate (BMR equations often are not well adjusted for adolescent athletes requiring the use of specific methods, such as the golden standard indirect calorimetry (IC. Therefore, we had the aim to analyse the agreement between the BMR of adolescents pentathletes measured by IC and estimated by commonly used predictive equations.Twenty-eight athletes (17 males and 11 females were evaluated for BMR, using IC and the predictive equations Harris and Benedict (HB, Cunningham (CUN, Henry and Rees (HR and FAO/WHO/UNU (FAO. Body composition was obtained using DXA and sexual maturity data were retrieved through validated questionnaires. The correlations among anthropometric variables an IC were analysed by T-student test and ICC, while the agreement between IC and the predictive equations was analysed according to Bland and Altman and by survival-agreement plotting.The whole sample average BMR measured by IC was significantly different from the estimated by FAO (p<0.05. Adjusting data by gender FAO and HR equations were statistically different from IC (p <0.05 among males, while female differed only for the HR equation (p <0.05.The FAO equation underestimated athletes' BMR when compared with IC (T Test. When compared to the golden standard IC, using Bland and Altman, ICC and Survival-Agreement, the equations underestimated the energy needs of adolescent pentathlon athletes up to 300kcal/day. Therefore, they should be used with caution when estimating individual energy requirements in such populations.
International Nuclear Information System (INIS)
Kozhevnikova, L M; Mukminov, F Kh
2000-01-01
A quasilinear system of parabolic equations with energy inequality is considered in a cylindrical domain {t>0}xΩ. In a broad class of unbounded domains Ω two geometric characteristics of a domain are identified which determine the rate of convergence to zero as t→∞ of the L 2 -norm of a solution. Under additional assumptions on the coefficients of the quasilinear system estimates of the derivatives and uniform estimates of the solution are obtained; they are proved to be best possible in the order of convergence to zero in the case of one semilinear equation
Zaman, Sojib Bin
2017-01-01
Introduction Chronic kidney disease (CKD) is a global threat due to its high mortality. It is essential to know the actual magnitude of diabetic CKD to design a specific management program. However, there is limited knowledge regarding the most suitable equation to measure CKD in patients with Type 2 diabetes mellitus (T2DM). This paper aimed to analyze estimated glomerular filtration rate (eGFR) based on different equations to detect the CKD among T2DM.? Methods A hospital-based cross-sectio...
International Nuclear Information System (INIS)
Tariq, M.; Khan, I.A.
2003-01-01
A time dependent Finite Element simulation of penetration of a rigid cylindrical bar impacting on a copper plate is conducted, to demonstrate how material behavior appears to change when Johnson-Cook plasticity rule is employed along with a Gruneisen, equation of state with cubic shock velocity-particle relationship, and defining pressure both for compressed and expanded materials, as compared to the behavior when only isotropic strain-hardening model is employed. The bar impacts the plate with a velocity of 1000 m/s, and penetrates the plate, a portion of it coming out of the other side. Results are obtained and compared taking both an isotropic strain-hardening model, and a model incorporating Johnson-Cook flow rule along with Gruneisen equation of state. (author)
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Maisarah Jalalonmuhali
2017-01-01
Full Text Available Aim. To validate the accuracy of estimated glomerular filtration rate (eGFR equations in Malay population attending our hospital in comparison with radiolabeled measured GFR. Methods. A cross-sectional study recruiting volunteered patients in the outpatient setting. Chromium EDTA (51Cr-EDTA was used as measured GFR. The predictive capabilities of Cockcroft-Gault equation corrected for body surface area (CGBSA, four-variable Modification of Diet in Renal Disease (4-MDRD, and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI equations were calculated. Results. A total of 51 subjects were recruited with mean measured GFR 42.04 (17.70–111.10 ml/min/1.73 m2. Estimated GFR based on CGBSA, 4-MDRD, and CKD-EPI were 40.47 (16.52–115.52, 35.90 (14.00–98.00, and 37.24 (14.00–121.00, respectively. Higher accuracy was noted in 4-MDRD equations throughout all GFR groups except for subgroup of GFR ≥ 60 ml/min/1.73 m2 where CGBSA was better. Conclusions. The 4-MDRD equation seems to perform better in estimating GFR in Malay CKD patients generally and specifically in the subgroup of GFR < 60 ml/min/1.73 m2 and both BMI subgroups.
Loureiro, Luiz Lannes; Fonseca, Sidnei; Castro, Natalia Gomes Casanova de Oliveira e; dos Passos, Renata Baratta; Porto, Cristiana Pedrosa Melo; Pierucci, Anna Paola Trindade Rocha
2015-01-01
Purpose The accurate estimative of energy needs is crucial for an optimal physical performance among athletes and the basal metabolic rate (BMR) equations often are not well adjusted for adolescent athletes requiring the use of specific methods, such as the golden standard indirect calorimetry (IC). Therefore, we had the aim to analyse the agreement between the BMR of adolescents pentathletes measured by IC and estimated by commonly used predictive equations. Methods Twenty-eight athletes (17 males and 11 females) were evaluated for BMR, using IC and the predictive equations Harris and Benedict (HB), Cunningham (CUN), Henry and Rees (HR) and FAO/WHO/UNU (FAO). Body composition was obtained using DXA and sexual maturity data were retrieved through validated questionnaires. The correlations among anthropometric variables an IC were analysed by T-student test and ICC, while the agreement between IC and the predictive equations was analysed according to Bland and Altman and by survival-agreement plotting. Results The whole sample average BMR measured by IC was significantly different from the estimated by FAO (pBMR when compared with IC (T Test). When compared to the golden standard IC, using Bland and Altman, ICC and Survival-Agreement, the equations underestimated the energy needs of adolescent pentathlon athletes up to 300kcal/day. Therefore, they should be used with caution when estimating individual energy requirements in such populations. PMID:26569101
Omuse, Geoffrey; Maina, Daniel; Mwangi, Jane; Wambua, Caroline; Kanyua, Alice; Kagotho, Elizabeth; Amayo, Angela; Ojwang, Peter; Erasmus, Rajiv
2017-12-20
Several equations have been developed to estimate glomerular filtration rate (eGFR). The common equations used were derived from populations predominantly comprised of Caucasians with chronic kidney disease (CKD). Some of the equations provide a correction factor for African-Americans due to their relatively increased muscle mass and this has been extrapolated to black Africans. Studies carried out in Africa in patients with CKD suggest that using this correction factor for the black African race may not be appropriate. However, these studies were not carried out in healthy individuals and as such the extrapolation of the findings to an asymptomatic black African population is questionable. We sought to compare the proportion of asymptomatic black Africans reported as having reduced eGFR using various eGFR equations. We further compared the association between known risk factors for CKD with eGFR determined using the different equations. We used participant and laboratory data collected as part of a global reference interval study conducted by the Committee of Reference Intervals and Decision Limits (C-RIDL) under the International Federation of Clinical Chemistry (IFCC). Serum creatinine values were used to calculate eGFR using the Cockcroft-Gault (CG), re-expressed 4 variable modified diet in renal disease (4v-MDRD), full age spectrum (FAS) and chronic kidney disease epidemiology collaboration equations (CKD-EPI). CKD classification based on eGFR was determined for every participant. A total of 533 participants were included comprising 273 (51.2%) females. The 4v-MDRD equation without correction for race classified the least number of participants (61.7%) as having an eGFR equivalent to CKD stage G1 compared to 93.6% for CKD-EPI with correction for race. Only age had a statistically significant linear association with eGFR across all equations after performing multiple regression analysis. The multiple correlation coefficients for CKD risk factors were higher for
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Bittl, J.A.; DeLayre, J.; Ingwall, J.S.
1987-01-01
Brain, heart, and skeletal muscle contain four different creatine kinase isozymes and various concentrations of substrates for the creatine kinase reaction. To identify if the velocity of the creatine kinase reaction under cellular conditions is regulated by enzyme activity and substrate concentrations as predicted by the rate equation, the authors used 31 P NMR and spectrophotometric techniques to measure reaction velocity, enzyme content, isozyme distribution, and concentrations of substrates in brain, heart, and skeletal muscle of living rat under basal or resting conditions. The total tissue activity of creatine kinase in the direction of MgATP synthesis provided an estimate for V/sub max/ and exceeded the NMR-determined in vivo reaction velocities by an order of magnitude. The isozyme composition varied among the three tissues: >99% BB for brain; 14% MB, 61% MM, and 25% mitochondrial for heart; and 98% MM and 2% mitochondrial for skeletal muscle. The NMR-determined reaction velocities agreed with predicted values from the creatine kinase rate equation. The concentrations of free creatine and cytosolic MgADP, being less than or equal to the dissociation constants for each isozyme, were dominant terms in the creatine kinase rate equation for predicting the in vivo reaction velocity. Thus, they observed that the velocity of the creatine kinase reaction is regulated by total tissue enzyme activity and by the concentrations of creatine and MgADP in a manner that is independent of isozyme distribution
de Oliveira da Silva, Patricia; Miguez Nery Guimarães, Joanna; Härter Griep, Rosane; Caetano Prates Melo, Enirtes; Maria Alvim Matos, Sheila; Del Carmem Molina, Maria; Maria Barreto, Sandhi; de Jesus Mendes da Fonseca, Maria
2018-04-18
This study investigated whether the association between body image dissatisfaction and poor self-rated health is mediated by insufficient physical activity and unhealthy eating habits. The participants were 6727 men and 8037 women from the baseline (2008–2010) of the Longitudinal Study of Adult Health (Estudo Longitudinal de Saúde do Adulto, ELSA-Brasil). Structural equation modelling was used. Associations were found between body image dissatisfaction and poor self-rated health in both sexes. Insufficient physical activity was a mediator. However, unhealthy eating habits were found to exert a mediator effect only via insufficient physical activity. Body image dissatisfaction was found to associate, both directly and possibly indirectly, with poor self-rated health, mediated by insufficient physical activity and unhealthy eating habits. Accordingly, encouraging physical activity and healthy eating can contribute to reducing body image dissatisfaction and favour better self-rated health.
Karimzadeh, Iman; Khalili, Hossein
2016-06-06
Serum cystatin C (Cys C) has a number of advantages over serum creatinine in the evaluation of kidney function. Apart from Cys C level itself, several formulas have also been introduced in different clinical settings for the estimation of glomerular filtration rate (GFR) based upon serum Cys C level. The aim of the present study was to compare a serum Cys C-based equation with Cockcroft-Gault serum creatinine-based formula, both used in the calculation of GFR, in patients receiving amphotericin B. Fifty four adult patients with no history of acute or chronic kidney injury having been planned to receive conventional amphotericin B for an anticipated duration of at least 1 week for any indication were recruited. At three time points during amphotericin B treatment, including days 0, 7, and 14, serum cystatin C as well as creatinine levels were measured. GFR at the above time points was estimated by both creatinine (Cockcroft-Gault) and serum Cys C based equations. There was significant correlation between creatinine-based and Cys C-based GFR values at days 0 (R = 0.606, P = 0.001) and 7 (R = 0.714, P creatinine-and a cystatin C-based glomerular filtration rate equation in patients receiving amphotericin B.
Kuster, Nils; Cristol, Jean-Paul; Cavalier, Etienne; Bargnoux, Anne-Sophie; Halimi, Jean-Michel; Froissart, Marc; Piéroni, Laurence; Delanaye, Pierre
2014-01-20
The National Kidney Disease Education Program group demonstrated that MDRD equation is sensitive to creatinine measurement error, particularly at higher glomerular filtration rates. Thus, MDRD-based eGFR above 60 mL/min/1.73 m² should not be reported numerically. However, little is known about the impact of analytical error on CKD-EPI-based estimates. This study aimed at assessing the impact of analytical characteristics (bias and imprecision) of 12 enzymatic and 4 compensated Jaffe previously characterized creatinine assays on MDRD and CKD-EPI eGFR. In a simulation study, the impact of analytical error was assessed on a hospital population of 24084 patients. Ability using each assay to correctly classify patients according to chronic kidney disease (CKD) stages was evaluated. For eGFR between 60 and 90 mL/min/1.73 m², both equations were sensitive to analytical error. Compensated Jaffe assays displayed high bias in this range and led to poorer sensitivity/specificity for classification according to CKD stages than enzymatic assays. As compared to MDRD equation, CKD-EPI equation decreases impact of analytical error in creatinine measurement above 90 mL/min/1.73 m². Compensated Jaffe creatinine assays lead to important errors in eGFR and should be avoided. Accurate enzymatic assays allow estimation of eGFR until 90 mL/min/1.73 m² with MDRD and 120 mL/min/1.73 m² with CKD-EPI equation. Copyright © 2013 Elsevier B.V. All rights reserved.
Cabrerizo-García, José Luis; Díez-Manglano, Jesús; García-Arilla, Ernesto; Revillo-Pinilla, Paz; Ramón-Puertas, José; Sebastián-Royo, Mariano
2015-01-06
The Modification of Diet in Renal Disease (MDRD) equation is recommended by most scientific societies to calculate the estimated glomerular filtration rate (GFR). Recently the group Chronic Kidney Disease Epidemiology Collaboration (CKP-EPI) has published a new, more precise and accurate equation. We have analyzed its behavior in a group of polypathological patients (PP) and compared it with the classic MDRD-4.version Multicenter, observational, descriptive and transversal study. We calculated GFR by MDRD-4 and CKD-EPI in 425 PP. Each stage was assigned according to the GFR: 1:>90; 2: 60-89; 3: 30-59; 4: 15-29; and 5 renal insufficiency, especially in older women. Copyright © 2013 Elsevier España, S.L.U. All rights reserved.
Luceta McRoy; George Rust; Junjun Xu
2017-01-01
Background: Asthma is one of the leading causes of emergency department visits and school absenteeism among school-aged children in the United States, but there is significant local-area variation in emergency department visit rates, as well as significant differences across racial-ethnic groups. Analysis: We first calculated emergency department (ED) visit rates among Medicaid-enrolled children age 5–12 with asthma using a multi-state dataset. We then performed exploratory factor analysis u...
Al-Wakeel, Jamal Saleh
2016-01-01
Predictive equations for estimating glomerular filtration rate (GFR) in different clinical conditions should be validated by comparing with the measurement of GFR using inulin clearance, a highly accurate measure of GFR. Our aim was to validate the Chronic Kidney Disease-Epidemiology Collaboration (CKD-EPI) and Modification of Diet in Renal Disease (MDRD) equations by comparing it to the GFR measured using inulin clearance in chronic kidney disease (CKD) patients. Cross-sectional study performed in adult Saudi patients with CKD. King Saud University Affiliated Hospital, Riyadh, Saudi Arabia in 2014. We compared GFR measured by inulin clearance with the estimated GFR calculated using CKD-EPI and MDRD predictive formulas. Correlation, bias, precision and accuracy between the estimated GFR and inulin clearance. Comparisons were made in 31 participants (23 CKD and 8 transplanted), including 19 males (mean age 42.2 [15] years and weight 68.7 [18] kg). GFR using inulin was 51.54 (33.8) mL/min/1.73 m2 in comparison to inulin clearance, the GFR by the predictive equations was: CKD-EPI creatinine 52.6 (34.4) mL/ min/1.73 m2 (P=.490), CKD-EPI cystatin C 41.39 (30.30) mL/min/1.73 m2 (P=.002), CKD creatinine-cystatin C 45.03 (30.9) mL/min/1.73 m2 (P=.004) and MDRD GFR 48.35 (31.5) mL/min/1.73 m2 (P=.028) (statistical comparisons vs inulin). Bland-Altman plots demonstrated that GFR estimated by the CKD-EPI creatinine was the most accurate compared with inulin clearance, having a mean difference (estimated bias) and limits of agreement of -1.1 (15.6,-17.7). By comparison the mean differences for predictive equations were: CKD-EPI cystatin C 10.2 (43.7,-23.4), CKD creatinine-cystatin C 6.5 (29.3,-16.3) and MDRD 3.2 (18.3,-11.9). except for CKD-EPI creatinine, all of the equations underestimated GFR in comparison with inulin clearance. When compared with inulin clearance, the CKD-EPI creatinine equation is the most accurate, precise and least biased equation for estimation of GFR
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Jia-fu Feng
Full Text Available OBJECTIVE: To establish equations for the estimation of glomerular filtration rates (eGFRs based on serum creatinine (SCr and/or serum cystatin C (SCysC in Chinese patients with chronic kidney disease (CKD, and to compare the new equations with both the reference GFR (rGFR and the literature equations to evaluate their applicability. METHODS: The 788 Chinese CKD patients were randomly divided into two groups, the training group and the testing group, to establish new eGFR-formulas based on serum CysC and to validate the established formulas, respectively. (99mTc-DTPA clearance (as the rGFR, serum Cr, and serum CysC were determined for all patients, and GFR was calculated using the Cockcroft-Gault equation (eGFR1, the MDRD formula (eGFR2, the CKD-EPI formulas (eGFR3, eGFR4, and the Chinese eGFR Investigation Collaboration formulas (eGFR5, eGFR6. The accuracy of each eGFR was compared with the rGFR. RESULTS: The training and testing groups' mean GFRs were 50.84±31.36 mL/min/1.73 m(2 and 54.16±29.45 mL/min/1.73 m(2, respectively. The two newly developed eGFR formulas were fitted using iterative computation: [Formula: see text] and [Formula: see text]. Significant correlation was observed between each eGFR and the rGFR. However, proportional errors and constant errors were observed between rGFR and eGFR1, eGFR2, eGFR4, eGFR5 or eGFR6, and constant errors were observed between eGFR3 and rGFR, as revealed by the Passing & Bablok plot analysis. The Bland-Altman analysis illustrated that the 95% limits of agreement of all equations exceeded the previously accepted limits of <60 mL/min •1.73 m(2, except the equations of eGFR7 and eGFR8. CONCLUSION: The newly developed formulas, eGFR7 and eGFR8, provide precise and accurate GFR estimation using serum CysC detection alone or in combination with serum Cr detection. Differences in detection methods should be carefully considered when choosing literature eGFR equations to avoid misdiagnosis and
International Nuclear Information System (INIS)
Zeng, Hongtao; Lan, Tian; Chen, Qiming
2016-01-01
Two lifetime distributions derived from Perks' mortality rate function, one with 4 parameters and the other with 5 parameters, for the modeling of bathtub-shaped failure rates are proposed in this paper. The Perks' mortality/failure rate functions have historically been used for human life modeling in life insurance industry. Although this distribution is no longer used in insurance industry, considering many nice and some unique features of this function, it is necessary to revisit it and introduce it to the reliability community. The parameters of the distributions can control the scale, shape, and location of the PDF. The 4-parameter distribution can be used to model the bathtub failure rate. This model is applied to three previously published groups of lifetime data. This study shows they fit very well. The 5-parameter version can potentially model constant hazard rates of the later life of some devices in addition to the good features of 4-parameter version. Both the 4 and 5-parameter versions have closed form PDF and CDF. The truncated distributions of both versions stay within the original distribution family with simple parameter transformation. This nice feature is normally considered to be only possessed by the simple exponential distribution - Highlights: • Two new distributions are proposed to model bathtub shaped hazard rate. • Derive the close-form PDF, CDF and feature of scalability and truncatability. • Perks4 is verified to be good to model common bathtub shapes through comparison. • Perks5 has the potential to model the stabilization of hazard rate at later life.
