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Analytical Approximation (analytical + approximation)
Selected AbstractsTemporal autocorrelation and stochastic population growthECOLOGY LETTERS, Issue 3 2006Shripad Tuljapurkar Abstract How much does environmental autocorrelation matter to the growth of structured populations in real life contexts? Interannual variances in vital rates certainly do, but it has been suggested that between-year correlations may not. We present an analytical approximation to stochastic growth rate for multistate Markovian environments and show that it is accurate by testing it in two empirically based examples. We find that temporal autocorrelation has sizeable effect on growth rates of structured populations, larger in many cases than the effect of interannual variability. Our approximation defines a sensitivity to autocorrelated variability, showing how demographic damping and environmental pattern interact to determine a population's stochastic growth rate. [source] An Euler system source term that develops prototype Z-pinch implosions intended for the evaluation of shock-hydro methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2009J. W. Banks Abstract In this paper, a phenomenological model for a magnetic drive source term for the momentum and total energy equations of the Euler system is described. This body force term is designed to produce a Z-pinch like implosion that can be used in the development and evaluation of shock-hydrodynamics algorithms that are intended to be used in Z-pinch simulations. The model uses a J × B Lorentz force, motivated by a 0-D analysis of a thin shell (or liner implosion), as a source term in the equations and allows for arbitrary current drives to be simulated. An extension that would include the multi-physics aspects of a proposed combined radiation hydrodynamics (rad-hydro) capability is also discussed. The specific class of prototype problems that are developed is intended to illustrate aspects of liner implosions into a near vacuum and with idealized pre-fill plasma effects. In this work, a high-resolution flux-corrected-transport method implemented on structured overlapping meshes is used to demonstrate the application of such a model to these idealized shock-hydrodynamic studies. The presented results include an asymptotic solution based on a limiting-case thin-shell analytical approximation in both (x, y) and (r, z). Additionally, a set of more realistic implosion problems that include density profiles approximating plasma pre-fill and a set of perturbed liner geometries that excite a hydro-magnetic like Rayleigh,Taylor instability in the implosion dynamics are demonstrated. Finally, as a demonstration of including and evaluating multiphysics effects in the Euler system, a simple radiation model is included and self-convergence results for two types of (r, z) implosions are presented. Copyright © 2008 John Wiley & Sons, Ltd. [source] Bias in the estimation of non-linear transformations of the integrated variance of returnsJOURNAL OF FORECASTING, Issue 7 2006Richard D. F. Harris Abstract Volatility models such as GARCH, although misspecified with respect to the data-generating process, may well generate volatility forecasts that are unconditionally unbiased. In other words, they generate variance forecasts that, on average, are equal to the integrated variance. However, many applications in finance require a measure of return volatility that is a non-linear function of the variance of returns, rather than of the variance itself. Even if a volatility model generates forecasts of the integrated variance that are unbiased, non-linear transformations of these forecasts will be biased estimators of the same non-linear transformations of the integrated variance because of Jensen's inequality. In this paper, we derive an analytical approximation for the unconditional bias of estimators of non-linear transformations of the integrated variance. This bias is a function of the volatility of the forecast variance and the volatility of the integrated variance, and depends on the concavity of the non-linear transformation. In order to estimate the volatility of the unobserved integrated variance, we employ recent results from the realized volatility literature. As an illustration, we estimate the unconditional bias for both in-sample and out-of-sample forecasts of three non-linear transformations of the integrated standard deviation of returns for three exchange rate return series, where a GARCH(1, 1) model is used to forecast the integrated variance. Our estimation results suggest that, in practice, the bias can be substantial.,,Copyright © 2006 John Wiley & Sons, Ltd. [source] Design of a thermally balanced membrane reformer for hydrogen productionAICHE JOURNAL, Issue 10 2008David S. A. Simakov Abstract Hydrogen production by autothermal methane steam reforming in a catalytic fixed bed membrane reactor has been analyzed and simulated. The two-compartment reactor indirectly couples the endothermic steam reforming with methane oxidation, while hydrogen is separated by a permselective Pd membrane. Simulations of the reactor, using published kinetics, map the acceptable domain of operation and the optimal set of operating parameters. The simulations exhibit slow-moving thermal fronts and the steady-state operation domains bounded by stationary fronts, separating domains of upstream and downstream-moving fronts. Front velocity depends on thermal coupling and hydrogen separation. An analytical approximation for the thermal front velocity in a thermally balanced reactor has been developed. © 2008 American Institute of Chemical Engineers AIChE J, 2008 [source] Pricing American options on foreign currency with stochastic volatility, jumps, and stochastic interest ratesTHE JOURNAL OF FUTURES MARKETS, Issue 9 2007Jia-Hau Guo By applying the Heath,Jarrow,Morton (HJM) framework, an analytical approximation for pricing American options on foreign currency under stochastic volatility and double jump is derived. This approximation is also applied to other existing models for the purpose of comparison. There is evidence that such types of jumps can have a critical impact on earlyexercise premiums that will be significant for deep out-of-the-money options with short maturities. Moreover, the importance of the term structure of interest rates to early-exercise premiums is demonstrated as is the sensitivity of these premiums to correlation-related parameters. