Research Outputs

Permanent URI for this communityhttps://hdl.handle.net/20.500.14288/2

Browse

Filters

1995 - 199932010 - 20131

Advanced Search

Filter by

Settings

Department: search.filters.department.Department of MathematicsSubject: search.filters.subject.Chemistry

Search Results

Now showing 1 - 4 of 4
  • Placeholder
    PublicationMetadata only
    Laser beam propagation in a thermally loaded absorber
    (Optica Publishing Group, 1996) Department of Physics; Department of Mathematics; Department of Mathematics; Sennaroğlu, Alphan; Aşkar, Attila; Atay, Fatihcan; Faculty Member; Faculty Member; Faculty Member; Department of Physics; Department of Mathematics; College of Sciences; College of Sciences; College of Sciences; 23851; 178822; 253074
    Beam propagation in a thermally loaded absorber is analyzed by a novel method. The formulation identifies a dimensionless parameter controlling the strength of thermal effects.
  • Thumbnail Image
    PublicationOpen Access
    Quantum fluid dynamics in the Lagrangian representation and applications to photodissociation problems
    (American Institute of Physics (AIP) Publishing, 1999) Rabitz, H. A.; Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; N/A; 178822
    This paper considers the practical utility of quantum fluid dynamics (QFD) whereby the time-dependent Schrodinger's equation is transformed to observing the dynamics of an equivalent "gas continuum." The density and velocity of this equivalent gas continuum are respectively the probability density and the gradient of the phase of the wave function. The numerical implementation of the QFD equations is carried out within the Lagrangian approach, which transforms the solution of Schrodinger's equation into following the trajectories of a set of mass points, i.e., subparticles, obtained by discretization of the continuum equations. The quantum dynamics of the subparticles which arise in the present formalism through numerical discretization are coupled by the density and the quantum potential. Numerical illustrations are performed for photodissociation of nocl and NO2 treated as two-dimensional models. The dissociation cross sections sigma(omega) are evaluated in the dramatically short CPU times of 33 s for nocl and 40 s for NO2 on a Pentium-200 mhz PC machine. The computational efficiency comes from a combination of (a) the QFD representation dealing with the near monotonic amplitude and phase as dependent variables, (b) the Lagrangian description concentrating the computation effort at all times into regions of highest probability as an optimal adaptive grid, and (c) the use of an explicit time integrator whereby the computational effort grows only linearly with the number of discrete points.
  • Placeholder
    PublicationMetadata only
    Subspace molecular dynamics for long time phenomena
    (Kluwer Academic Publ, 1995) Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822
    N/A
  • Placeholder
    PublicationMetadata only
    The comparison of parametric and nonparametric bootstrap methods for reference interval computation in small sample size groups
    (Springer, 2013) Coşkun, Abdurrahman; İnal, Tamer C.; Serteser, Mustafa; Ünsal, İbrahim; Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/A
    According to the IFCC, to determine the population-based reference interval (RI) of a test, 120 reference individuals are required. However, for some age groups such as newborns and preterm babies, it is difficult to obtain enough reference individuals. In this study, we consider both parametric and nonparametric bootstrap methods for estimating RIs and the associated confidence intervals (CIs) in small sample size groups. We used data from four different tests [glucose, creatinine, blood urea nitrogen (BUN), and triglycerides], each in 120 individuals, to calculate the RIs and the associated CIs using nonparametric and parametric approaches. Also for each test, we selected small groups (m = 20, 30,aEuro broken vertical bar, 120) from among the 120 individuals and applied parametric and nonparametric bootstrap methods. The glucose and creatinine data were normally distributed, and the parametric bootstrap method provided more precise RIs (i.e., the associated CIs were narrower). In contrast, the BUN and triglyceride data were not normally distributed, and the nonparametric bootstrap method provided better results. With the bootstrap methods, the RIs and CIs of small groups were similar to those of the 120 subjects required for the nonparametric method, with a slight loss of precision. For original data with normal or close to normal distribution, the parametric bootstrap approach should be used, instead of nonparametric methods. For original data that deviate significantly from a normal distribution, the nonparametric bootstrap should be applied. Using the bootstrap methods, fewer samples are required for computing RIs, with only a slightly increased uncertainty around the end points.