International Nuclear Information System (INIS)
Bojtsov, V.V.; Tsepin, M.A.; Karpilyanskij, N.N.; Ershov, A.N.
1982-01-01
Results of statistical analysis of the description accuracy of superplasticity S-form curve by different analytic expressions, suggested on the basis of phenomenological and metallophysical concepts about the nature of superplastic deformation, are given. Experimental investigations into the dependence of flow stresses on the deformation rate were conducted on VT3-1 two-phase titanium alloy. Test samples were cut out of a rod, 30 mm in diameter, produced by lengthwise rolling in α+#betta#-region. Optimal temperature of superplasticity manifestation was determined by the method of stress relaxation from a relaxation time value to a given stress. It was established that the Smirnov phemonemological equation describes in the best way the rate dependence of flow stress of superplastic material. This equation can be used for solution of problems of studying mechanism, physical nature of superplastic deformation, analysing strain-stress state and the structure of deformation zone during the processes of pressure shaping of superplastic materials, when considerably wide range (in the limits of 7-8 orders) of deformation rate variation takes place
Xu, Meng; Yan, Yaming; Liu, Yanying; Shi, Qiang
2018-04-01
The Nakajima-Zwanzig generalized master equation provides a formally exact framework to simulate quantum dynamics in condensed phases. Yet, the exact memory kernel is hard to obtain and calculations based on perturbative expansions are often employed. By using the spin-boson model as an example, we assess the convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation. The exact memory kernels are calculated by combining the hierarchical equation of motion approach and the Dyson expansion of the exact memory kernel. High order expansions of the memory kernels are obtained by extending our previous work to calculate perturbative expansions of open system quantum dynamics [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. It is found that the high order expansions do not necessarily converge in certain parameter regimes where the exact kernel show a long memory time, especially in cases of slow bath, weak system-bath coupling, and low temperature. Effectiveness of the Padé and Landau-Zener resummation approaches is tested, and the convergence of higher order rate constants beyond Fermi's golden rule is investigated.
Gottlieb, M H; Sollner, K
1968-05-01
The electrical resistances and rates of self-exchange of univalent critical ions across several types of collodion matrix membranes of high ionic selectivity were studied over a wide range of conditions. The relationship which was observed between these quantities with membranes of a certain type, namely those activated with poly-2-vinyl-N-methyl pyridinium bromide, cannot be explained on the basis of current concepts of the movement of ions across ion exchange membranes. Rates of self-exchange across these membranes were several times greater than those calculated from the electrical resistances of the membranes on the basis of an expression derived by the use of the Nernst-Einstein equation. The magnitude of the discrepancy was greatest at low concentrations of the ambient electrolyte solution and was independent of the species of both critical and noncritical ions. The data obtained with other types of collodion matrix membranes were, at least approximately, in agreement with the predictions based on the Nernst-Einstein equation. Self-exchange rates across the anion permeable protamine collodion membranes, and across the cation permeable polystyrene sulfonic acid collodion membranes, were about 20% less than those calculated from the electrical resistances. The direction and magnitude of these differences, also observed by other investigators, are qualitatively understood as an electroosmotic effect. With cation permeable membranes prepared by the oxidation of preformed collodion membranes, almost exact agreement was obtained between measured and calculated self-exchange rates; the cause of the apparent absence of an electroosmotic effect with these membranes is unknown.
Osipov, Vladimir Al.; Pullerits, Tõnu
2017-10-01
Application of the phase-modulated pulsed light for advance spectroscopic measurements is the area of growing interest. The phase modulation of the light causes modulation of the signal. Separation of the spectral components of the modulations allows to distinguish the contributions of various interaction pathways. The lasers with high repetition rate used in such experiments can lead to appearance of the accumulation effects, which become especially pronounced in systems with long-living excited states. Recently it was shown that such accumulation effects can be used to evaluate parameters of the dynamical processes in the material. In this work we demonstrate that the accumulation effects are also important in the quantum characteristics measurements provided by modulation spectroscopy. In particular, we consider a model of quantum two-level system driven by a train of phase-modulated light pulses, organized in analogy with the two-dimensional spectroscopy experiments. We evaluate the harmonics' amplitudes in the fluorescent signal and calculate corrections appearing from the accumulation effects. We show that the corrections can be significant and have to be taken into account at analysis of experimental data.
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Watanabe, Nami; Sugai Yukio; Komatani, Akio; Yamaguchi, Koichi; Takahashi, Kazuei
1999-01-01
This study was designed to investigate the empirical tubular extraction rate (TER) of the normal renal function in childhood and then propose a new equation to obtain TER theoretically. The empirical TER was calculated using Russell's method for determination of single-sample plasma clearance and 99m Tc-MAG 3 in 40 patients with renal disease younger than 10 years of age who were classified as having normal renal function using diagnostic criteria defined by the Paediatric Task Group of EANM. First, we investigated the relationships of the empirical value of absolute TER to age, body weight, body surface area (BSA) and distribution volume. Next we investigated the relationships of the empirical value of BSA corrected TER to age, body weight, BSA and distribution volume. Linear relationship was indicated between the absolute TER and each body dimensional factors, especially regarding to BSA, its correlation coefficient was 0.90 (p value). The BSA-corrected TER showed a logarithmic relationship with BSA, but linear regression did not show any significant correlation. Therefore, it was thought that the normal value of TER could be calculated theoretically using the body surface area, and here we proposed the following linear regression equation; Theoretical TER (ml/min/1.73 m 2 )=(-39.8+257.2 x BSA)/BSA/1.73. The theoretical TER could be one of the reference values of the renal function in the period of the renal maturation. (author)
Blitz, M A; Green, N J B; Shannon, R J; Pilling, M J; Seakins, P W; Western, C M; Robertson, S H
2015-07-16
Rate coefficients for the CH3 + CH3 reaction, over the temperature range 300-900 K, have been corrected for errors in the absorption coefficients used in the original publication ( Slagle et al., J. Phys. Chem. 1988 , 92 , 2455 - 2462 ). These corrections necessitated the development of a detailed model of the B̃(2)A1' (3s)-X̃(2)A2″ transition in CH3 and its validation against both low temperature and high temperature experimental absorption cross sections. A master equation (ME) model was developed, using a local linearization of the second-order decay, which allows the use of standard matrix diagonalization methods for the determination of the rate coefficients for CH3 + CH3. The ME model utilized inverse Laplace transformation to link the microcanonical rate constants for dissociation of C2H6 to the limiting high pressure rate coefficient for association, k∞(T); it was used to fit the experimental rate coefficients using the Levenberg-Marquardt algorithm to minimize χ(2) calculated from the differences between experimental and calculated rate coefficients. Parameters for both k∞(T) and for energy transfer ⟨ΔE⟩down(T) were varied and optimized in the fitting procedure. A wide range of experimental data were fitted, covering the temperature range 300-2000 K. A high pressure limit of k∞(T) = 5.76 × 10(-11)(T/298 K)(-0.34) cm(3) molecule(-1) s(-1) was obtained, which agrees well with the best available theoretical expression.
Lee, Pyoung Jik; Lee, Byung Kwon; Jeon, Jin Yong; Zhang, Mei; Kang, Jian
2016-01-01
This study uses a structural equation model to examine the effects of noise on self-rated job satisfaction and health in open-plan offices. A total of 334 employees from six open-plan offices in China and Korea completed a questionnaire survey. The questionnaire included questions assessing noise disturbances and speech privacy, as well as job satisfaction and health. The results indicated that noise disturbance affected self-rated health. Contrary to popular expectation, the relationship between noise disturbance and job satisfaction was not significant. Rather, job satisfaction and satisfaction with the environment were negatively correlated with lack of speech privacy. Speech privacy was found to be affected by noise sensitivity, and longer noise exposure led to decreased job satisfaction. There was also evidence that speech privacy was a stronger predictor of satisfaction with environment and job satisfaction for participants with high noise sensitivity. In addition, fit models for employees from China and Korea showed slight differences. This study is motivated by strong evidence that noise is the key source of complaints in open-plan offices. Survey results indicate that self-rated job satisfaction of workers in open-plan offices was negatively affected by lack of speech privacy and duration of disturbing noise.
International Nuclear Information System (INIS)
Divine, J.R.; Bowen, W.M.; Mackey, D.B.; Bates, D.J.; Pool, K.H.
1985-06-01
Even though the interest in the corrosion of radwaste tanks goes back to the mid-1940's when waste storage was begun, and a fair amount of corrosion work has been done since then, the changes in processes and waste types have outpaced the development of new data pertinent to the new double shell tanks. As a consequence, Pacific Northwest Laboratory (PNL) began a development of corrosion data on a broad base of waste compositions in 1980. The objective of the program was to provide operations personnel with corrosion rate data as a function of waste temperature and composition. The work performed in this program examined A-537 tank steel in Double Shell Slurry and Future PUREX Wastes, at temperatures between 40 and 180 0 C as well as in Hanford Facilities Waste at 25 and 50 0 C. In general, the corrosion rates were less than 1 mpy (0.001 in./y) and usually less than 0.5 mpy. Excessive corrosion rates (>1 mpy) were only found in dilute waste compositions or in concentrated caustic compositions at temperatures above 140 0 C. Stress corrosion cracking was only observed under similar conditions. The results are presented as polynomial prediction equations with examples of the output of existing computer codes. The codes are not provided in the text but are available from the authors. 12 refs., 5 figs., 19 tabs
Weil, Joyce; Hutchinson, Susan R; Traxler, Karen
2014-11-01
Data from the Women's Health and Aging Study were used to test a model of factors explaining depressive symptomology. The primary purpose of the study was to explore the association between performance-based measures of functional ability and depression and to examine the role of self-rated physical difficulties and perceived instrumental support in mediating the relationship between performance-based functioning and depression. The inclusion of performance-based measures allows for the testing of functional ability as a clinical precursor to disability and depression: a critical, but rarely examined, association in the disablement process. Structural equation modeling supported the overall fit of the model and found an indirect relationship between performance-based functioning and depression, with perceived physical difficulties serving as a significant mediator. Our results highlight the complementary nature of performance-based and self-rated measures and the importance of including perception of self-rated physical difficulties when examining depression in older persons. © The Author(s) 2014.
2013-01-01
Introduction Estimation of kidney function in critically ill patients with acute kidney injury (AKI), is important for appropriate dosing of drugs and adjustment of therapeutic strategies, but challenging due to fluctuations in kidney function, creatinine metabolism and fluid balance. Data on the agreement between estimating and gold standard methods to assess glomerular filtration rate (GFR) in early AKI are lacking. We evaluated the agreement of urinary creatinine clearance (CrCl) and three commonly used estimating equations, the Cockcroft Gault (CG), the Modification of Diet in Renal Disease (MDRD) and the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations, in comparison to GFR measured by the infusion clearance of chromium-ethylenediaminetetraacetic acid (51Cr-EDTA), in critically ill patients with early AKI after complicated cardiac surgery. Methods Thirty patients with early AKI were studied in the intensive care unit, 2 to 12 days after complicated cardiac surgery. The infusion clearance for 51Cr-EDTA obtained as a measure of GFR (GFR51Cr-EDTA) was calculated from the formula: GFR (mL/min/1.73m2) = (51Cr-EDTA infusion rate × 1.73)/(arterial 51Cr-EDTA × body surface area) and compared with the urinary CrCl and the estimated GFR (eGFR) from the three estimating equations. Urine was collected in two 30-minute periods to measure urine flow and urine creatinine. Urinary CrCl was calculated from the formula: CrCl (mL/min/1.73m2) = (urine volume × urine creatinine × 1.73)/(serum creatinine × 30 min × body surface area). Results The within-group error was lower for GFR51Cr-EDTA than the urinary CrCl method, 7.2% versus 55.0%. The between-method bias was 2.6, 11.6, 11.1 and 7.39 ml/min for eGFRCrCl, eGFRMDRD, eGFRCKD-EPI and eGFRCG, respectively, when compared to GFR51Cr-EDTA. The error was 103%, 68.7%, 67.7% and 68.0% for eGFRCrCl, eGFRMDRD, eGFRCKD-EPI and eGFRCG, respectively, when compared to GFR51Cr-EDTA. Conclusions The study
Lu, Benzhuo; Zhou, Y.C.
2011-01-01
The effects of finite particle size on electrostatics, density profiles, and diffusion have been a long existing topic in the study of ionic solution. The previous size-modified Poisson-Boltzmann and Poisson-Nernst-Planck models are revisited in this article. In contrast to many previous works that can only treat particle species with a single uniform size or two sizes, we generalize the Borukhov model to obtain a size-modified Poisson-Nernst-Planck (SMPNP) model that is able to treat nonuniform particle sizes. The numerical tractability of the model is demonstrated as well. The main contributions of this study are as follows. 1), We show that an (arbitrarily) size-modified PB model is indeed implied by the SMPNP equations under certain boundary/interface conditions, and can be reproduced through numerical solutions of the SMPNP. 2), The size effects in the SMPNP effectively reduce the densities of highly concentrated counterions around the biomolecule. 3), The SMPNP is applied to the diffusion-reaction process for the first time, to our knowledge. In the case of low substrate density near the enzyme reactive site, it is observed that the rate coefficients predicted by SMPNP model are considerably larger than those by the PNP model, suggesting both ions and substrates are subject to finite size effects. 4), An accurate finite element method and a convergent Gummel iteration are developed for the numerical solution of the completely coupled nonlinear system of SMPNP equations. PMID:21575582
Directory of Open Access Journals (Sweden)
Yang Ho Kang
2016-09-01
Full Text Available BackgroundIt is known that metabolic syndrome (MetS is associated with chronic kidney disease. We evaluated and compared the prevalence of reduced kidney function in MetS and its components by estimated glomerular filtration rate (eGFR using an equation based on creatinine (eGFRcr, cystatin C (eGFRcys, and combined creatinine-cystatin C (eGFRcr-cys in Korean adults.MethodsWe analyzed data from 3,649 adults who participated in a comprehensive health examination.ResultsMean values of eGFRcys were higher compared with mean values of eGFRcr (96.1±18.2 mL/min/1.73 m2 vs. 91.2±13.6 mL/min/1.73 m2 in total subjects. The prevalence of reduced kidney function increased with age (9.6% for eGFRcys vs. 5.8% for eGFRcr-cys vs. 4.9% for eGFRcr, in subjects aged ≥60 years, and significantly increased with MetS, abdominal obesity, hypertension, high triglyceride, low high density lipoprotein (HDL, and high insulin resistance. The prevalence of MetS, abdominal obesity, hypertension, high insulin resistance, low HDL, and hepatic steatosis was significantly increased in subjects with reduced kidney function. This increased prevalence and the odds ratio of reduced kidney function for prevalence of MetS was highest for eGFRcys, followed by those of eGFRcr-cys, and eGFRcr.ConclusionThe prevalence of reduced kidney function by eGFR was significantly increased in subjects with MetS and its related components. eGFRcys and eGFRcr-cys were superior to eGFRcr in detecting reduced kidney function.
Directory of Open Access Journals (Sweden)
Fernando Bustos-Guadaño
2017-03-01
Conclusions: The GFR estimations obtained with BS1 equation are not interchangeable with MDRD-IDMS or CKD-EPI equations. BIS1 estimates lower GFR values than MDRD-IDMS and CKD-EPI and tends to classify the patients in a more advanced chronic kidney disease stage, especially for estimated GFR higher than 29 mL/min/1.73 m2.
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
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
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.
Leion, Felicia; Hegbrant, Josefine; den Bakker, Emil; Jonsson, Magnus; Abrahamson, Magnus; Nyman, Ulf; Björk, Jonas; Lindström, Veronica; Larsson, Anders; Bökenkamp, Arend; Grubb, Anders
2017-09-01
Estimating glomerular filtration rate (GFR) in adults by using the average of values obtained by a cystatin C- (eGFR cystatin C ) and a creatinine-based (eGFR creatinine ) equation shows at least the same diagnostic performance as GFR estimates obtained by equations using only one of these analytes or by complex equations using both analytes. Comparison of eGFR cystatin C and eGFR creatinine plays a pivotal role in the diagnosis of Shrunken Pore Syndrome, where low eGFR cystatin C compared to eGFR creatinine has been associated with higher mortality in adults. The present study was undertaken to elucidate if this concept can also be applied in children. Using iohexol and inulin clearance as gold standard in 702 children, we studied the diagnostic performance of 10 creatinine-based, 5 cystatin C-based and 3 combined cystatin C-creatinine eGFR equations and compared them to the result of the average of 9 pairs of a eGFR cystatin C and a eGFR creatinine estimate. While creatinine-based GFR estimations are unsuitable in children unless calibrated in a pediatric or mixed pediatric-adult population, cystatin C-based estimations in general performed well in children. The average of a suitable creatinine-based and a cystatin C-based equation generally displayed a better diagnostic performance than estimates obtained by equations using only one of these analytes or by complex equations using both analytes. Comparing eGFR cystatin and eGFR creatinine may help identify pediatric patients with Shrunken Pore Syndrome.
