492 research outputs found
Fractional compartmental models and multi-term MittagâLeffler response functions
Systems of fractional differential equations (SFDE) have been increasingly used to represent physical and control system, and have been recently proposed for use in pharmacokinetics (PK) by (J Pharmacokinet Pharmacodyn 36:165â178, 2009) and (J Phamacokinet Pharmacodyn, 2010). We contribute to the development of a theory for the use of SFDE in PK by, first, further clarifying the nature of systems of FDE, and in particular point out the distinction and properties of commensurate versus non-commensurate ones. The second purpose is to show that for both types of systems, relatively simple response functions can be derived which satisfy the requirements to represent single-input/single-output PK experiments. The response functions are composed of sums of single- (for commensurate) or two-parameters (for non-commensurate) MittagâLeffler functions, and establish a direct correspondence with the familiar sums of exponentials used in PK
Absolute dimensions of the unevolved B-type eclipsing binary GG Orionis
We present photometric observations in B and V as well as spectroscopic
observations of the detached, eccentric 6.6-day double-lined eclipsing binary
GG Ori, a member of the Orion OB1 association. Absolute dimensions of the
components, which are virtually identical, are determined to high accuracy
(better than 1% in the masses and better than 2% in the radii) for the purpose
of testing various aspects of theoretical modeling. We obtain M(A) = 2.342 +/-
0.016 solar masses and R(A) = 1.852 +/- 0.025 solar radii for the primary, and
M(B) = 2.338 +/- 0.017 solar masses and R(B) = 1.830 +/- 0.025 solar radii for
the secondary. The effective temperature of both stars is 9950 +/- 200 K,
corresponding to a spectral type of B9.5. GG Ori is very close to the ZAMS, and
comparison with current stellar evolution models gives ages of 65-82 Myr or 7.7
Myr depending on whether the system is considered to be burning hydrogen on the
main sequence or still in the final stages of pre-main sequence contraction. We
have detected apsidal motion in the binary at a rate of dw/dt = 0.00061 +/-
0.00025 degrees per cycle, corresponding to an apsidal period of U = 10700 +/-
4500 yr. A substantial fraction of this (approximately 70%) is due to the
contribution from General Relativity.Comment: To appear in The Astronomical Journal, December 200
The Chemical Compositions of the Type II Cepheids -- The BL Her and W Vir Variables
Abundance analyses from high-resolution optical spectra are presented for 19
Type II Cepheids in the Galactic field. The sample includes both short-period
(BL Her) and long-period (W Vir) stars. This is the first extensive abundance
analysis of these variables. The C, N, and O abundances with similar spreads
for the BL Her and W Vir show evidence for an atmosphere contaminated with
-process and CN-cycling products. A notable anomaly of the BL Her
stars is an overabundance of Na by a factor of about five relative to their
presumed initial abundances. This overabundance is not seen in the W Vir stars.
The abundance anomalies running from mild to extreme in W Vir stars but not
seen in the BL Her stars are attributed to dust-gas separation that provides an
atmosphere deficient in elements of high condensation temperature, notably Al,
Ca, Sc, Ti, and -process elements. Such anomalies have previously been seen
among RV Tau stars which represent a long-period extension of the variability
enjoyed by the Type II Cepheids. Comments are offered on how the contrasting
abundance anomalies of BL Her and W Vir stars may be explained in terms of the
stars' evolution from the blue horizontal branch.Comment: 41 pages including 11 figures and 4 tables; Accepted for publication
in Ap
A Search for Hierarchical Triples using Kepler Eclipse Timing
We present the first results of a Kepler survey of 41 eclipsing binaries that
we undertook to search for third star companions. Such tertiaries will
periodically alter the eclipse timings through light travel time and dynamical
effects. We discuss the prevalence of starspots and pulsation among these
binaries and how these phenomena influence the eclipse times. There is no
evidence of short period companions (P < 700 d) among this sample, but we do
find evidence for long term timing variations in 14 targets (34%). We argue
that this finding is consistent with the presence of tertiary companions among
a significant fraction of the targets, especially if many have orbits measured
in decades. This result supports the idea that the formation of close binaries
involves the deposition of angular momentum into the orbital motion of a third
star.Comment: AJ, in press, 104 pages, 2 figure sets plus 1 regular figur
Retarding Sub- and Accelerating Super-Diffusion Governed by Distributed Order Fractional Diffusion Equations
We propose diffusion-like equations with time and space fractional
derivatives of the distributed order for the kinetic description of anomalous
diffusion and relaxation phenomena, whose diffusion exponent varies with time
and which, correspondingly, can not be viewed as self-affine random processes
possessing a unique Hurst exponent. We prove the positivity of the solutions of
the proposed equations and establish the relation to the Continuous Time Random
Walk theory. We show that the distributed order time fractional diffusion
equation describes the sub-diffusion random process which is subordinated to
the Wiener process and whose diffusion exponent diminishes in time (retarding
sub-diffusion) leading to superslow diffusion, for which the square
displacement grows logarithmically in time. We also demonstrate that the
distributed order space fractional diffusion equation describes super-diffusion
phenomena when the diffusion exponent grows in time (accelerating
super-diffusion).Comment: 11 pages, LaTe
Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux-Crum Transformations
Simple derivation is presented of the four families of infinitely many shape
invariant Hamiltonians corresponding to the exceptional Laguerre and Jacobi
polynomials. Darboux-Crum transformations are applied to connect the well-known
shape invariant Hamiltonians of the radial oscillator and the
Darboux-P\"oschl-Teller potential to the shape invariant potentials of
Odake-Sasaki. Dutta and Roy derived the two lowest members of the exceptional
Laguerre polynomials by this method. The method is expanded to its full
generality and many other ramifications, including the aspects of generalised
Bochner problem and the bispectral property of the exceptional orthogonal
polynomials, are discussed.Comment: LaTeX2e with amsmath, amssymb, amscd 26 pages, no figure
Fractional dynamics pharmacokineticsâpharmacodynamic models
While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokineticsâpharmacodynamic (PKPD) literature. One of the reasons is computational: while the analytical solution of fractional differential equations is available in special cases, it this turns out that even the simplest PKPD models that can be constructed using fractional calculus do not allow an analytical solution. In this paper, we first introduce new families of PKPD models incorporating fractional order integrals and differential equations, and, second, exemplify and investigate their qualitative behavior. The families represent extensions of frequently used PK link and PD direct and indirect action models, using the tools of fractional calculus. In addition the PD models can be a function of a variable, the active drug, which can smoothly transition from concentration to exposure, to hyper-exposure, according to a fractional integral transformation. To investigate the behavior of the models we propose, we implement numerical algorithms for fractional integration and for the numerical solution of a system of fractional differential equations. For simplicity, in our investigation we concentrate on the pharmacodynamic side of the models, assuming standard (integer order) pharmacokinetics
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