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:867,891, 2007 [source] Improved analytical approximation to arbitrary l -state solutions of the Schrödinger equation for the hyperbolical potentialsANNALEN DER PHYSIK, Issue 10-11 2009S.M. Ikhdair Abstract The Schrödinger equation for the rotational-vibrational (ro-vibrational) motion of a diatomic molecule with empirical potential functions is solved approximately by means of the Nikiforov-Uvarov method. The approximate energy spectra and the corresponding normalized total wavefunctions are calculated in closed form and expressed in terms of the hypergeometric functions or Jacobi polynomials Pn(,, ,) (x), where , >,1, , >,1 and x in [,1, +1]. The s-waves analytic solution is obtained. The numerical energy eigenvalues for selected H2 and Ar2 molecules are also calculated and compared with the previous models and experiments. [source] Improved analytical approximation to arbitrary l -state solutions of the Schrödinger equation for the hyperbolical potentialsANNALEN DER PHYSIK, Issue 10-11 2009S.M. Ikhdair Abstract The Schrödinger equation for the rotational-vibrational (ro-vibrational) motion of a diatomic molecule with empirical potential functions is solved approximately by means of the Nikiforov-Uvarov method. The approximate energy spectra and the corresponding normalized total wavefunctions are calculated in closed form and expressed in terms of the hypergeometric functions or Jacobi polynomials Pn(,, ,) (x), where , >,1, , >,1 and x in [,1, +1]. The s-waves analytic solution is obtained. The numerical energy eigenvalues for selected H2 and Ar2 molecules are also calculated and compared with the previous models and experiments. [source] Improved analytical approximation to arbitrary l-state solutions of the Schrödinger equation for the hyperbolical potentialANNALEN DER PHYSIK, Issue 4 2009S.M. Ikhdair Abstract A new approximation scheme to the centrifugal term is proposed to obtain the l =, 0 bound-state solutions of the Schrödinger equation for an exponential-type potential in the framework of the hypergeometric method. The corresponding normalized wave functions are also found in terms of the Jacobi polynomials. To show the accuracy of the new proposed approximation scheme, we calculate the energy eigenvalues numerically for arbitrary quantum numbers n and l with two different values of the potential parameter ,0. Our numerical results are of high accuracy like the other numerical results obtained by using program based on a numerical integration procedure for short-range and long-range potentials. The energy bound-state solutions for the s-wave (l = 0) and ,0 = 1 cases are given. [source] Metal enrichment of the intracluster medium: SN-driven galactic windsASTRONOMISCHE NACHRICHTEN, Issue 9-10 2009V. Baumgartner Abstract We investigate the role of supernova (SN)-driven galactic winds in the chemical enrichment of the intracluster medium (ICM). Such outflows on galactic scales have their origin in huge star forming regions and expel metal enriched material out ofthe galaxies into their surroundings as observed, for example, in the nearby starburst galaxy NGC 253. As massive stars in OB-associations explode sequentially, shock waves are driven into the interstellar medium (ISM) of a galaxy and merge, forming a superbubble (SB). These SBs expand in a direction perpendicular to the disk plane following the density gradient of the ISM. We use the 2D analytical approximation by Kompaneets (1960) to model the expansion of SBs in an exponentially stratified ISM. This is modified in order to describe the sequence of SN-explosions as a time-dependent process taking into account the main-sequence life-time of the SN-progenitors and using an initial mass function to get the number of massive stars per mass interval. The evolution of the bubble in space and time is calculated analytically, from which the onset of Rayleigh-Taylor instabilities in the shell can be determined. In its further evolution, the shell will break up and high-metallicity gas will be ejected into the halo ofthe galaxy and even into the ICM. We derive the number of stars needed for blow-out depending on the scale height and density ofthe ambient medium, as well as the fraction of alpha- and iron peak elements contained in the hot gas. Finally, the amount of metals injected by Milky Way-type galaxies to the ICM is calculated confirming the importance ofthis enrichment process (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Assessment of Agreement under Nonstandard Conditions Using Regression Models for Mean and VarianceBIOMETRICS, Issue 1 2006Pankaj K. Choudhary Summary The total deviation index of Lin (2000, Statistics in Medicine19, 255,270) and Lin et al. (2002, Journal of the American Statistical Association97, 257,270) is an intuitive approach for the assessment of agreement between two methods of measurement. It assumes that the differences of the paired measurements are a random sample from a normal distribution and works essentially by constructing a probability content tolerance interval for this distribution. We generalize this approach to the case when differences may not have identical distributions,a common scenario in applications. In particular, we use the regression approach to model the mean and the variance of differences as functions of observed values of the average of the paired measurements, and describe two methods based on asymptotic theory of maximum likelihood estimators for constructing a simultaneous probability content