Czech Academy of Sciences Publication Activity Database
Roubíček, Tomáš
2014-01-01
Roč. 199, č. 1 (2014), s. 286-295 ISSN 0956-540X R&D Projects: GA ČR GAP201/10/0357 Institutional support: RVO:61388998 Keywords : non-linear differential equations * heat flow * plasticity Subject RIV: DC - Siesmology, Volcanology, Earth Structure Impact factor: 2.724, year: 2013 http://gji.oxfordjournals.org/content/199/1/286.full.pdf?keytype=ref&ijkey=Bxq4QAJg1lMyhdk
Computing generalized Langevin equations and generalized Fokker-Planck equations.
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.
International Nuclear Information System (INIS)
Frank, T.D.
2011-01-01
We study the stability of solutions of a particular type of multistable selection equations proposed by Starke, Schanz and Haken in the case of an inhomogeneous spectrum of growth parameters. We determine how the stability of feasible solutions depends on the inhomogeneity of the spectrum. We show that the strength of the competitive interaction between feasible solutions can act as a control parameter that induces bifurcations reducing the degree of multistability. - Research highlights: → Feasible solutions can be stable in the case of inhomogeneous growth parameters. → Changing coupling strength can induce bifurcations of feasible solutions. → Optimal solutions are obtained when selected winnings are relatively large.
Indian Academy of Sciences (India)
regarding nature of forces hold equally for liquids, even though the ... particle. Figure A. A fluid particle is a very small imaginary blob of fluid, here shown sche- matically in .... picture gives important information about the flow field. ... Bernoulli's equation is derived assuming ideal flow, .... weight acting in the flow direction S is.
International Nuclear Information System (INIS)
Gross, F.
1986-01-01
Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs
First-order partial differential equations
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
DEFF Research Database (Denmark)
Mocroft, A; Nielsen, Lene Ryom; Reiss, P
2014-01-01
The aim of this study was to determine whether the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI)- or Cockcroft-Gault (CG)-based estimated glomerular filtration rates (eGFRs) performs better in the cohort setting for predicting moderate/advanced chronic kidney disease (CKD) or end...
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
Tveito, Aslak; Lines, Glenn T; Edwards, Andrew G; McCulloch, Andrew
2016-07-01
Markov models are ubiquitously used to represent the function of single ion channels. However, solving the inverse problem to construct a Markov model of single channel dynamics from bilayer or patch-clamp recordings remains challenging, particularly for channels involving complex gating processes. Methods for solving the inverse problem are generally based on data from voltage clamp measurements. Here, we describe an alternative approach to this problem based on measurements of voltage traces. The voltage traces define probability density functions of the functional states of an ion channel. These probability density functions can also be computed by solving a deterministic system of partial differential equations. The inversion is based on tuning the rates of the Markov models used in the deterministic system of partial differential equations such that the solution mimics the properties of the probability density function gathered from (pseudo) experimental data as well as possible. The optimization is done by defining a cost function to measure the difference between the deterministic solution and the solution based on experimental data. By evoking the properties of this function, it is possible to infer whether the rates of the Markov model are identifiable by our method. We present applications to Markov model well-known from the literature. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.
Directory of Open Access Journals (Sweden)
Paula Guedes Cocate
2009-10-01
Full Text Available A taxa metabólica de repouso (TMR pode ser determinada por calorimetria indireta (CI. Porém, em função da praticidade, na prática clínica na maioria das vezes esta é estimada por equações de predição, as quais foram desenvolvidas em estudos envolvendo indivíduos não atletas. Apesar de alguns autores terem indicado que tais equações não estimam adequadamente a TMR, estas têm sido bastante utilizadas para calculá-la e prescrever dietas, inclusive para atletas. O objetivo deste estudo foi comparar a TMR determinada por CI com a estimada pelas equações de Harris & Benedict (HB, Schofield, FAO/WHO/UNU e Henry & Rees (HR, em 15 homens ciclistas, de 24,4 ± 3,68 anos, apresentando índice de massa corporal de 21,97 ± 1,46kg/m² e VO2máx de 70,00 ± 5,32mL(kg.min-1. Para comparar a TMR determinada por CI e pelas equações, utilizou-se o tratamento estatístico testes t de Student (variáveis com distribuição normal e de Mann-Whitney (variáveis sem distribuição normal, considerando p The resting metabolic rate (RMR can be determined by indirect calorimetry (IC. However, the clinical estimation of this parameter has been done using mathematical equations, which were developed in studies involving non-athletes. Although some authors have indicated that such equations do not estimate correctly the RMR, they have been constantly used to estimate such parameter and to prescribe diets, including for athletes. The objective of this study was to compare the RMR determined by IC with the ones estimated using the equations proposed by Harris & Benedict (HB, Schofield, FAO/WHO/UNU and Henry & Rees (HR, in 15 male cyclists, aged 24.4±3.68 years, body mass index of 21.97±1.46 kg/m² and VO2max of 70.00±5.32 mL(kg.min-1. Student's t test (when data presented normal distribution and Mann-Whitney (when data did not present normal distribution were used to compare the RMR determined by IC and the ones estimated by the equations. Probability
Partial Differential Equations
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.
Equating error in observed-score equating
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
Directory of Open Access Journals (Sweden)
Tae-Dong Jeong
2013-10-01
Full Text Available Background: We compared the accuracy of the Modification of Diet in Renal Disease (MDRD study and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI equations in Korean patients and evaluated the difference in CKD prevalence determined using the two equations in the Korean general population. Methods: The accuracy of the two equations was evaluated in 607 patients who underwent a chromium-51-ethylenediaminetetraacetic acid GFR measurement. Additionally, we compared the difference in CKD prevalence determined by the two equations among 5,822 participants in the fifth Korea National Health and Nutrition Examination Survey, 2010. Results: Among the 607 subjects, the median bias of the CKD-EPI equation was significantly lower than that of the MDRD study equation (0.9 vs. 2.2, p=0.020. The accuracy of the two equations was not significantly different in patients with mGFR 2; however, the accuracy of the CKD-EPI equation was significantly higher than that of the MDRD study equation in patients with GFR ≥60 mL/min/1.73m2. The prevalences of the CKD stages 1, 2 and 3 in the Korean general population were 47.56, 49.23, and 3.07%, respectively, for the MDRD study equation; and were 68.48, 28.89, and 2.49%, respectively, for the CKD-EPI equation. Conclusions: These data suggest that the CKD-EPI equation might be more useful in clinical practice than the MDRD study equation in Koreans.
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
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)
Handbook of integral equations
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.
Miyake, Y.; Noda, H.
2017-12-01
Earthquake sequences involve many processes in a wide range of time scales, from quasistatic loading to dynamic rupture. At a depth of brittle-plastic transitional and deeper, rock behaves as a viscous fluid in a long timescale, but as an elastic material in a short timescale. Viscoelastic stress relaxation may be important in the interseismic periods at the depth, near the deeper limit of the seismogenic layer or the region of slow slip events (SSEs) [Namiki et al., 2014 and references therein]. In the present study, we implemented the viscoelastic effect (Maxwell material) in fully-dynamic earthquake sequence simulations using a spectral boundary integral equation method (SBIEM) [e.g., Lapusta et al., 2000]. SBIEM is efficient in calculation of convolutional terms for dynamic stress transfer, and the problem size is limited by the amount of memory available. Linear viscoelasticity could be implemented by convolution of slip rate history and Green's function, but this method requires additional memory and thus not suitable for the implementation to the present code. Instead, we integrated the evolution of "effective slip" distribution, which gives static stress distribution when convolved with static elastic Green's function. This method works only for simple viscoelastic property distributions, but such models are suitable for numerical experiments aiming basic understanding of the system behavior because of the virtue of SBIEM, the ability of fine on-fault spatial resolution and efficient computation utilizing the fast Fourier transformation. In the present study, we examined the effect of viscoelasticity on earthquake sequences of a fault with a rate-weakening patch. A series of simulations with various relaxation time tc revealed that as decreasing tc, recurrence intervals of earthquakes increases and seismicity ultimately disappears. As long as studied, this transition to aseismic behavior is NOT associated with SSEs. In a case where the rate-weakening patch
On the Saha Ionization Equation
Indian Academy of Sciences (India)
the equation in terms of rate theory. ... that the said theory is said to be the harbinger of modern astro- ... Parichay (An Introduction to the Universe). Tagore ..... where |e| is the magnitude of the electron's charge and E is the electric field intensity ...
Sinc-collocation method for solving the Blasius equation
International Nuclear Information System (INIS)
Parand, K.; Dehghan, Mehdi; Pirkhedri, A.
2009-01-01
Sinc-collocation method is applied for solving Blasius equation which comes from boundary layer equations. It is well known that sinc procedure converges to the solution at an exponential rate. Comparison with Howarth and Asaithambi's numerical solutions reveals that the proposed method is of high accuracy and reduces the solution of Blasius' equation to the solution of a system of algebraic equations.
Introduction to differential equations
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
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
Diffusion phenomenon for linear dissipative wave equations
Said-Houari, Belkacem
2012-01-01
In this paper we prove the diffusion phenomenon for the linear wave equation. To derive the diffusion phenomenon, a new method is used. In fact, for initial data in some weighted spaces, we prove that for {equation presented} decays with the rate {equation presented} [0,1] faster than that of either u or v, where u is the solution of the linear wave equation with initial data {equation presented} [0,1], and v is the solution of the related heat equation with initial data v 0 = u 0 + u 1. This result improves the result in H. Yang and A. Milani [Bull. Sci. Math. 124 (2000), 415-433] in the sense that, under the above restriction on the initial data, the decay rate given in that paper can be improved by t -γ/2. © European Mathematical Society.
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
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
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
Ordinary differential equations
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
Beginning partial differential equations
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
Coopersmith, Michael; Gambardella, Pascal J.
2016-01-01
This article is an extension of the work of one of us (Coopersmith, 2011) in deriving the relationship between certain interest rates and the inflation rate of a two component economic system. We use the well-known Fisher relation between the difference of the nominal interest rate and its inflation adjusted value to eliminate the inflation rate and obtain a delay differential equation. We provide computer simulated solutions for this equation over regimes of interest. This paper could be of ...
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)
Singular stochastic differential equations
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.
Stochastic differential equation model to Prendiville processes
Energy Technology Data Exchange (ETDEWEB)
Granita, E-mail: granitafc@gmail.com [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); Bahar, Arifah [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); UTM Center for Industrial & Applied Mathematics (UTM-CIAM) (Malaysia)
2015-10-22
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.
Stochastic differential equation model to Prendiville processes
International Nuclear Information System (INIS)
Granita; Bahar, Arifah
2015-01-01
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution
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)
Nonadiabatic quantum Vlasov equation for Schwinger pair production
International Nuclear Information System (INIS)
Kim, Sang Pyo; Schubert, Christian
2011-01-01
Using Lewis-Riesenfeld theory, we derive an exact nonadiabatic master equation describing the time evolution of the QED Schwinger pair-production rate for a general time-varying electric field. This equation can be written equivalently as a first-order matrix equation, as a Vlasov-type integral equation, or as a third-order differential equation. In the last version it relates to the Korteweg-de Vries equation, which allows us to construct an exact solution using the well-known one-soliton solution to that equation. The case of timelike delta function pulse fields is also briefly considered.
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
Functional equations with causal operators
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.
Partial differential equations
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...
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.
Differential equations for dummies
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.
Degenerate nonlinear diffusion equations
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...
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.
Solving Ordinary Differential Equations
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.
Reactimeter dispersion equation
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...
Differential equations I essentials
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.
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.)
State-dependent neutral delay equations from population dynamics.
Barbarossa, M V; Hadeler, K P; Kuttler, C
2014-10-01
A novel class of state-dependent delay equations is derived from the balance laws of age-structured population dynamics, assuming that birth rates and death rates, as functions of age, are piece-wise constant and that the length of the juvenile phase depends on the total adult population size. The resulting class of equations includes also neutral delay equations. All these equations are very different from the standard delay equations with state-dependent delay since the balance laws require non-linear correction factors. These equations can be written as systems for two variables consisting of an ordinary differential equation (ODE) and a generalized shift, a form suitable for numerical calculations. It is shown that the neutral equation (and the corresponding ODE--shift system) is a limiting case of a system of two standard delay equations.
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
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
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.
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
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
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 ...
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
The generalized Fermat equation
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
Applied partial differential equations
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...
Mélykúti, Bence; Burrage, Kevin; Zygalakis, Konstantinos C.
2010-01-01
The Chemical Langevin Equation (CLE), which is a stochastic differential equation driven by a multidimensional Wiener process, acts as a bridge between the discrete stochastic simulation algorithm and the deterministic reaction rate equation when
Nonlocal higher order evolution equations
Rossi, Julio D.
2010-06-01
In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the solution of the higher order problem with the right-hand side given by powers of the Laplacian when the kernel J is rescaled in an appropriate way. Moreover, we prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. © 2010 Taylor & Francis.
Hyperbolic partial differential equations
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
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
Differential equations problem solver
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
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
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
Beginning partial differential equations
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
Ordinary differential equations
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
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.
Multiplicity Control in Structural Equation Modeling
Cribbie, Robert A.
2007-01-01
Researchers conducting structural equation modeling analyses rarely, if ever, control for the inflated probability of Type I errors when evaluating the statistical significance of multiple parameters in a model. In this study, the Type I error control, power and true model rates of famsilywise and false discovery rate controlling procedures were…
Applied partial differential equations
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...
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.
Tsintsadze, Nodar L.; Tsintsadze, Levan N.
2008-01-01
A general derivation of the charging equation of a dust grain is presented, and indicated where and when it can be used. A problem of linear fluctuations of charges on the surface of the dust grain is discussed.
Equations For Rotary Transformers
Salomon, Phil M.; Wiktor, Peter J.; Marchetto, Carl A.
1988-01-01
Equations derived for input impedance, input power, and ratio of secondary current to primary current of rotary transformer. Used for quick analysis of transformer designs. Circuit model commonly used in textbooks on theory of ac circuits.
Problems in differential equations
Brenner, J L
2013-01-01
More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.
Applied partial differential equations
DuChateau, Paul
2012-01-01
Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.
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
Saaty, Thomas L
1981-01-01
Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.
Money market rates and implied CCAPM rates: some international evidence
Yamin Ahmad
2004-01-01
New Neoclassical Synthesis models equate the instrument of monetary policy to the implied CCAPM rate arising from an Euler equation. This paper identifies monetary policy shocks within six of the G7 countries and examines the movement of money market and implied CCAPM rates. The key result is that an increase in the nominal interest rate leads to a fall in the implied CCAPM rate. Incorporating habit still yields the same result. The findings suggest that the movement of these two rates implie...
Fokker-Planck equation in mirror research
International Nuclear Information System (INIS)
Post, R.F.
1983-01-01
Open confinement systems based on the magnetic mirror principle depend on the maintenance of particle distributions that may deviate substantially from Maxwellian distributions. Mirror research has therefore from the beginning relied on theoretical predictions of non-equilibrium rate processes obtained from solutions to the Fokker-Planck equation. The F-P equation plays three roles: Design of experiments, creation of classical standards against which to compare experiment, and predictions concerning mirror based fusion power systems. Analytical and computational approaches to solving the F-P equation for mirror systems will be reviewed, together with results and examples that apply to specific mirror systems, such as the tandem mirror
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
SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER
Collier, D.M.; Meeks, L.A.; Palmer, J.P.
1960-05-10
A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.
Structural Equations and Causation
Hall, Ned
2007-01-01
Structural equations have become increasingly popular in recent years as tools for understanding causation. But standard structural equations approaches to causation face deep problems. The most philosophically interesting of these consists in their failure to incorporate a distinction between default states of an object or system, and deviations therefrom. Exploring this problem, and how to fix it, helps to illuminate the central role this distinction plays in our causal thinking.
Rules of thumb and useful equations
International Nuclear Information System (INIS)
Anon.
1992-01-01
Useful ''rules of thumb'' for dose rates, exposure, and penetration from alpha and beta emitters, fallout, neutrons, and gamma and x rays introduce some of the practical aspects of health physics in this chapter. The mathematical relationships important in determining radioactivity and radiation exposure are presented through a series of equations. Also included in this chapter are commonly employed equations expressing logarithmic, and wave and quantum relationships, as well as those used in classical physics and electrostatics
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
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.
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)
Differential Equation over Banach Algebra
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.
Deriving the bond pricing equation
Directory of Open Access Journals (Sweden)
Kožul Nataša
2014-01-01
Full Text Available Given the recent focus on Eurozone debt crisis and the credit rating downgrade not only of US debt, but that of other countries and many UK major banking institutions, this paper aims to explain the concept of bond yield, its different measures and bond pricing equation. Yields on capital market instruments are rarely quoted on the same basis, which makes direct comparison between different as investment choices impossible. Some debt instruments are quoted on discount basis, whilst coupon-bearing ones accrue interest differently, offer different compounding opportunities, have different coupon payment frequencies, and manage non-business day maturity dates differently. Moreover, rules governing debt vary across countries, markets and currencies, making yield calculation and comparison a rather complex issue. Thus, some fundamental concepts applicable to debt instrument yield measurement, with focus on bond equation, are presented here. In addition, bond equation expressed in annuity form and used to apply Newton-Raphson algorithm to derive true bond yield is also shown.
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
Introduction to partial differential equations
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.
Quadratic Diophantine equations
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.
Stochastic porous media equations
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.
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...
Equations of mathematical physics
Tikhonov, A N
2011-01-01
Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri
Iteration of adjoint equations
International Nuclear Information System (INIS)
Lewins, J.D.
1994-01-01
Adjoint functions are the basis of variational methods and now widely used for perturbation theory and its extension to higher order theory as used, for example, in modelling fuel burnup and optimization. In such models, the adjoint equation is to be solved in a critical system with an adjoint source distribution that is not zero but has special properties related to ratios of interest in critical systems. Consequently the methods of solving equations by iteration and accumulation are reviewed to show how conventional methods may be utilized in these circumstances with adequate accuracy. (author). 3 refs., 6 figs., 3 tabs
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....
Partial differential equations
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
Generalized estimating equations
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
Li, Tatsien
2017-01-01
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Differential Equations Models to Study Quorum Sensing.
Pérez-Velázquez, Judith; Hense, Burkhard A
2018-01-01
Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. ODE models allow describing changes in one independent variable, for example, time. PDE models can be used to follow changes in more than one independent variable, for example, time and space. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.
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
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…
Test equating methods and practices
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...
Electron transfer dynamics: Zusman equation versus exact theory
International Nuclear Information System (INIS)
Shi Qiang; Chen Liping; Nan Guangjun; Xu Ruixue; Yan Yijing
2009-01-01
The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature approximation of the hierarchical theory is equivalent to the Zusman equation in describing electron transfer dynamics. Thus the exact hierarchical formalism naturally extends the Zusman equation to include quantum nuclear dynamics at low temperatures. This new finding has also inspired us to rescale the original hierarchical equations and incorporate a filtering algorithm to efficiently propagate the hierarchical equations. Numerical exact results are also presented for the electron transfer reaction dynamics and rate constant calculations.
Hypocoercivity for linear kinetic equations conserving mass
Dolbeault, Jean; Mouhot, Clé ment; Schmeiser, Christian
2015-01-01
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf
Hypocoercivity for linear kinetic equations conserving mass
Dolbeault, Jean
2015-02-03
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf
Modelling conjugation with stochastic differential equations
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik
2010-01-01
Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared......Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two...... using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared...
Indian Academy of Sciences (India)
The Raychaudhuri equation is central to the understanding of gravitational attraction in ... of K Gödel on the ideas of shear and vorticity in cosmology (he defines the shear. (eq. (8) in [1]) .... which follows from the definition of the scale factor l.
Generalized reduced magnetohydrodynamic equations
International Nuclear Information System (INIS)
Kruger, S.E.
1999-01-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics
Calculus & ordinary differential equations
Pearson, David
1995-01-01
Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.
Indian Academy of Sciences (India)
research, teaching and practice related to the analysis and design ... its variants, are present in a large number of ma- chines used in daily ... with advanced electronics, sensors, control systems and computing ... ted perfectly well with the rapidly developing comput- .... velopment of the Freudenstein equation using Figure 3.
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
ABSTRACT. Analysis of underground circular cylindrical shell is carried out in this work. The forth order differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the assumptions of P. L Pasternak. Laplace transformation was used to solve the governing ...
Equational binary decision diagrams
J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)
2000-01-01
textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and
Directory of Open Access Journals (Sweden)
Hatem Mejjaoli
2008-12-01
Full Text Available We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2013-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…
ANTHROPOMETRIC PREDICTIVE EQUATIONS FOR ...
African Journals Online (AJOL)
Keywords: Anthropometry, Predictive Equations, Percentage Body Fat, Nigerian Women, Bioelectric Impedance ... such as Asians and Indians (Pranav et al., 2009), ... size (n) of at least 3o is adjudged as sufficient for the ..... of people, gender and age (Vogel eta/., 1984). .... Fish Sold at Ile-Ife Main Market, South West Nigeria.
Indian Academy of Sciences (India)
However, one can associate the term with any solution of nonlinear partial differential equations (PDEs) which (i) represents a wave of permanent form, (ii) is localized ... In the past several decades, many methods have been proposed for solving nonlinear PDEs, such as ... space–time fractional derivative form of eq. (1) and ...
Fay, Temple H.
2010-01-01
Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…
Guiding center drift equations
International Nuclear Information System (INIS)
Boozer, A.H.
1979-03-01
The quations for particle guiding center drift orbits are given in a new magnetic coordinate system. This form of the equations not only separates the fast motion along the lines from the slow motion across, but also requires less information about the magnetic field than many other formulations of the problem
dimensional nonlinear evolution equations
Indian Academy of Sciences (India)
in real-life situations, it is important to find their exact solutions. Further, in ... But only little work is done on the high-dimensional equations. .... Similarly, to determine the values of d and q, we balance the linear term of the lowest order in eq.
Stochastic nonlinear beam equations
Czech Academy of Sciences Publication Activity Database
Brzezniak, Z.; Maslowski, Bohdan; Seidler, Jan
2005-01-01
Roč. 132, č. 1 (2005), s. 119-149 ISSN 0178-8051 R&D Projects: GA ČR(CZ) GA201/01/1197 Institutional research plan: CEZ:AV0Z10190503 Keywords : stochastic beam equation * stability Subject RIV: BA - General Mathematics Impact factor: 0.896, year: 2005
Savoy, L. G.
1988-01-01
Describes a study of students' ability to balance equations. Answers to a test on this topic were analyzed to determine the level of understanding and processes used by the students. Presented is a method to teach this skill to high school chemistry students. (CW)
Kevill, Dennis Neil; Kim, Chang-Bae; D'Souza, Malcolm John
2018-03-01
A Grunwald-Winstein treatment of the specific rates of solvolysis of α-bromoisobutyrophenone in 100% methanol and in several aqueous ethanol, methanol, acetone, 2,2,2-trifluoroethanol (TFE), and 1,1,1,3,3,3-hexafluoro-2-propanol (HFIP) mixtures gives a good logarithmic correlation against a linear combination of N T (solvent nucleophilicity) and Y Br (solvent ionizing power) values. The l and m sensitivity values are compared to those previously reported for α-bromoacetophenone and to those obtained from parallel treatments of literature specific rate values for the solvolyses of several tertiary mesylates containing a C(=O)R group attached at the α-carbon. Kinetic data obtained earlier by Pasto and Sevenair for the solvolyses of the same substrate in 75% aqueous ethanol (by weight) in the presence of silver perchlorate and perchloric acid are analyzed using multiple regression analysis.
Melanin binding study of clinical drugs with cassette dosing and rapid equilibrium dialysis inserts
Pelkonen L; Tengvall-Unadike U; Ruponen M; Kidron H; del Amo EM; Reinisalo M; Urtti A
2017-01-01
Melanin pigment is a negatively charged polymer found in pigmented human tissues. In the eye, iris, ciliary body, choroid and retinal pigment epithelium (RPE) are heavily pigmented. Several drug molecules are known to bind to melanin, but larger sets of drugs have not been compared often in similar test conditions. In this study, we introduce a powerful tool for screening of melanin binding. The binding of a set of 34 compounds to isolated porcine RPE melanin was determined by cassette (n-in-...
Lectures on partial differential equations
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.
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)
Elements of partial differential equations
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
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.
Cunningham, Kevin
2007-01-01
This article presents an assignment in which students are to research and report on a chemical reaction whose increased or decreased rate is of practical importance. Specifically, students are asked to represent the reaction they have chosen with an acceptable chemical equation, identify a factor that influences its rate and explain how and why it…
Constitutive equations for Zr1Nb. II
International Nuclear Information System (INIS)
Novak, J.
1986-01-01
Based on existing knowledge and constitutive equations for non-irradiated material, constitutive equations were written for Zr1Nb irradiated at 573 K at deformation in the direction of forming. Constitutive equations express the following material characteristics: dependence of shear strength on fast neutron fluence, superposition of deformation hardening and subsequent radiation hardening, the effect of stress on deformation rate, and for fluences above ca. 10 24 n.m -2 (E>1 MeV) the course of the deformation curve for various fluence levels. The values apply for temperatures and rates of deformation which are characteristic of transient processes during changes in the power output of fuel elements of pressurized water reactors. (J.B.)
Methods for Equating Mental Tests.
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
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.
Fractional Bhatnagar-Gross-Krook kinetic equation
Goychuk, Igor
2017-11-01
The linear Boltzmann equation (LBE) approach is generalized to describe fractional superdiffusive transport of the Lévy walk type in external force fields. The time distribution between scattering events is assumed to have a finite mean value and infinite variance. It is completely characterized by the two scattering rates, one fractional and a normal one, which defines also the mean scattering rate. We formulate a general fractional LBE approach and exemplify it with a particularly simple case of the Bohm and Gross scattering integral leading to a fractional generalization of the Bhatnagar, Gross and Krook (BGK) kinetic equation. Here, at each scattering event the particle velocity is completely randomized and takes a value from equilibrium Maxwell distribution at a given fixed temperature. We show that the retardation effects are indispensable even in the limit of infinite mean scattering rate and argue that this novel fractional kinetic equation provides a viable alternative to the fractional Kramers-Fokker-Planck (KFP) equation by Barkai and Silbey and its generalization by Friedrich et al. based on the picture of divergent mean time between scattering events. The case of divergent mean time is also discussed at length and compared with the earlier results obtained within the fractional KFP. Also a phenomenological fractional BGK equation without retardation effects is proposed in the limit of infinite scattering rates. It cannot be, however, rigorously derived from a scattering model, being rather clever postulated. It this respect, this retardationless equation is similar to the fractional KFP by Barkai and Silbey. However, it corresponds to the opposite, much more physical limit and, therefore, also presents a viable alternative.
Solórzano, S.; Mendoza, M.; Succi, S.; Herrmann, H. J.
2018-01-01
We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.
DEFF Research Database (Denmark)
Dyre, Jeppe
1995-01-01
energies chosen randomly according to a Gaussian. The random-walk model is here derived from Newton's laws by making a number of simplifying assumptions. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk modelthe energy master equation...... (EME)is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures...... of the random-walk model. The EME allows a calculation of the energy probability distribution at realistic laboratory time scales for an arbitrarily varying temperature as function of time. The EME is probably the only realistic equation available today with this property that is also explicitly consistent...
Classical Diophantine equations
1993-01-01
The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, ...
Flavored quantum Boltzmann equations
International Nuclear Information System (INIS)
Cirigliano, Vincenzo; Lee, Christopher; Ramsey-Musolf, Michael J.; Tulin, Sean
2010-01-01
We derive from first principles, using nonequilibrium field theory, the quantum Boltzmann equations that describe the dynamics of flavor oscillations, collisions, and a time-dependent mass matrix in the early universe. Working to leading nontrivial order in ratios of relevant time scales, we study in detail a toy model for weak-scale baryogenesis: two scalar species that mix through a slowly varying time-dependent and CP-violating mass matrix, and interact with a thermal bath. This model clearly illustrates how the CP asymmetry arises through coherent flavor oscillations in a nontrivial background. We solve the Boltzmann equations numerically for the density matrices, investigating the impact of collisions in various regimes.
Causal electromagnetic interaction equations
International Nuclear Information System (INIS)
Zinoviev, Yury M.
2011-01-01
For the electromagnetic interaction of two particles the relativistic causal quantum mechanics equations are proposed. These equations are solved for the case when the second particle moves freely. The initial wave functions are supposed to be smooth and rapidly decreasing at the infinity. This condition is important for the convergence of the integrals similar to the integrals of quantum electrodynamics. We also consider the singular initial wave functions in the particular case when the second particle mass is equal to zero. The discrete energy spectrum of the first particle wave function is defined by the initial wave function of the free-moving second particle. Choosing the initial wave functions of the free-moving second particle it is possible to obtain a practically arbitrary discrete energy spectrum.
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.
Equations of multiparticle dynamics
International Nuclear Information System (INIS)
Chao, A.W.
1987-01-01
The description of the motion of charged-particle beams in an accelerator proceeds in steps of increasing complexity. The first step is to consider a single-particle picture in which the beam is represented as a collection on non-interacting test particles moving in a prescribed external electromagnetic field. Knowing the external field, it is then possible to calculate the beam motion to a high accuracy. The real beam consists of a large number of particles, typically 10 11 per beam bunch. It is sometimes inconvenient, or even impossible, to treat the real beam behavior using the single particle approach. One way to approach this problem is to supplement the single particle by another qualitatively different picture. The commonly used tools in accelerator physics for this purpose are the Vlasov and the Fokker-Planck equations. These equations assume smooth beam distributions and are therefore strictly valid in the limit of infinite number of micro-particles, each carrying an infinitesimal charge. The hope is that by studying the two extremes -- the single particle picture and the picture of smooth beam distributions -- we will be able to describe the behavior of our 10 11 -particle system. As mentioned, the most notable use of the smooth distribution picture is the study of collective beam instabilities. However, the purpose of this lecture is not to address this more advanced subject. Rather, it has the limited goal to familiarize the reader with the analytical tools, namely the Vlasov and the Fokker-Planck equations, as a preparation for dealing with the more advanced problems at later times. We will first derive these equations and then illustrate their applications by several examples which allow exact solutions
Electroweak evolution equations
International Nuclear Information System (INIS)
Ciafaloni, Paolo; Comelli, Denis
2005-01-01
Enlarging a previous analysis, where only fermions and transverse gauge bosons were taken into account, we write down infrared-collinear evolution equations for the Standard Model of electroweak interactions computing the full set of splitting functions. Due to the presence of double logs which are characteristic of electroweak interactions (Bloch-Nordsieck violation), new infrared singular splitting functions have to be introduced. We also include corrections related to the third generation Yukawa couplings
Differential equations with Mathematica
Abell, Martha L
2004-01-01
The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners.* Focuses on the most often used features of Mathematica for the beginning Mathematica user* New applications from a variety of fields, including engineering, biology, and physics* All applications were completed using recent versions of Mathematica
Damped nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Nicholson, D.R.; Goldman, M.V.
1976-01-01
High frequency electrostatic plasma oscillations described by the nonlinear Schrodinger equation in the presence of damping, collisional or Landau, are considered. At early times, Landau damping of an initial soliton profile results in a broader, but smaller amplitude soliton, while collisional damping reduces the soliton size everywhere; soliton speeds at early times are unchanged by either kind of damping. For collisional damping, soliton speeds are unchanged for all time
Fun with Differential Equations
Indian Academy of Sciences (India)
IAS Admin
tion of ® with ¼=2. One can use the uniqueness of solutions of differential equations to prove the addition formulae for sin(t1 +t2), etc. But instead of continuing with this thought process, let us do something more interesting. Now we shall consider another system. Fix 0 < < 1. I am looking for three real-valued functions x(t), ...
Mathematics and Maxwell's equations
International Nuclear Information System (INIS)
Boozer, Allen H
2010-01-01
The universality of mathematics and Maxwell's equations is not shared by specific plasma models. Computations become more reliable, efficient and transparent if specific plasma models are used to obtain only the information that would otherwise be missing. Constraints of high universality, such as those from mathematics and Maxwell's equations, can be obscured or lost by integrated computations. Recognition of subtle constraints of high universality is important for (1) focusing the design of control systems for magnetic field errors in tokamaks from perturbations that have little effect on the plasma to those that do, (2) clarifying the limits of applicability to astrophysics of computations of magnetic reconnection in fields that have a double periodicity or have B-vector =0 on a surface, as in a Harris sheet. Both require a degree of symmetry not expected in natural systems. Mathematics and Maxwell's equations imply that neighboring magnetic field lines characteristically separate exponentially with distance along a line. This remarkably universal phenomenon has been largely ignored, though it defines a trigger for reconnection through a critical magnitude of exponentiation. These and other examples of the importance of making distinctions and understanding constraints of high universality are explained.
Directory of Open Access Journals (Sweden)
M. Paul Gough
2008-07-01
Full Text Available LandauerÃ¢Â€Â™s principle is applied to information in the universe. Once stars began forming there was a constant information energy density as the increasing proportion of matter at high stellar temperatures exactly compensated for the expanding universe. The information equation of state was close to the dark energy value, w = -1, for a wide range of redshifts, 10 > z > 0.8, over one half of cosmic time. A reasonable universe information bit content of only 1087 bits is sufficient for information energy to account for all dark energy. A time varying equation of state with a direct link between dark energy and matter, and linked to star formation in particular, is clearly relevant to the cosmic coincidence problem. In answering the Ã¢Â€Â˜Why now?Ã¢Â€Â™ question we wonder Ã¢Â€Â˜What next?Ã¢Â€Â™ as we expect the information equation of state to tend towards w = 0 in the future.c
Generalized reduced MHD equations
International Nuclear Information System (INIS)
Kruger, S.E.; Hegna, C.C.; Callen, J.D.
1998-07-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson
Spectral theories for linear differential equations
International Nuclear Information System (INIS)
Sell, G.R.
1976-01-01
The use of spectral analysis in the study of linear differential equations with constant coefficients is not only a fundamental technique but also leads to far-reaching consequences in describing the qualitative behaviour of the solutions. The spectral analysis, via the Jordan canonical form, will not only lead to a representation theorem for a basis of solutions, but will also give a rather precise statement of the (exponential) growth rates of various solutions. Various attempts have been made to extend this analysis to linear differential equations with time-varying coefficients. The most complete such extensions is the Floquet theory for equations with periodic coefficients. For time-varying linear differential equations with aperiodic coefficients several authors have attempted to ''extend'' the Foquet theory. The precise meaning of such an extension is itself a problem, and we present here several attempts in this direction that are related to the general problem of extending the spectral analysis of equations with constant coefficients. The main purpose of this paper is to introduce some problems of current research. The primary problem we shall examine occurs in the context of linear differential equations with almost periodic coefficients. We call it ''the Floquet problem''. (author)
Nuclear fission with a Langevin equation
International Nuclear Information System (INIS)
Boilley, D.; Suraud, E.; Abe, Yasuhisa
1992-01-01
A microscopically derived Langevin equation is applied to thermally induced nuclear fission. An important memory effect is pointed out and discussed. A strong friction coefficient, estimated from microscopic quantities, tends to decrease the stationary limit of the fission rate and to increase the transient time. The calculations are performed with a collective mass depending on the collective variable and with a constant mass. Fission rates calculated at different temperatures are shown and compared with previous available results. (author) 23 refs.; 7 figs
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.