tolerance band. The first method uses bootstrap to approximate the critical point and the second method is an analytical approximation. Simulation shows that the first method works well for sample sizes as small as 30 and the second method is preferable for large sample sizes. We also extend the methodology for the case when the mean function is modeled using penalized splines via a mixed model representation. Two real data applications are presented. [source] When do localized natural enemies increase species richness?ECOLOGY LETTERS, Issue 4 2005Frederick R. Adler Abstract The Janzen,Connell hypothesis states that local species-specific density dependence, mediated through specialist enemies of offspring such as fungal pathogens and insect seed predators, can facilitate coexistence of species by preventing recruitment near conspecific adults. We use spatially explicit simulation models and analytical approximations to evaluate how spatial scales of offspring and enemy dispersal affect species richness. In comparison with model communities in which both offspring and enemies disperse long distances, species richness is substantially decreased when offspring disperse long distances and enemies disperse short distances. In contrast, when both offspring and enemies disperse short distances species richness more than doubles and adults of each species are highly spatially clumped. For the range of conditions typical of tropical forests, locally dispersing specialist enemies may decrease species richness relative to enemies that disperse long distances. In communities where dispersal distances of both offspring and enemies are short, local effects may enhance species richness. [source] ADAPTIVE EVOLUTION OF ASEXUAL POPULATIONS UNDER MULLER'S RATCHETEVOLUTION, Issue 7 2004Doris Bachtrog Abstract We study the population genetics of adaptation in nonequilibrium haploid asexual populations. We find that the accumulation of deleterious mutations, due to the operation of Muller's ratchet, can considerably reduce the rate of fixation of advantageous alleles. Such reduction can be approximated reasonably well by a reduction in the effective population size. In the absence of Muller's ratchet, a beneficial mutation can only become fixed if it creates the best possible genotype; if Muller's ratchet operates, however, mutations initially arising in a nonoptimal genotype can also become fixed in the population, since the loss of the least-loaded class implies that an initially nonoptimal background can become optimal. We show that, while the rate at which adaptive mutations become fixed is reduced, the rate of fixation of deleterious mutations due to the ratchet is not changed by the presence of beneficial mutations as long as the rate of their occurrence is low and the deleterious effects of mutations (sd) are higher than the beneficial effects (sa). When sa>sd, the advantage of a beneficial mutation can outweigh the deleterious effects of associated mutations. Under these conditions, a beneficial allele can drag to fixation deleterious mutations initially associated with it at a higher rate than in the absence of advantageous alleles. We propose analytical approximations for the rates of accumulation of deleterious and beneficial mutations. Furthermore, when allowing for the possible occurrence of interference between beneficial alleles, we find that the presence of deleterious mutations of either very weak or very strong effect can marginally increase the rate of accumulation of beneficial mutations over that observed in the absence of such deleterious mutations. [source] Discrete Bose-Einstein systems in a box with low adiabatic invariantFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 4-5 2003V.I. Vlad The Bose-Einstein energy spectrum of an ideal quantum gas confined in a box is discrete and strongly dependent on the box geometry and temperature, for low product of the atomic mass number, Aat and the adiabatic invariant, TV2/3, i.e. on , = Aat TV2/3. Even within the approximation of non-interacting particles in the gas, the calculation of the thermodynamic properties of Bose-Einstein systems turns out to be a difficult mathematical problem. The present study compares the total number of particles, the total energy and the specific heat obtained by sums over the discrete states to the results of the approximate integrals (for defined values of ,) and shows the noticeable errors of the last ones at low adiabatic invariant (around condensation). Then, more rigorous and precise analytical approximations of sums are found in the case of finite number of atoms (correlated with the existence of a zero energy level) and the finite volume of the gas. The corrected thermodynamic functions depend on , (for fixed fugacity). The condensation temperature is corrected also in order to describe more accurately the discrete Bose-Einstein systems. Under these circumstances, the analysis of the specific heat leads to the conclusion that it shows no discontinuity, for the entire range of , values. [source] Resonant frequencies of a combination of split rings: Experimental, analytical and numerical studyMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 5 2005A. Radkovskaya Abstract The resonant frequencies of five different ring resonators are measured with the aid of a network analyser within the frequency range of about 1.5 to 2.8 GHz. The resonant frequencies for those configurations are also determined from numerical calculations using the commercially available MICRO-STRIPES package. The experimental and numerical results are shown to be very close to each other. Analytical results from various authors, available for three of the configurations, are also compared with the experimental results; one of them leads to a large discrepancy, but the other analytical approximations are shown to be not too far off. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 46: 473,476, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21021 [source] | |||||||||||||||||||