Reduction operators of Burgers equation.
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.
Directory of Open Access Journals (Sweden)
Vivian Wahrlich
2001-02-01
Full Text Available OBJETIVO: Medir a taxa metabólica basal em mulheres de 20 a 40 anos, não-gestantes ou lactantes, e comparar o valor medido com os valores de taxa metabólica basal estimados por equações de predição. MÉTODOS: A taxa metabólica basal foi medida por calorimetria indireta, pela manhã, durante a fase folicular do ciclo menstrual, em 60 voluntárias residentes no município de Porto Alegre, RS, sob condições padronizadas de jejum, repouso e ambiente. RESULTADOS: A média (± desvio-padrão da taxa metabólica basal medida foi 1.185,3±148,6 kcal em 24 horas. A taxa metabólica basal, estimada por equações, foi significativamente maior (7% a 17% do que a taxa metabólica basal medida. CONCLUSÕES: Os dados evidenciaram que as equações de predição não são adequadas para estimar a taxa metabólica basal nas mulheres avaliadas. O emprego dessas equações podem superestimar os requerimentos energéticos para mulheres com características semelhantes.OBJECTIVE: To measure the basal metabolic rate of women (aged 20 to 40 years living in Porto Alegre, Brazil, and to compare it with estimated values bored on published predictive equations. METHODS: Basal metabolic rate was measured by indirect calorimetry under standard conditions in the follicular phase of the menstrual cycle of 60 volunteers. RESULTS: Mean measured basal metabolic rate (± standard deviation was 1,185.3± 148.6 kcal/24 hours. Estimated basal metabolic rates were significantly greater (7% to 17% than measured basal metabolic rate (p<0.0001. CONCLUSIONS: These results show that predictive equations are not suitable to estimate basal metabolic rate in these groups of women and that the use of estimated basal metabolic rate will lead to an overestimation of energy requirements in women with similar characteristics.
International Nuclear Information System (INIS)
Nishimura, M.
1998-04-01
To predict thermal-hydraulic phenomena in actual plant under various conditions accurately, adequate simulation of laminar-turbulent flow transition is of importance. A low Reynolds number turbulence model is commonly used for a numerical simulation of the laminar-turbulent transition. The existing low Reynolds number turbulence models generally demands very thin mesh width between a wall and a first computational node from the wall, to keep accuracy and stability of numerical analyses. There is a criterion for the distance between the wall and the first computational node in which non-dimensional distance y + must be less than 0.5. Due to this criterion the suitable distance depends on Reynolds number. A liquid metal sodium is used for a coolant in first reactors therefore, Reynolds number is usually one or two order higher than that of the usual plants in which air and water are used for the work fluid. This makes the load of thermal-hydraulic numerical simulation of the liquid sodium relatively heavier. From above context, a new method is proposed for providing wall boundary condition of turbulent kinetic energy dissipation rate ε. The present method enables the wall-first node distance 10 times larger compared to the existing models. A function of the ε wall boundary condition has been constructed aided by a direct numerical simulation (DNS) data base. The method was validated through calculations of a turbulent Couette flow and a fully developed pipe flow and its laminar-turbulent transition. Thus the present method and modeling are capable of predicting the laminar-turbulent transition with less mesh numbers i.e. lighter computational loads. (J.P.N.)
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
Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating
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…
Differential Equations as Actions
DEFF Research Database (Denmark)
Ronkko, Mauno; Ravn, Anders P.
1997-01-01
We extend a conventional action system with a primitive action consisting of a differential equation and an evolution invariant. The semantics is given by a predicate transformer. The weakest liberal precondition is chosen, because it is not always desirable that steps corresponding to differential...... actions shall terminate. It is shown that the proposed differential action has a semantics which corresponds to a discrete approximation when the discrete step size goes to zero. The extension gives action systems the power to model real-time clocks and continuous evolutions within hybrid systems....
Partial differential equations
Levine, Harold
1997-01-01
The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters.
Ordinary differential equations
Cox, William
1995-01-01
Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further
Partial differential equations
Sloan, D; Süli, E
2001-01-01
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight in
Elliptic partial differential equations
Han, Qing
2011-01-01
Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things abo
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 ...
Equationally Noetherian property of Ershov algebras
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.
Receptor binding kinetics equations: Derivation using the Laplace transform method.
Hoare, Sam R J
Measuring unlabeled ligand receptor binding kinetics is valuable in optimizing and understanding drug action. Unfortunately, deriving equations for estimating kinetic parameters is challenging because it involves calculus; integration can be a frustrating barrier to the pharmacologist seeking to measure simple rate parameters. Here, a well-known tool for simplifying the derivation, the Laplace transform, is applied to models of receptor-ligand interaction. The method transforms differential equations to a form in which simple algebra can be applied to solve for the variable of interest, for example the concentration of ligand-bound receptor. The goal is to provide instruction using familiar examples, to enable investigators familiar with handling equilibrium binding equations to derive kinetic equations for receptor-ligand interaction. First, the Laplace transform is used to derive the equations for association and dissociation of labeled ligand binding. Next, its use for unlabeled ligand kinetic equations is exemplified by a full derivation of the kinetics of competitive binding equation. Finally, new unlabeled ligand equations are derived using the Laplace transform. These equations incorporate a pre-incubation step with unlabeled or labeled ligand. Four equations for measuring unlabeled ligand kinetics were compared and the two new equations verified by comparison with numerical solution. Importantly, the equations have not been verified with experimental data because no such experiments are evident in the literature. Equations were formatted for use in the curve-fitting program GraphPad Prism 6.0 and fitted to simulated data. This description of the Laplace transform method will enable pharmacologists to derive kinetic equations for their model or experimental paradigm under study. Application of the transform will expand the set of equations available for the pharmacologist to measure unlabeled ligand binding kinetics, and for other time
International Nuclear Information System (INIS)
Thaller, B.
1992-01-01
This monograph treats most of the usual material to be found in texts on the Dirac equation such as the basic formalism of quantum mechanics, representations of Dirac matrices, covariant realization of the Dirac equation, interpretation of negative energies, Foldy-Wouthuysen transformation, Klein's paradox, spherically symmetric interactions and a treatment of the relativistic hydrogen atom, etc., and also provides excellent additional treatments of a variety of other relevant topics. The monograph contains an extensive treatment of the Lorentz and Poincare groups and their representations. The author discusses in depth Lie algebaic and projective representations, covering groups, and Mackey's theory and Wigner's realization of induced representations. A careful classification of external fields with respect to their behavior under Poincare transformations is supplemented by a basic account of self-adjointness and spectral properties of Dirac operators. A state-of-the-art treatment of relativistic scattering theory based on a time-dependent approach originally due to Enss is presented. An excellent introduction to quantum electrodynamics in external fields is provided. Various appendices containing further details, notes on each chapter commenting on the history involved and referring to original research papers and further developments in the literature, and a bibliography covering all relevant monographs and over 500 articles on the subject, complete this text. This book should satisfy the needs of a wide audience, ranging from graduate students in theoretical physics and mathematics to researchers interested in mathematical physics
International Nuclear Information System (INIS)
Sydoriak, S.G.
1976-01-01
Although criteria for cryostatic stability of superconducting magnets cooled by pool boiling of liquid helium have been widely discussed the same cannot be said for magnets cooled by natural convection or forced flow boiling in channels. Boiling in narrow channels is shown to be qualitatively superior to pool boiling because the recovery heat flux equals the breakaway flux for narrow channels, whereas the two are markedly different in pool boiling. A second advantage of channel boiling is that it is well understood and calculable; pool peak nucleate boiling heat flux has been adequately measured only for boiling from the top of an immersed heated body. Peak boiling from the bottom is much less and (probably) depends strongly on the extent of the bottom surface. Equations are presented by which one can calculate the critical boiling heat flux for parallel wall vertical channels subject to either natural convection or forced flow boiling, with one or both walls heated. The one-heated-wall forced flow equation is discussed with regard to design of a spiral wound solenoid (pancake magnet) having a slippery insulating tape between the windings
Solving Nonlinear Coupled Differential Equations
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.
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.)
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)
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 ...
Spatial evolution equation of wind wave growth
Institute of Scientific and Technical Information of China (English)
WANG; Wei; (王; 伟); SUN; Fu; (孙; 孚); DAI; Dejun; (戴德君)
2003-01-01
Based on the dynamic essence of air-sea interactions, a feedback type of spatial evolution equation is suggested to match reasonably the growing process of wind waves. This simple equation involving the dominant factors of wind wave growth is able to explain the transfer of energy from high to low frequencies without introducing the concept of nonlinear wave-wave interactions, and the results agree well with observations. The rate of wave height growth derived in this dissertation is applicable to both laboratory and open sea, which solidifies the physical basis of using laboratory experiments to investigate the generation of wind waves. Thus the proposed spatial evolution equation provides a new approach for the research on dynamic mechanism of air-sea interactions and wind wave prediction.
Statistical equilibrium equations for trace elements in stellar atmospheres
Kubat, Jiri
2010-01-01
The conditions of thermodynamic equilibrium, local thermodynamic equilibrium, and statistical equilibrium are discussed in detail. The equations of statistical equilibrium and the supplementary equations are shown together with the expressions for radiative and collisional rates with the emphasize on the solution for trace elements.
Asymptotic behaviour of solutions of a degenerate quasilinear hyperbolic equation
International Nuclear Information System (INIS)
Pereira, D.C.
1988-10-01
The decay as t->∞ of the solutions of equation u''(t)|A 1/2 u(t)| 2 Au(t)+Au'(t)=0 where A is a self-adjoint operator in a Hilbert space H with norm |.| is studied. A decay of algebraic rate for the energy associated to the studied equation is obtained. (author) [pt
Analyticity estimates for the Navier-Stokes equations
DEFF Research Database (Denmark)
Herbst, I.; Skibsted, Erik
We study spatial analyticity properties of solutions of the Navier-Stokes equation and obtain new growth rate estimates for the analyticity radius. We also study stability properties of strong global solutions of the Navier-Stokes equation with data in and prove a stability result...
A novel numerical flux for the 3D Euler equations with general equation of state
Toro, Eleuterio F.
2015-09-30
Here we extend the flux vector splitting approach recently proposed in (E F Toro and M E Vázquez-Cendón. Flux splitting schemes for the Euler equations. Computers and Fluids. Vol. 70, Pages 1-12, 2012). The scheme was originally presented for the 1D Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on general meshes; (ii) we use a general equation of state; and (iii) we achieve high order of accuracy in both space and time through application of the semi-discrete ADER methodology on general meshes. The resulting methods are systematically assessed for accuracy, robustness and efficiency on a carefully selected suite of test problems. Formal high accuracy is assessed through convergence rates studies for schemes of up to 4th order of accuracy in both space and time on unstructured meshes.
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)
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.
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)
Directory of Open Access Journals (Sweden)
Taouil Hajer
2012-08-01
Full Text Available This paper is devoted to the helices processes, i.e. the solutions H : ℝ × Ω → ℝd, (t, ω ↦ H(t, ω of the helix equation egin{eqnarray} H(0,o=0; quad H(s+t,o= H(s,Phi(t,o +H(t,oonumber end{eqnarray} H ( 0 ,ω = 0 ; H ( s + t,ω = H ( s, Φ ( t,ω + H ( t,ω where Φ : ℝ × Ω → Ω, (t, ω ↦ Φ(t, ω is a dynamical system on a measurable space (Ω, ℱ. More precisely, we investigate dominated solutions and non differentiable solutions of the helix equation. For the last case, the Wiener helix plays a fundamental role. Moreover, some relations with the cocycle equation defined by Φ, are investigated. Ce papier est consacré aux hélices, c’est-à-dire les solutions H : ℝ × Ω → ℝd, (t, ω ↦ H(t, ω de l’équation fonctionnelle egin{eqnarray} H(0,o=0; quad H(s+t,o= H(s,Phi(t,o +H(t,o onumber end{eqnarray} H ( 0 ,ω = 0 ; H ( s + t,ω = H ( s, Φ ( t,ω + H ( t,ω où Φ : ℝ × Ω → Ω, (t, ω ↦ Φ(t, ω est un système dynamique défini sur un espace mesurable (Ω, ℱ. Plus présisément, nous déterminons d’abord les hélices dominées puis nous caractérisons les hélices non différentiables. Dans ce dernier cas, l’hélice de Wiener joue un rôle important. Nous précisons aussi quelques relations des hélices avec les cocycles définis par Φ.
p-Euler equations and p-Navier-Stokes equations
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.
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)
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
Wave Partial Differential Equation
Szöllös, Alexandr
2009-01-01
Práce se zabývá diferenciálními rovnicemi, jejich využitím při analýze vedení, experimenty s vedením a možnou akcelerací výpočtu v GPU s využitím prostředí nVidia CUDA. This work deals with diffrential equations, with the possibility of using them for analysis of the line and the possibility of accelerating the computations in GPU using nVidia CUDA. C
Gomez, Humberto
2016-06-01
The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter Λ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting Λ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the Λ algorithm.
Scaling of differential equations
Langtangen, Hans Petter
2016-01-01
The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and exam...
Parabolized stability equations
Herbert, Thorwald
1994-01-01
The parabolized stability equations (PSE) are a new approach to analyze the streamwise evolution of single or interacting Fourier modes in weakly nonparallel flows such as boundary layers. The concept rests on the decomposition of every mode into a slowly varying amplitude function and a wave function with slowly varying wave number. The neglect of the small second derivatives of the slowly varying functions with respect to the streamwise variable leads to an initial boundary-value problem that can be solved by numerical marching procedures. The PSE approach is valid in convectively unstable flows. The equations for a single mode are closely related to those of the traditional eigenvalue problems for linear stability analysis. However, the PSE approach does not exploit the homogeneity of the problem and, therefore, can be utilized to analyze forced modes and the nonlinear growth and interaction of an initial disturbance field. In contrast to the traditional patching of local solutions, the PSE provide the spatial evolution of modes with proper account for their history. The PSE approach allows studies of secondary instabilities without the constraints of the Floquet analysis and reproduces the established experimental, theoretical, and computational benchmark results on transition up to the breakdown stage. The method matches or exceeds the demonstrated capabilities of current spatial Navier-Stokes solvers at a small fraction of their computational cost. Recent applications include studies on localized or distributed receptivity and prediction of transition in model environments for realistic engineering problems. This report describes the basis, intricacies, and some applications of the PSE methodology.
Pomeau, Yves; Piasecki, Jarosław
2017-11-01
The existence of atoms has been long predicted by philosophers and scientists. The development of thermodynamics and of the statistical interpretation of its concepts at the end of the nineteenth century and in the early years of the twentieth century made it possible to bridge the gap of scales between the macroscopic world and the world of atoms. Einstein and Smoluchowski showed in 1905 and 1906 that the Brownian motion of particles of measurable size is a manifestation of the motion of atoms in fluids. Their derivation was completely different from each other. Langevin showed in 1908 how to put in a coherent framework the subtle effect of the randomness of the atomic world, responsible for the fluctuating force driving the motion of the Brownian particle and the viscosity of the "macroscopic" flow taking place around the same Brownian particle. Whereas viscous forces were already well understood at this time, the "Langevin" force appears there for the first time: it represents the fluctuating part of the interaction between the Brownian particle and the surrounding fluid. We discuss the derivation by Einstein and Smoluchowski as well as a previous paper by Sutherland on the diffusion coefficient of large spheres. Next we present Langevin's short note and explain the fundamental splitting into a random force and a macroscopic viscous force. This brings us to discuss various points, like the kind of constraints on Langevin-like equations. We insist in particular on the one arising from the time-reversal symmetry of the equilibrium fluctuations. Moreover, we discuss another constraint, raised first by Lorentz, which implies that, if the Brownian particle is not very heavy, the viscous force cannot be taken as the standard Stokes drag on an object moving at uniform speed. Lastly, we examine the so-called Langevin-Heisenberg and/or Langevin-Schrödinger equation used in quantum mechanics.
Michaelis - Menten equation for degradation of insoluble substrate
DEFF Research Database (Denmark)
Andersen, Morten; Kari, Jeppe; Borch, Kim
2017-01-01
substrate it is difficult to assess whether the requirement of the MM equation is met. In this paper we study a simple kinetic model, where removal of attack sites expose new ones which preserve the total accessible substrate, and denote this approach the substrate conserving model. The kinetic equations...... are solved in closed form, both steady states and progress curves, for any admissible values of initial conditions and rate constants. The model is shown to merge with the MM equation and the reverse MM equation when these are valid. The relation between available molar concentration of attack sites and mass...
Derivation and application of hydraulic equation for variable-rate ...
African Journals Online (AJOL)
use
2011-12-12
Dec 12, 2011 ... and a lever element having a cam engaging element which engages the cam surface, the lever element being operatively coupled to the valve such that the contour of the cam surface causes the ... When. 0. →∆ t. , there are. 0. →∆ α and. OA. OB → . The wetted area of the VRCS S. ∆ during this very short ...
Kinetic equation for spin-polarized plasmas
International Nuclear Information System (INIS)
Cowley, S.C.; Kulsrud, R.M.; Valeo, E.
1984-07-01
The usual kinetic description of a plasma is extended to include variables to describe the spin. The distribution function, over phase-space and the new spin variables, provides a sufficient description of a spin-polarized plasma. The evolution equation for the distribution function is given. The equations derived are used to calculate depolarization due to four processes, inhomogeneous fields, collisions, collisions in inhomogeneous fields, and waves. It is found that depolarization by field inhomogeneity on scales large compared with the gyroradius is totally negligible. The same is true for collisional depolarization. Collisions in inhomogeneous fields yield a depolarization rate of order 10 -4 S -1 for deuterons and a negligible rate for tritons in a typical fusion reactor design. This is still sufficiently small on reactor time scales. However, small amplitude magnetic fluctuations (of order one gauss) resonant with the spin precession frequency can lead to significant depolarization (depolarises triton in ten seconds and deuteron in a hundred seconds.)
Introduction to partial differential equations
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.
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
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.
Differential equations methods and applications
Said-Houari, Belkacem
2015-01-01
This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory. To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included. The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations. .
Integral equations and their applications
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...
Stochastic partial differential equations
Lototsky, Sergey V
2017-01-01
Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected ...
Energy Technology Data Exchange (ETDEWEB)
Menikoff, Ralph [Los Alamos National Laboratory
2015-12-15
The JWL equation of state (EOS) is frequently used for the products (and sometimes reactants) of a high explosive (HE). Here we review and systematically derive important properties. The JWL EOS is of the Mie-Grueneisen form with a constant Grueneisen coefficient and a constants specific heat. It is thermodynamically consistent to specify the temperature at a reference state. However, increasing the reference state temperature restricts the EOS domain in the (V, e)-plane of phase space. The restrictions are due to the conditions that P ≥ 0, T ≥ 0, and the isothermal bulk modulus is positive. Typically, this limits the low temperature regime in expansion. The domain restrictions can result in the P-T equilibrium EOS of a partly burned HE failing to have a solution in some cases. For application to HE, the heat of detonation is discussed. Example JWL parameters for an HE, both products and reactions, are used to illustrate the restrictions on the domain of the EOS.
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.
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.
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
Introduction to ordinary differential equations
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
On matrix fractional differential equations
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...
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.
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
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.)
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.
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
Difference equations theory, applications and advanced topics
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...
Differential equations a dynamical systems approach ordinary differential equations
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.
Physical entropy, information entropy and their evolution equations
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Inspired by the evolution equation of nonequilibrium statistical physics entropy and the concise statistical formula of the entropy production rate, we develop a theory of the dynamic information entropy and build a nonlinear evolution equation of the information entropy density changing in time and state variable space. Its mathematical form and physical meaning are similar to the evolution equation of the physical entropy: The time rate of change of information entropy density originates together from drift, diffusion and production. The concise statistical formula of information entropy production rate is similar to that of physical entropy also. Furthermore, we study the similarity and difference between physical entropy and information entropy and the possible unification of the two statistical entropies, and discuss the relationship among the principle of entropy increase, the principle of equilibrium maximum entropy and the principle of maximum information entropy as well as the connection between them and the entropy evolution equation.
Asymptotic behavior of the plasma equation
International Nuclear Information System (INIS)
Kwong, Y.C.
1984-01-01
This paper is concerned with the plasma equation on a bounded smooth domain the N-dimensional Euclidean Space, with non-negative initial data and a homogenous Dirichlet boundary condition. It is known that there exists a finite extinction time T such that the solution decays to zero at T. Berryman and Holland investigated the stability of the profile of the solution as t is approaching T. However, they obtained their results at the expense of some very strong regularity assumptions. By invoking both the nonlinear semi-group theory and a standard regularizing scheme for the equation, the same results are proved without those assumptions by measuring the rate of decay of the solution and estimates are obtained on the time derivative as t is approaching T. As motivated by the regularity assumptions, both the interior and boundary regularities of the solution are studied. Finally, the nonlinearity of the plasma equation is perturbed and the same aspects for the perturbed equation are studied
Exact solutions to the Mo-Papas and Landau-Lifshitz equations
Rivera, R.; Villarroel, D.
2002-10-01
Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics.
Exact solutions to the Mo-Papas and Landau-Lifshitz equations
International Nuclear Information System (INIS)
Rivera, R.; Villarroel, D.
2002-01-01
Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics
Solutions to Arithmetic Convolution Equations
Czech Academy of Sciences Publication Activity Database
Glöckner, H.; Lucht, L.G.; Porubský, Štefan
2007-01-01
Roč. 135, č. 6 (2007), s. 1619-1629 ISSN 0002-9939 R&D Projects: GA ČR GA201/04/0381 Institutional research plan: CEZ:AV0Z10300504 Keywords : arithmetic functions * Dirichlet convolution * polynomial equations * analytic equations * topological algebras * holomorphic functional calculus Subject RIV: BA - General Mathematics Impact factor: 0.520, year: 2007
On Degenerate Partial Differential Equations
Chen, Gui-Qiang G.
2010-01-01
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial differential equations, are presented, which arise naturally in some longstanding, fundamental problems in fluid mechanics and differential geometry. The solution to these fundamental problems greatly requires a deep understanding of nonlinear degenerate parti...
Differential equations a concise course
Bear, H S
2011-01-01
Concise introduction for undergraduates includes, among other topics, a survey of first order equations, discussions of complex-valued solutions, linear differential operators, inverse operators and variation of parameters method, the Laplace transform, Picard's existence theorem, and an exploration of various interpretations of systems of equations. Numerous clearly stated theorems and proofs, examples, and problems followed by solutions.
Differential equations and finite groups
Put, Marius van der; Ulmer, Felix
2000-01-01
The classical solution of the Riemann-Hilbert problem attaches to a given representation of the fundamental group a regular singular linear differential equation. We present a method to compute this differential equation in the case of a representation with finite image. The approach uses Galois
Saturation and linear transport equation
International Nuclear Information System (INIS)
Kutak, K.
2009-03-01
We show that the GBW saturation model provides an exact solution to the one dimensional linear transport equation. We also show that it is motivated by the BK equation considered in the saturated regime when the diffusion and the splitting term in the diffusive approximation are balanced by the nonlinear term. (orig.)
Lie symmetries in differential equations
International Nuclear Information System (INIS)
Pleitez, V.
1979-01-01
A study of ordinary and Partial Differential equations using the symmetries of Lie groups is made. Following such a study, an application to the Helmholtz, Line-Gordon, Korleweg-de Vries, Burguer, Benjamin-Bona-Mahony and wave equations is carried out [pt
Introduction to nonlinear dispersive equations
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...
Students' Understanding of Quadratic Equations
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-01-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…
Solving equations by topological methods
Directory of Open Access Journals (Sweden)
Lech Górniewicz
2005-01-01
Full Text Available In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in differential equations.
Generalized Fermat equations: A miscellany
Bennett, M.A.; Chen, I.; Dahmen, S.R.; Yazdani, S.
2015-01-01
This paper is devoted to the generalized Fermat equation xp + yq = zr, where p, q and r are integers, and x, y and z are nonzero coprime integers. We begin by surveying the exponent triples (p, q, r), including a number of infinite families, for which the equation has been solved to date, detailing
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...
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.)
Directory of Open Access Journals (Sweden)
Patrícia Schneider
2005-06-01
Full Text Available As equações de predição conhecidas podem apresentar valores de taxa metabólica basal (TMB diferentes daqueles medidos por calorimetria indireta. Os objetivos deste estudo foram descrever a TMB, por meio de calorimetria indireta, em meninos com sobrepeso e obesidade, de 12 a 17 anos de idade, residentes em Porto Alegre, Brasil, e comparar o valor medido com os valores de TMB estimados por equações de predição. A TMB foi medida por calorimetria indireta, pela manhã, em 35 voluntários, sob condições padronizadas de jejum, repouso e ambiente. A média (± desvio-padrão da TMB medida foi de 1.900,5 ± 248,8kcal em 24 horas. A estimativa da TMB por equações foi significativamente maior, em três das quatro equações (6,5 a 9,5%, do que a TMB medida (p Las ecuaciones de predicción conocidas pueden presentar valores de tasa metabólica basal (TMB diferentes de aquellos medidos por calorimetria indirecta. Los objetivos de este estudio fueron describir la TMB, por medio de calorimetría indirecta, en chicos con sobrepeso y obesidad, de 12 a 17 años de edad residentes en Porto Alegre, Brasil, y comparar el valor medido con los valores de TMB estimados por ecuaciones de predicción. La TMB fué medida por calorimetria indirecta, por la mañana, en 35 voluntarios, sobre condiciones padronizadas de ayuno, reposo y ambiente. La media (± DP de la TMB medida fué 1.900,5 ± 248,8 kcal en 24 horas. La estimativa de la TMB por ecuaciones fué significativamente mayor, en tres de las cuatro ecuaciones (6,5 a 9,5%, de que la TMB medida (p The known predictive equations can present different values for basal metabolic rate (BMR compared to those measured through indirect calorimetry. The objective of this study was to describe BMR through indirect calorimetry of overweight and obese boys (with ages between 12 and 17 years old living in Porto Alegre, Brazil, and to compare the measured value with values estimated by predictive equations. Thirty
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.)
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…
Standardization of equations for radiochemical calculations
International Nuclear Information System (INIS)
Danahy, R.J.; Dugan, T.A.; Tomlinson, F.K.; Jones, H.W.
1994-01-01
In mid 1993, the Fernald Environmental Restoration Management Corporation (FERMCO), with USEPA approval implemented a project quality assurance plan containing performance-based specifications for radiochemical sample analyses conducted in support of the Fernald site remediation activities. FERMCO's initial approach to acquiring performance-based radioanalytical services was to provide limited guidance regarding equations for computation of the quantities required in each analysis report. It became evident that there was a significant divergence of opinion on how to compute some very basic radiochemical quantities. The use of a standardized set of equations was needed in order to ensure comparability of data from different laboratories. In a remediation project of this magnitude, use of multiple laboratories is a virtual necessity. Consequently comparability of data becomes an extremely important issue. A critical issue in the Remedial Investigation/Feasibility Study (RI/FS) phase of the dean up project is to avoid the occurrence of excessive false positive sample results. Such results could lead to unnecessary clean up and significant additional cost. This paper describes the specific formulas FERMCO is currently using to define such quantities as net sample count rate, sample radionuclide concentration, radiometric tracer and gravimetric carrier recovery. Equations have also been produced to define the uncertainty in each of the above quantities. Equations for the Total Propagated Uncertainty (TPU) and for a sample-specific Minimum Detectable Concentration (MDC) have also been specified. Generalized equations have been reformulated to address the specific conditions which apply to the analysis of FERMCO samples. In particular, FERMCO requires results which have been corrected for the radioactivity in the blank while in other instances, sample results without blank correction are required
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
Bubble dynamics equations in Newton fluid
International Nuclear Information System (INIS)
Xiao, J
2008-01-01
For the high-speed flow of Newton fluid, bubble is produced and expanded when it moves toward the surface of fluid. Bubble dynamics is a very important research field to understand the intrinsic feature of bubble production and motion. This research formulates the bubble expansion by expansion-local rotation transformation, which can be calculated by the measured velocity field. Then, the related dynamic equations are established to describe the interaction between the fluid and the bubble. The research shows that the bubble production condition can be expressed by critical vortex value and fluid pressure; and the bubble expansion rate can be obtained by solving the non-linear dynamic equation of bubble motion. The results may help the related research as it shows a special kind of fluid motion in theoretic sense. As an application example, the nanofiber radium-voltage relation and threshold voltage-surface tension relation in electrospinning process are discussed
Hartman-Wintner growth results for sublinear functional differential equations
Directory of Open Access Journals (Sweden)
John A. D. Appleby
2017-01-01
Full Text Available This article determines the rate of growth to infinity of scalar autonomous nonlinear functional and Volterra differential equations. In these equations, the right-hand side is a positive continuous linear functional of f(x. We assume f grows sublinearly, leading to subexponential growth in the solutions. The main results show that the solution of the functional differential equations are asymptotic to that of an auxiliary autonomous ordinary differential equation with right-hand side proportional to f. This happens provided f grows more slowly than l(x=x/log(x. The linear-logarithmic growth rate is also shown to be critical: if f grows more rapidly than l, the ODE dominates the FDE; if f is asymptotic to a constant multiple of l, the FDE and ODE grow at the same rate, modulo a constant non-unit factor; if f grows more slowly than l, the ODE and FDE grow at exactly the same rate. A partial converse of the last result is also proven. In the case when the growth rate is slower than that of the ODE, sharp bounds on the growth rate are determined. The Volterra and finite memory equations can have differing asymptotic behaviour and we explore the source of these differences.
Approximate solutions to Mathieu's equation
Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.
2018-06-01
Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.
Soliton equations and Hamiltonian systems
Dickey, L A
2002-01-01
The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also becau
Galois theory of difference equations
Put, Marius
1997-01-01
This book lays the algebraic foundations of a Galois theory of linear difference equations and shows its relationship to the analytic problem of finding meromorphic functions asymptotic to formal solutions of difference equations. Classically, this latter question was attacked by Birkhoff and Tritzinsky and the present work corrects and greatly generalizes their contributions. In addition results are presented concerning the inverse problem in Galois theory, effective computation of Galois groups, algebraic properties of sequences, phenomena in positive characteristics, and q-difference equations. The book is aimed at advanced graduate researchers and researchers.
Integral equation methods for electromagnetics
Volakis, John
2012-01-01
This text/reference is a detailed look at the development and use of integral equation methods for electromagnetic analysis, specifically for antennas and radar scattering. Developers and practitioners will appreciate the broad-based approach to understanding and utilizing integral equation methods and the unique coverage of historical developments that led to the current state-of-the-art. In contrast to existing books, Integral Equation Methods for Electromagnetics lays the groundwork in the initial chapters so students and basic users can solve simple problems and work their way up to the mo
Bridging the Knowledge Gaps between Richards' Equation and Budyko Equation
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.
Iterative Splitting Methods for Differential Equations
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
Nonlinear integrodifferential equations as discrete systems
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.
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)
Generalized Smoluchowski equation with correlation between clusters
International Nuclear Information System (INIS)
Sittler, Lionel
2008-01-01
In this paper we compute new reaction rates of the Smoluchowski equation which takes into account correlations. The new rate K = K MF + K C is the sum of two terms. The first term is the known Smoluchowski rate with the mean-field approximation. The second takes into account a correlation between clusters. For this purpose we introduce the average path of a cluster. We relate the length of this path to the reaction rate of the Smoluchowski equation. We solve the implicit dependence between the average path and the density of clusters. We show that this correlation length is the same for all clusters. Our result depends strongly on the spatial dimension d. The mean-field term K MF i,j = (D i + D j )(r j + r i ) d-2 , which vanishes for d = 1 and is valid up to logarithmic correction for d = 2, is the usual rate found with the Smoluchowski model without correlation (where r i is the radius and D i is the diffusion constant of the cluster). We compute a new rate: the correlation rate K i,j C = (D i +D j )(r j +r i ) d-1 M((d-1)/d f ) is valid for d ≥ 1(where M(α) = Σ +∞ i=1 i α N i is the moment of the density of clusters and d f is the fractal dimension of the cluster). The result is valid for a large class of diffusion processes and mass-radius relations. This approach confirms some analytical solutions in d = 1 found with other methods. We also show Monte Carlo simulations which illustrate some exact new solvable models
40 CFR 60.2975 - What equations must I use?
2010-07-01
... (CONTINUED) STANDARDS OF PERFORMANCE FOR NEW STATIONARY SOURCES Operator Training and Qualification Equations... rate. To determine the maximum charge rate, use one of two methods: (1) For very small municipal waste.... Calculate the maximum number of batches by dividing 24 by the number of hours needed to process one batch...
Comparison of equations for dosing of medications in renal impairment.
Khanal, Aarati; Peterson, Gregory M; Jose, Matthew D; Castelino, Ronald L
2017-06-01
The aim of this study is to determine the concordance among the Cockcroft-Gault, the Modification of Diet in Renal Disease and the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations in hypothetical dosing of renally cleared medications. A total of 2163 patients prescribed at least one of the 31 renally cleared drugs under review were included in the study. Kidney function was estimated using the three equations. We compared actual prescribed dosages of the same drug with recommended dosages based on the kidney function as calculated by each of the equations and applying dosing recommendations in the Australian Medicines Handbook. There was a significant difference in the kidney function values estimated from the three equations (P < 0.001). Despite the good overall agreement in renal drug dosing, we found selected but potentially important discrepancies among the doses rendered from the equations. The CKD-EPI equation non-normalized for body surface area had a greater rate of concordance with the Cockcroft-Gault equation than the Modification of Diet in Renal Disease equation for renal drug dosing. There is need for a long-term multi-centre study in a diverse population to define the clinical effects of the discrepancies among the equations for drug dosing. Given the greater concordance of the non-normalized CKD-EPI equation with the Cockcroft-Gault equation for dosing, the recommendation by Kidney Health Australia and the United States National Kidney Disease Education Program that 'dosing based on either eCrCl or an eGFR with body surface area normalization removed are acceptable' seems suitable and practicable for the purpose of dosing of non-critical drugs in the primary care setting. © 2016 Asian Pacific Society of Nephrology.
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
Geophysical interpretation using integral equations
Eskola, L
1992-01-01
Along with the general development of numerical methods in pure and applied to apply integral equations to geophysical modelling has sciences, the ability improved considerably within the last thirty years or so. This is due to the successful derivation of integral equations that are applicable to the modelling of complex structures, and efficient numerical algorithms for their solution. A significant stimulus for this development has been the advent of fast digital computers. The purpose of this book is to give an idea of the principles by which boundary-value problems describing geophysical models can be converted into integral equations. The end results are the integral formulas and integral equations that form the theoretical framework for practical applications. The details of mathematical analysis have been kept to a minimum. Numerical algorithms are discussed only in connection with some illustrative examples involving well-documented numerical modelling results. The reader is assu med to have a back...
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quan- tum gravity ... than the observation verifying the prediction of theory. This gave .... which was now expanding, would have had a singular beginning in a hot Big Bang.
Kinetic equations in dirty superconductors
International Nuclear Information System (INIS)
Kraehenbuehl, Y.
1981-01-01
Kinetic equations for superconductors in the dirty limit are derived using a method developed for superfluid systems, which allows a systematic expansion in small parameters; exact charge conservation is obeyed. (orig.)
International Nuclear Information System (INIS)
Skyrme, T.H.R.
1994-01-01
In a model quantum theory of interacting mesons, the motion of certain conserved particle-like structures is discussed. It is shown how collective coordinates may be introduced to describe them, leading, in lowest approximation, to a Dirac equation. (author)
Solving Differential Equations in R
Although R is still predominantly applied for statistical analysis and graphical representation, it is rapidly becoming more suitable for mathematical computing. One of the fields where considerable progress has been made recently is the solution of differential equations. Here w...
Wave-equation dispersion inversion
Li, Jing; Feng, Zongcai; Schuster, Gerard T.
2016-01-01
We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained
International Nuclear Information System (INIS)
Jannussis, A.; Streclas, A.; Sourlas, D.; Vlachos, K.
1977-01-01
Using the theorem of the derivative of a function of operators with respect to any parameter, we can find the equation of motion of a system in classical mechanics, in canonical as well as in non-canonical mechanics
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
Lorentz Covariance of Langevin Equation
International Nuclear Information System (INIS)
Koide, T.; Denicol, G.S.; Kodama, T.
2008-01-01
Relativistic covariance of a Langevin type equation is discussed. The requirement of Lorentz invariance generates an entanglement between the force and noise terms so that the noise itself should not be a covariant quantity. (author)
Equational theories of tropical sernirings
DEFF Research Database (Denmark)
Aceto, Luca; Esik, Zoltan; Ingolfsdottir, Anna
2003-01-01
examples of such structures are the (max,+) semiring and the tropical semiring. It is shown that none of the exotic semirings commonly considered in the literature has a finite basis for its equations, and that similar results hold for the commutative idempotent weak semirings that underlie them. For each......This paper studies the equational theories of various exotic semirings presented in the literature. Exotic semirings are semirings whose underlying carrier set is some subset of the set of real numbers equipped with binary operations of minimum or maximum as sum, and addition as product. Two prime...... of these commutative idempotent weak semirings, the paper offers characterizations of the equations that hold in them, decidability results for their equational theories, explicit descriptions of the free algebras in the varieties they generate, and relative axiomatization results. Udgivelsesdato: APR 11...
Global dynamics and control of a comprehensive nonlinear beam equation
International Nuclear Information System (INIS)
You Yuncheng; Taboada, M.
1994-01-01
A nonlinear hinged extensible elastic beam equation with the structural damping and Balakrishnan-Taylor damping of full exponent is studied as a general model for large space structures. It is proved that there exists an absorbing set in the energy space and that there exist inertial manifolds whose exponential attracting rates however are nonuniform. The control spillover problem associated with the stabilization of this equation is resolved by constructing a linear finite-dimensional feedback control based on the existence of inertial manifolds of the uncontrolled equation. Moreover, the results obtained are robust with respect to uncertainty in the structural parameters. (author). 5 refs
Feynman integrals and difference equations
International Nuclear Information System (INIS)
Moch, S.; Schneider, C.
2007-09-01
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called ΠΣ * -fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)
Hidden Statistics of Schroedinger Equation
Zak, Michail
2011-01-01
Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schr dinger equation; i.e., to expose the transitional stochastic process as a "bridge" to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods.
Feynman integrals and difference equations
Energy Technology Data Exchange (ETDEWEB)
Moch, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation
2007-09-15
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called {pi}{sigma}{sup *}-fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)
Illness-death model: statistical perspective and differential equations.
Brinks, Ralph; Hoyer, Annika
2018-01-27
The aim of this work is to relate the theory of stochastic processes with the differential equations associated with multistate (compartment) models. We show that the Kolmogorov Forward Differential Equations can be used to derive a relation between the prevalence and the transition rates in the illness-death model. Then, we prove mathematical well-definedness and epidemiological meaningfulness of the prevalence of the disease. As an application, we derive the incidence of diabetes from a series of cross-sections.
Numerical Analysis for Stochastic Partial Differential Delay Equations with Jumps
Li, Yan; Hu, Junhao
2013-01-01
We investigate the convergence rate of Euler-Maruyama method for a class of stochastic partial differential delay equations driven by both Brownian motion and Poisson point processes. We discretize in space by a Galerkin method and in time by using a stochastic exponential integrator. We generalize some results of Bao et al. (2011) and Jacob et al. (2009) in finite dimensions to a class of stochastic partial differential delay equations with jumps in infinite dimensions.
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
Computational partial differential equations using Matlab
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
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
Equationally Compact Acts : Coproducts / Peeter Normak
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
Validation of constitutive equations for steel
International Nuclear Information System (INIS)
Valentin, T.; Magain, P.; Quik, M.; Labibes, K.; Albertini, C.
1997-01-01
High strain rate mechanical properties are a major concern for each steel manufacturer, especially with respect to thin sheet steel used in the automotive branch. We began to study this topic by starting a project with the following goals: acquiring reliable experimental data, understanding in depth the energy absorption in thin sheet steel and finding the right constitutive material equation. The first part of the project has been presented in. In this paper we present data computation and comparison with the existing material model theories to exploit the experimental data. (orig.)
Spectrum of the ballooning Schroedinger equation
International Nuclear Information System (INIS)
Dewar, R.L.
1997-01-01
The ballooning Schroedinger equation (BSE) is a model equation for investigating global modes that can, when approximated by a Wentzel-Kramers-Brillouin (WKB) ansatz, be described by a ballooning formalism locally to a field line. This second order differential equation with coefficients periodic in the independent variable θ k is assumed to apply even in cases where simple WKB quantization conditions break down, thus providing an alternative to semiclassical quantization. Also, it provides a test bed for developing more advanced WKB methods: e.g. the apparent discontinuity between quantization formulae for open-quotes trappedclose quotes and open-quotes passingclose quotes modes, whose ray paths have different topologies, is removed by extending the WKB method to include the phenomena of tunnelling and reflection. The BSE is applied to instabilities with shear in the real part of the local frequency, so that the dispersion relation is inherently complex. As the frequency shear is increased, it is found that trapped modes go over to passing modes, reducing the maximum growth rate by averaging over θ k
Iterative solution of the Helmholtz equation
Energy Technology Data Exchange (ETDEWEB)
Larsson, E.; Otto, K. [Uppsala Univ. (Sweden)
1996-12-31
We have shown that the numerical solution of the two-dimensional Helmholtz equation can be obtained in a very efficient way by using a preconditioned iterative method. We discretize the equation with second-order accurate finite difference operators and take special care to obtain non-reflecting boundary conditions. We solve the large, sparse system of equations that arises with the preconditioned restarted GMRES iteration. The preconditioner is of {open_quotes}fast Poisson type{close_quotes}, and is derived as a direct solver for a modified PDE problem.The arithmetic complexity for the preconditioner is O(n log{sub 2} n), where n is the number of grid points. As a test problem we use the propagation of sound waves in water in a duct with curved bottom. Numerical experiments show that the preconditioned iterative method is very efficient for this type of problem. The convergence rate does not decrease dramatically when the frequency increases. Compared to banded Gaussian elimination, which is a standard solution method for this type of problems, the iterative method shows significant gain in both storage requirement and arithmetic complexity. Furthermore, the relative gain increases when the frequency increases.
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.)
Abstract methods in partial differential equations
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.
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.)
ON THE EQUIVALENCE OF THE ABEL EQUATION
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This article uses the reflecting function of Mironenko to study some complicated differential equations which are equivalent to the Abel equation. The results are applied to discuss the behavior of solutions of these complicated differential equations.
Exact solitary waves of the Fisher equation
International Nuclear Information System (INIS)
Kudryashov, Nikolai A.
2005-01-01
New method is presented to search exact solutions of nonlinear differential equations. This approach is used to look for exact solutions of the Fisher equation. New exact solitary waves of the Fisher equation are given
Differential equations with applications in cancer diseases.
Ilea, M; Turnea, M; Rotariu, M
2013-01-01
Mathematical modeling is a process by which a real world problem is described by a mathematical formulation. The cancer modeling is a highly challenging problem at the frontier of applied mathematics. A variety of modeling strategies have been developed, each focusing on one or more aspects of cancer. The vast majority of mathematical models in cancer diseases biology are formulated in terms of differential equations. We propose an original mathematical model with small parameter for the interactions between these two cancer cell sub-populations and the mathematical model of a vascular tumor. We work on the assumption that, the quiescent cells' nutrient consumption is long. One the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. MATLAB simulations obtained for transition rate from the quiescent cells' nutrient consumption is long, we show a similar asymptotic behavior for two solutions of the perturbed problem. In this system, the small parameter is an asymptotic variable, different from the independent variable. The graphical output for a mathematical model of a vascular tumor shows the differences in the evolution of the tumor populations of proliferating, quiescent and necrotic cells. The nutrient concentration decreases sharply through the viable rim and tends to a constant level in the core due to the nearly complete necrosis in this region. Many mathematical models can be quantitatively characterized by ordinary differential equations or partial differential equations. The use of MATLAB in this article illustrates the important role of informatics in research in mathematical modeling. The study of avascular tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.
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
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.
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
Differential equations, mechanics, and computation
Palais, Richard S
2009-01-01
This book provides a conceptual introduction to the theory of ordinary differential equations, concentrating on the initial value problem for equations of evolution and with applications to the calculus of variations and classical mechanics, along with a discussion of chaos theory and ecological models. It has a unified and visual introduction to the theory of numerical methods and a novel approach to the analysis of errors and stability of various numerical solution algorithms based on carefully chosen model problems. While the book would be suitable as a textbook for an undergraduate or elementary graduate course in ordinary differential equations, the authors have designed the text also to be useful for motivated students wishing to learn the material on their own or desiring to supplement an ODE textbook being used in a course they are taking with a text offering a more conceptual approach to the subject.
Generalized equations of gravitational field
International Nuclear Information System (INIS)
Stanyukovich, K.P.; Borisova, L.B.
1985-01-01
Equations for gravitational fields are obtained on the basis of a generalized Lagrangian Z=f(R) (R is the scalar curvature). Such an approach permits to take into account the evolution of a gravitation ''constant''. An expression for the force Fsub(i) versus the field variability is obtained. Conservation laws are formulated differing from the standard ones by the fact that in the right part of new equations the value Fsub(i) is present that goes to zero at an ultimate passage to the standard Einstein theory. An equation of state is derived for cosmological metrics for a particular case, f=bRsup(1+α) (b=const, α=const)
Numerical optimization using flow equations
Punk, Matthias
2014-12-01
We develop a method for multidimensional optimization using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimizing functional correspond to fixed points of the flow equation. While ideas based on Bayesian inference such as the maximum entropy method always depend on a prior probability, the additional step in our approach is to perform a continuous update of the prior during the homotopy flow. The prior probability thus enters the flow equation only as an initial condition. We demonstrate the applicability of this optimization method for two paradigmatic problems in theoretical condensed matter physics: numerical analytic continuation from imaginary to real frequencies and finding (variational) ground states of frustrated (quantum) Ising models with random or long-range antiferromagnetic interactions.
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.
Introductory course on differential equations
Gorain, Ganesh C
2014-01-01
Introductory Course on DIFFERENTIAL EQUATIONS provides an excellent exposition of the fundamentals of ordinary and partial differential equations and is ideally suited for a first course of undergraduate students of mathematics, physics and engineering. The aim of this book is to present the elementary theories of differential equations in the forms suitable for use of those students whose main interest in the subject are based on simple mathematical ideas. KEY FEATURES: Discusses the subject in a systematic manner without sacrificing mathematical rigour. A variety of exercises drill the students in problem solving in view of the mathematical theories explained in the book. Worked out examples illustrated according to the theories developed in the book with possible alternatives. Exhaustive collection of problems and the simplicity of presentation differentiate this book from several others. Material contained will help teachers as well as aspiring students of different competitive examinations.
The respiratory system in equations
Maury, Bertrand
2013-01-01
The book proposes an introduction to the mathematical modeling of the respiratory system. A detailed introduction on the physiological aspects makes it accessible to a large audience without any prior knowledge on the lung. Different levels of description are proposed, from the lumped models with a small number of parameters (Ordinary Differential Equations), up to infinite dimensional models based on Partial Differential Equations. Besides these two types of differential equations, two chapters are dedicated to resistive networks, and to the way they can be used to investigate the dependence of the resistance of the lung upon geometrical characteristics. The theoretical analysis of the various models is provided, together with state-of-the-art techniques to compute approximate solutions, allowing comparisons with experimental measurements. The book contains several exercises, most of which are accessible to advanced undergraduate students.
Dynamics of partial differential equations
Wayne, C Eugene
2015-01-01
This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties, and results about radiation damping where waves lose energy through radiation. The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equ...
Evolution equations for Killing fields
International Nuclear Information System (INIS)
Coll, B.
1977-01-01
The problem of finding necessary and sufficient conditions on the Cauchy data for Einstein equations which insure the existence of Killing fields in a neighborhood of an initial hypersurface has been considered recently by Berezdivin, Coll, and Moncrief. Nevertheless, it can be shown that the evolution equations obtained in all these cases are of nonstrictly hyperbolic type, and, thus, the Cauchy data must belong to a special class of functions. We prove here that, for the vacuum and Einstein--Maxwell space--times and in a coordinate independent way, one can always choose, as evolution equations for the Killing fields, a strictly hyperbolic system: The above theorems can be thus extended to all Cauchy data for which the Einstein evolution problem has been proved to be well set
Quasisymmetry equations for conventional stellarators
International Nuclear Information System (INIS)
Pustovitov, V.D.
1994-11-01
General quasisymmetry condition, which demands the independence of B 2 on one of the angular Boozer coordinates, is reduced to two equations containing only geometrical characteristics and helical field of a stellarator. The analysis is performed for conventional stellarators with a planar circular axis using standard stellarator expansion. As a basis, the invariant quasisymmetry condition is used. The quasisymmetry equations for stellarators are obtained from this condition also in an invariant form. Simplified analogs of these equations are given for the case when averaged magnetic surfaces are circular shifted torii. It is shown that quasisymmetry condition can be satisfied, in principle, in a conventional stellarator by a proper choice of two satellite harmonics of the helical field in addition to the main harmonic. Besides, there appears a restriction on the shift of magnetic surfaces. Thus, in general, the problem is closely related with that of self-consistent description of a configuration. (author)
The generalized good cut equation
International Nuclear Information System (INIS)
Adamo, T M; Newman, E T
2010-01-01
The properties of null geodesic congruences (NGCs) in Lorentzian manifolds are a topic of considerable importance. More specifically NGCs with the special property of being shear-free or asymptotically shear-free (as either infinity or a horizon is approached) have received a great deal of recent attention for a variety of reasons. Such congruences are most easily studied via solutions to what has been referred to as the 'good cut equation' or the 'generalization good cut equation'. It is the purpose of this paper to study these equations and show their relationship to each other. In particular we show how they all have a four-complex-dimensional manifold (known as H-space, or in a special case as complex Minkowski space) as a solution space.
Integration rules for scattering equations
International Nuclear Information System (INIS)
Baadsgaard, Christian; Bjerrum-Bohr, N.E.J.; Bourjaily, Jacob L.; Damgaard, Poul H.
2015-01-01
As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints for any Möbius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory.
Coupled Higgs field equation and Hamiltonian amplitude equation ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 79; Issue 1. Coupled Higgs ﬁeld equation and ... School of Mathematics and Computer Applications, Thapar University, Patiala 147 004, India; Department of Mathematics, Jaypee University of Information Technology, Waknaghat, Distt. Solan 173 234, India ...
Coupled Higgs field equation and Hamiltonian amplitude equation ...
Indian Academy of Sciences (India)
the rational functions are obtained. Keywords. ... differential equations as is evident by the number of research papers, books and a new symbolic software .... Now using (2.11), (2.14) in (2.8) with C1 = 0 and integrating once we get. P. 2 = − β.
Lower Bounds for Possible Singular Solutions for the Navier-Stokes and Euler Equations Revisited
Cortissoz, Jean C.; Montero, Julio A.
2018-03-01
In this paper we give optimal lower bounds for the blow-up rate of the \\dot{H}s( T^3) -norm, 1/2Navier-Stokes equations, and we also present an elementary proof for a lower bound on blow-up rate of the Sobolev norms of possible singular solutions to the Euler equations when s>5/2.
International Nuclear Information System (INIS)
Kahana, S.
1986-01-01
The role of the nuclear equation of state in determining the fate of the collapsing cores of massive stars is examined in light of both recent theoretical advances in this subject and recent experimental measurements with relativistic heavy ions. The difficulties existing in attempts to bring the softer nuclear matter apparently required by the theory of Type II supernovae into consonance with the heavy ion data are discussed. Relativistic mean field theory is introduced as a candidate for derivation of the equation of state, and a simple form for the saturation compressibility is obtained. 28 refs., 4 figs., 1 tab
Kinetic equations with pairing correlations
International Nuclear Information System (INIS)
Fauser, R.
1995-12-01
The Gorkov equations are derived for a general non-equilibrium system. The Gorkov factorization is generalized by the cumulant expansion of the 2-particle correlation and by a generalized Wick theorem in the case of a perturbation expansion. A stationary solution for the Green functions in the Schwinger-Keldysh formalism is presented taking into account pairing correlations. Especially the effects of collisional broadening on the spectral functions and Green functions is discussed. Kinetic equations are derived in the quasi-particle approximation and in the case of particles with width. Explicit expressions for the self-energies are given. (orig.)
Partial differential equations an introduction
Colton, David
2004-01-01
Intended for a college senior or first-year graduate-level course in partial differential equations, this text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Classical topics presented in a modern context include coverage of integral equations and basic scattering theory. This complete and accessible treatment includes a variety of examples of inverse problems arising from improperly posed applications. Exercises at the ends of chapters, many with answers, offer a clear progression in developing an understanding of
Geometric approach to soliton equations
International Nuclear Information System (INIS)
Sasaki, R.
1979-09-01
A class of nonlinear equations that can be solved in terms of nxn scattering problem is investigated. A systematic geometric method of exploiting conservation laws and related equations, the so-called prolongation structure, is worked out. The nxn problem is reduced to nsub(n-1)x(n-1) problems and finally to 2x2 problems, which have been comprehensively investigated recently by the author. A general method of deriving the infinite numbers of polynomial conservation laws for an nxn problem is presented. The cases of 3x3 and 2x2 problems are discussed explicitly. (Auth.)
Sensitivity for the Smoluchowski equation
International Nuclear Information System (INIS)
Bailleul, I F
2011-01-01
This paper investigates the question of sensitivity of the solutions μ λ t of the Smoluchowski equation on R + * with respect to the parameters λ in the interaction kernel K λ . It is proved that μ λ t is a C 1 function of (t, λ) with values in a good space of measures under the hypotheses K λ (x, y) ≤ ψ(x) ψ(y), for some sub-linear function ψ, and ∫ψ 4+ε (x) μ 0 (dx) < ∞, and that the derivative is the unique solution of a related equation.
Basic linear partial differential equations
Treves, Francois
1975-01-01
Focusing on the archetypes of linear partial differential equations, this text for upper-level undergraduates and graduate students features most of the basic classical results. The methods, however, are decidedly nontraditional: in practically every instance, they tend toward a high level of abstraction. This approach recalls classical material to contemporary analysts in a language they can understand, as well as exploiting the field's wealth of examples as an introduction to modern theories.The four-part treatment covers the basic examples of linear partial differential equations and their
Energy Technology Data Exchange (ETDEWEB)
Kahana, S.
1986-01-01
The role of the nuclear equation of state in determining the fate of the collapsing cores of massive stars is examined in light of both recent theoretical advances in this subject and recent experimental measurements with relativistic heavy ions. The difficulties existing in attempts to bring the softer nuclear matter apparently required by the theory of Type II supernovae into consonance with the heavy ion data are discussed. Relativistic mean field theory is introduced as a candidate for derivation of the equation of state, and a simple form for the saturation compressibility is obtained. 28 refs., 4 figs., 1 tab.
Solution of the Baxter equation
International Nuclear Information System (INIS)
Janik, R.A.
1996-01-01
We present a method of construction of a family of solutions of the Baxter equation arising in the Generalized Leading Logarithmic Approximation (GLLA) of the QCD pomeron. The details are given for the exchange of N = 2 reggeons but everything can be generalized in a straightforward way to arbitrary N. A specific choice of solutions is shown to reproduce the correct energy levels for half integral conformal weights. It is shown that the Baxter's equation must be supplemented by an additional condition on the solution. (author)
Fundamentals of equations of state
Eliezer, Shalom; Hora, Heinrich
2002-01-01
The equation of state was originally developed for ideal gases, and proved central to the development of early molecular and atomic physics. Increasingly sophisticated equations of state have been developed to take into account molecular interactions, quantization, relativistic effects, etc. Extreme conditions of matter are encountered both in nature and in the laboratory, for example in the centres of stars, in relativistic collisions of heavy nuclei, in inertial confinement fusion (where a temperature of 10 9 K and a pressure exceeding a billion atmospheres can be achieved). A sound knowledg
Nielsen number and differential equations
Directory of Open Access Journals (Sweden)
Andres Jan
2005-01-01
Full Text Available In reply to a problem of Jean Leray (application of the Nielsen theory to differential equations, two main approaches are presented. The first is via Poincaré's translation operator, while the second one is based on the Hammerstein-type solution operator. The applicability of various Nielsen theories is discussed with respect to several sorts of differential equations and inclusions. Links with the Sharkovskii-like theorems (a finite number of periodic solutions imply infinitely many subharmonics are indicated, jointly with some further consequences like the nontrivial -structure of solutions of initial value problems. Some illustrating examples are supplied and open problems are formulated.
Applied analysis and differential equations
Cârj, Ovidiu
2007-01-01
This volume contains refereed research articles written by experts in the field of applied analysis, differential equations and related topics. Well-known leading mathematicians worldwide and prominent young scientists cover a diverse range of topics, including the most exciting recent developments. A broad range of topics of recent interest are treated: existence, uniqueness, viability, asymptotic stability, viscosity solutions, controllability and numerical analysis for ODE, PDE and stochastic equations. The scope of the book is wide, ranging from pure mathematics to various applied fields such as classical mechanics, biomedicine, and population dynamics.
Sequent Calculus and Equational Programming
Directory of Open Access Journals (Sweden)
Nicolas Guenot
2015-07-01
Full Text Available Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus. A typed functional language is presented, based on a sequent calculus, that we relate to the syntax and internal language of Agda. In particular, we discuss the use of patterns and case splittings, as well as rules implementing inductive reasoning and dependent products and sums.
Radar equations for modern radar
Barton, David K
2012-01-01
Based on the classic Radar Range-Performance Analysis from 1980, this practical volume extends that work to ensure applicability of radar equations to the design and analysis of modern radars. This unique book helps you identify what information on the radar and its environment is needed to predict detection range. Moreover, it provides equations and data to improve the accuracy of range calculations. You find detailed information on propagation effects, methods of range calculation in environments that include clutter, jamming and thermal noise, as well as loss factors that reduce radar perfo
Ground Motion Prediction Equations Empowered by Stress Drop Measurement
Miyake, H.; Oth, A.
2015-12-01
Significant variation of stress drop is a crucial issue for ground motion prediction equations and probabilistic seismic hazard assessment, since only a few ground motion prediction equations take into account stress drop. In addition to average and sigma studies of stress drop and ground motion prediction equations (e.g., Cotton et al., 2013; Baltay and Hanks, 2014), we explore 1-to-1 relationship for each earthquake between stress drop and between-event residual of a ground motion prediction equation. We used the stress drop dataset of Oth (2013) for Japanese crustal earthquakes ranging 0.1 to 100 MPa and K-NET/KiK-net ground motion dataset against for several ground motion prediction equations with volcanic front treatment. Between-event residuals for ground accelerations and velocities are generally coincident with stress drop, as investigated by seismic intensity measures of Oth et al. (2015). Moreover, we found faster attenuation of ground acceleration and velocities for large stress drop events for the similar fault distance range and focal depth. It may suggest an alternative parameterization of stress drop to control attenuation distance rate for ground motion prediction equations. We also investigate 1-to-1 relationship and sigma for regional/national-scale stress drop variation and current national-scale ground motion equations.
Efficient Estimating Functions for Stochastic Differential Equations
DEFF Research Database (Denmark)
Jakobsen, Nina Munkholt
The overall topic of this thesis is approximate martingale estimating function-based estimationfor solutions of stochastic differential equations, sampled at high frequency. Focuslies on the asymptotic properties of the estimators. The first part of the thesis deals with diffusions observed over...... a fixed time interval. Rate optimal and effcient estimators areobtained for a one-dimensional diffusion parameter. Stable convergence in distribution isused to achieve a practically applicable Gaussian limit distribution for suitably normalisedestimators. In a simulation example, the limit distributions...... multidimensional parameter. Conditions for rate optimality and effciency of estimatorsof drift-jump and diffusion parameters are given in some special cases. Theseconditions are found to extend the pre-existing conditions applicable to continuous diffusions,and impose much stronger requirements on the estimating...
Navier-Stokes equations on R3 × [0, T
Stenger, Frank; Baumann, Gerd
2016-01-01
In this monograph, leading researchers in the world of numerical analysis, partial differential equations, and hard computational problems study the properties of solutions of the Navier–Stokes partial differential equations on (x, y, z, t) ∈ ℝ3 × [0, T]. Initially converting the PDE to a system of integral equations, the authors then describe spaces A of analytic functions that house solutions of this equation, and show that these spaces of analytic functions are dense in the spaces S of rapidly decreasing and infinitely differentiable functions. This method benefits from the following advantages: The functions of S are nearly always conceptual rather than explicit Initial and boundary conditions of solutions of PDE are usually drawn from the applied sciences, and as such, they are nearly always piece-wise analytic, and in this case, the solutions have the same properties When methods of approximation are applied to functions of A they converge at an exponential rate, whereas methods of approximation ...
Equating accelerometer estimates among youth
DEFF Research Database (Denmark)
Brazendale, Keith; Beets, Michael W; Bornstein, Daniel B
2016-01-01
from one set of cutpoints into another. Bland Altman plots illustrate the agreement between actual MVPA and predicted MVPA values. RESULTS: Across the total sample, mean MVPA ranged from 29.7MVPAmind(-1) (Puyau) to 126.1MVPAmind(-1) (Freedson 3 METs). Across conversion equations, median absolute...
Variational linear algebraic equations method
International Nuclear Information System (INIS)
Moiseiwitsch, B.L.
1982-01-01
A modification of the linear algebraic equations method is described which ensures a variational bound on the phaseshifts for potentials having a definite sign at all points. The method is illustrated by the elastic scattering of s-wave electrons by the static field of atomic hydrogen. (author)
Integrodifferential equation approach. Pt. 1
International Nuclear Information System (INIS)
Oehm, W.; Sofianos, S.A.; Fiedeldey, H.; South Africa Univ., Pretoria. Dept. of Physics); Fabre de la Ripelle, M.; South Africa Univ., Pretoria. Dept. of Physics)
1990-02-01
A single integrodifferential equation in two variables, valid for A nucleons interacting by pure Wigner forces, which has previously only been solved in the extreme and uncoupled adiabatic approximations is now solved exactly for three- and four-nucleon systems. The results are in good agreement with the values obtained for the binding energies by means of an empirical interpolation formula. This validates all our previous conclusions, in particular that the omission of higher (than two) order correlations in our four-body equation only produces a rather small underbinding. The integrodifferential equation approach (IDEA) is here also extended to spin-dependent forces of the Malfliet-Tjon type, resulting in two coupled integrodifferential equations in two variables. The exact solution and the interpolated adiabatic approximation are again in good agreement. The inclusion of the hypercentral part of the two-body interaction in the definition of the Faddeev-type components again leads to substantial improvement for fully local potentials, acting in all partial waves. (orig.)
A generalized advection dispersion equation
Indian Academy of Sciences (India)
This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of.
Nonlocal higher order evolution equations
Rossi, Julio D.; Schö nlieb, Carola-Bibiane
2010-01-01
In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove
International Nuclear Information System (INIS)
Crowe, C.T.
1975-01-01
General features of a vapor-droplet flow are discussed and the equations expressing the conservation of mass, momentum, and energy for the vapor, liquid, and mixture using the control volume approach are derived. The phenomenological laws describing the exchange of mass, momentum, and energy between phases are also reviewed. The results have application to development of water-dominated geothermal resources
Saha equation in Rindler space
Indian Academy of Sciences (India)
Sanchari De
2017-05-31
May 31, 2017 ... scenario, the flat local geometry is called the Rindler space. For an illustration, let us consider two reference ... the local acceleration of the frame. To investigate Saha equation in a uniformly acceler- ... the best of our knowledge, the study of Saha equa- tion in Rindler space has not been reported earlier.
Slave equations for spin models
International Nuclear Information System (INIS)
Catterall, S.M.; Drummond, I.T.; Horgan, R.R.
1992-01-01
We apply an accelerated Langevin algorithm to the simulation of continuous spin models on the lattice. In conjunction with the evolution equation for the spins we use slave equations to compute estimators for the connected correlation functions of the model. In situations for which the symmetry of the model is sufficiently strongly broken by an external field these estimators work well and yield a signal-to-noise ratio for the Green function at large time separations more favourable than that resulting from the standard method. With the restoration of symmetry, however, the slave equation estimators exhibit an intrinsic instability associated with the growth of a power law tail in the probability distributions for the measured quantities. Once this tail has grown sufficiently strong it results in a divergence of the variance of the estimator which then ceases to be useful for measurement purposes. The instability of the slave equation method in circumstances of weak symmetry breaking precludes its use in determining the mass gap in non-linear sigma models. (orig.)
Pendulum Motion and Differential Equations
Reid, Thomas F.; King, Stephen C.
2009-01-01
A common example of real-world motion that can be modeled by a differential equation, and one easily understood by the student, is the simple pendulum. Simplifying assumptions are necessary for closed-form solutions to exist, and frequently there is little discussion of the impact if those assumptions are not met. This article presents a…
Elizarova, Tatiana G
2009-01-01
This book presents two interconnected mathematical models generalizing the Navier-Stokes system. The models, called the quasi-gas-dynamic and quasi-hydrodynamic equations, are then used as the basis of numerical methods solving gas- and fluid-dynamic problems.
Stability of Functional Differential Equations
Lemm, Jeffrey M
1986-01-01
This book provides an introduction to the structure and stability properties of solutions of functional differential equations. Numerous examples of applications (such as feedback systrems with aftereffect, two-reflector antennae, nuclear reactors, mathematical models in immunology, viscoelastic bodies, aeroautoelastic phenomena and so on) are considered in detail. The development is illustrated by numerous figures and tables.
Quantum adiabatic Markovian master equations
International Nuclear Information System (INIS)
Albash, Tameem; Zanardi, Paolo; Boixo, Sergio; Lidar, Daniel A
2012-01-01
We develop from first principles Markovian master equations suited for studying the time evolution of a system evolving adiabatically while coupled weakly to a thermal bath. We derive two sets of equations in the adiabatic limit, one using the rotating wave (secular) approximation that results in a master equation in Lindblad form, the other without the rotating wave approximation but not in Lindblad form. The two equations make markedly different predictions depending on whether or not the Lamb shift is included. Our analysis keeps track of the various time and energy scales associated with the various approximations we make, and thus allows for a systematic inclusion of higher order corrections, in particular beyond the adiabatic limit. We use our formalism to study the evolution of an Ising spin chain in a transverse field and coupled to a thermal bosonic bath, for which we identify four distinct evolution phases. While we do not expect this to be a generic feature, in one of these phases dissipation acts to increase the fidelity of the system state relative to the adiabatic ground state. (paper)
Weak solutions of magma equations
International Nuclear Information System (INIS)
Krishnan, E.V.
1999-01-01
Periodic solutions in terms of Jacobian cosine elliptic functions have been obtained for a set of values of two physical parameters for the magma equation which do not reduce to solitary-wave solutions. It was also obtained solitary-wave solutions for another set of these parameters as an infinite period limit of periodic solutions in terms of Weierstrass and Jacobian elliptic functions
Wave-equation dispersion inversion
Li, Jing
2016-12-08
We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.
Solutions of Einstein's field equations
Energy Technology Data Exchange (ETDEWEB)
Tomonaga, Y [Utsunomiya Univ. (Japan). Faculty of Education
1978-12-01
In this paper the author investigates the Einstein's field equations of the non-vacuum case and generalizes the solution of Robertson-Walker by the three dimensional Einstein spaces. In Section 2 the author shortly generalizes the dynamic space-time of G. Lemetre and A. Friedmann by a simple transformation.
Equations for formally real meadows
Bergstra, J.A.; Bethke, I.; Ponse, A.
2015-01-01
We consider the signatures Σm = (0,1,−,+,⋅,−1) of meadows and (Σm,s) of signed meadows. We give two complete axiomatizations of the equational theories of the real numbers with respect to these signatures. In the first case, we extend the axiomatization of zero-totalized fields by a single axiom
Wave equation of hydrogen atom
International Nuclear Information System (INIS)
Suwito.
1977-01-01
The calculation of the energy levels of the hydrogen atom using Bohr, Schroedinger and Dirac theories is reviewed. The result is compared with that obtained from infinite component wave equations theory which developed recently. The conclusion can be stated that the latter theory is better to describe the composit system than the former. (author)
Transport equation and shock waves
International Nuclear Information System (INIS)
Besnard, D.
1981-04-01
A multi-group method is derived from a one dimensional transport equation for the slowing down and spatial transport of energetic positive ions in a plasma. This method is used to calculate the behaviour of energetic charged particles in non homogeneous and non stationary plasma, and the effect of energy deposition of the particles on the heating of the plasma. In that purpose, an equation for the density of fast ions is obtained from the Fokker-Planck equation, and a closure condition for the second moment of this equation is deduced from phenomenological considerations. This method leads to a numerical method, simple and very efficient, which doesn't require much computer storage. Two types of numerical results are obtained. First, results on the slowing down of 3.5 MeV alpha particles in a 50 keV plasma plublished by Corman and al and Moses are compared with the results obtained with both our method and a Monte Carlo type method. Good agreement was obtained, even for energy deposition on the ions of the plasma. Secondly, we have calculated propagation of alpha particles heating a cold plasma. These results are in very good agreement with those given by an accurate Monte Carlo method, for both the thermal velocity, and the energy deposition in the plasma
Structural equations in language learning
Moortgat, M.J.
In categorial systems with a fixed structural component, the learning problem comes down to finding the solution for a set of typeassignment equations. A hard-wired structural component is problematic if one want to address issues of structural variation. Our starting point is a type-logical
Fractional Diffusion Equations and Anomalous Diffusion
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.
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
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.
Algebraic entropy for differential-delay equations
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.
Invariant imbedding equations for linear scattering problems
International Nuclear Information System (INIS)
Apresyan, L.
1988-01-01
A general form of the invariant imbedding equations is investigated for the linear problem of scattering by a bounded scattering volume. The conditions for the derivability of such equations are described. It is noted that the possibility of the explicit representation of these equations for a sphere and for a layer involves the separation of variables in the unperturbed wave equation
Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions
Directory of Open Access Journals (Sweden)
Zakieh Avazzadeh
2014-01-01
Full Text Available We solve some different type of Urysohn integral equations by using the radial basis functions. These types include the linear and nonlinear Fredholm, Volterra, and mixed Volterra-Fredholm integral equations. Our main aim is to investigate the rate of convergence to solve these equations using the radial basis functions which have normic structure that utilize approximation in higher dimensions. Of course, the use of this method often leads to ill-posed systems. Thus we propose an algorithm to improve the results. Numerical results show that this method leads to the exponential convergence for solving integral equations as it was already confirmed for partial and ordinary differential equations.
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
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....
Feynman-Kac equations for reaction and diffusion processes
Hou, Ru; Deng, Weihua
2018-04-01
This paper provides a theoretical framework for deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and reaction processes. Once given the diffusion type and reaction rate, a specific forward or backward Feynman-Kac equation can be obtained. The results in this paper include those for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we apply our findings to compute some physical (experimentally measurable) statistics, including the occupation time in half-space, the first passage time, and the occupation time in half-interval with an absorbing or reflecting boundary, for the physical system with anomalous diffusion and spontaneous evanescence.
Manhattan equation for the operational amplifier
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...
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
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
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.