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Multiphase PC/PL Relations: Comparison between Theory and observations

Cepheids are fundamental objects astrophysically in that they hold the key to a CMB independent estimate of Hubble's constant. A number of researchers have pointed out the possibilities of breaking degeneracies between Omega_Matter and H0 if there is a CMB independent distance scale accurate to a few percent (Hu 2005). Current uncertainties in the distance scale are about 10% but future observations, with, for example, the JWST, will be capable of estimating H0 to within a few percent. A crucial step in this process is the Cepheid PL relation. Recent evidence has emerged that the PL relation, at least in optical bands, is nonlinear and that neglect of such a nonlinearity can lead to errors in estimating H0 of up to 2 percent. Hence it is important to critically examine this possible nonlinearity both observationally and theoretically. Existing PC/PL relations rely exclusively on evaluating these relations at mean light. However, since such relations are the average of relations at different phases. Here we report on recent attempts to compare theory and observation in the multiphase PC/PL planes. We construct state of the art Cepheid pulsations models appropriate for the LMC/Galaxy and compare the resulting PC/PL relations as a function of phase with observations. For the LMC, the (V-I) period-color relation at minimum light can have quite a narrow dispersion (0.2-0.3 mags) and thus could be useful in placing constraints on models. At longer periods, the models predict significantly redder (by about 0.2-0.3 mags) V-I colors. We discuss possible reasons for this and also compare PL relations at various phases of pulsation and find clear evidence in both theory and observations for a nonlinear PL relation.Comment: 5 pages, 8 figures, proceeding for "Stellar Pulsation: Challenges for Theory and Observation", Santa Fe 200

Numerical investigation of three types of space and time fractional Bloch-Torrey equations in 2D

Recently, the fractional Bloch-Torrey model has been used to study anomalous diffusion in the human brain. In this paper, we consider three types of space and time fractional Bloch-Torrey equations in two dimensions: Model-1 with the Riesz fractional derivative; Model-2 with the one-dimensional fractional Laplacian operator; and Model-3 with the two-dimensional fractional Laplacian operator. Firstly, we propose a spatially second-order accurate implicit numerical method for Model-1 whereby we discretize the Riesz fractional derivative using a fractional centered difference. We consider a finite domain where the time and space derivatives are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Secondly, we utilize the matrix transfer technique for solving Model-2 and Model-3. Finally, some numerical results are given to show the behaviours of these three models especially on varying domain sizes with zero Dirichlet boundary conditions

Period-Color and Amplitude-Color Relations in Classical Cepheid Variables - VI. New Challenges for Pulsation Models

We present multiphase Period-Color/Amplitude-Color/Period-Luminosity relations using OGLE III and Galactic Cepheid data and compare with state of the art theoretical pulsation models. Using this new way to compare models and observations, we find convincing evidence that both Period-Color and Period-Luminosity Relations as a function of phase are dynamic and highly nonlinear at certain pulsation phases. We extend this to a multiphase Wesenheit function and find the same result. Hence our results cannot be due to reddening errors. We present statistical tests and the urls of movies depicting the Period-Color/Period Luminosity and Wesenheit relations as a function of phase for the LMC OGLE III Cepheid data: these tests and movies clearly demonstrate nonlinearity as a function of phase and offer a new window toward a deeper understanding of stellar pulsation. When comparing with models, we find that the models also predict this nonlinearity in both Period-Color and Period-Luminosity planes. The models with (Z=0.004, Y=0.25) fare better in mimicking the LMC Cepheid relations, particularly at longer periods, though the models predict systematically higher amplitudes than the observations

Fractional Hamilton formalism within Caputo's derivative

In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canonical Hamiltonian are given, and a set of fractional Hamiltonian equations are obtained. Using an example, it is shown that the canonical fractional Hamiltonian and the fractional Euler-Lagrange formulations lead to the same set of equations.Comment: 8 page

Constant Curvature Coefficients and Exact Solutions in Fractional Gravity and Geometric Mechanics

We study fractional configurations in gravity theories and Lagrange mechanics. The approach is based on Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical interactions and we formulate a method of nonholonomic deformations to other types of fractional derivatives. The main result of this paper consists in a proof that for corresponding classes of nonholonomic distributions a large class of physical theories are modelled as nonholonomic manifolds with constant matrix curvature. This allows us to encode the fractional dynamics of interactions and constraints into the geometry of curve flows and solitonic hierarchies.Comment: latex2e, 11pt, 27 pages, the variant accepted to CEJP; added and up-dated reference

Towards the Formalization of Fractional Calculus in Higher-Order Logic

Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to analyze a wide class of physical systems in various fields of science and engineering. In this paper, we describe an ongoing project which aims at formalizing the basic theories of fractional calculus in the HOL Light theorem prover. Mainly, we present the motivation and application of such formalization efforts, a roadmap to achieve our goals, current status of the project and future milestones.Comment: 9 page

Fractional compartmental models and multi-term Mittag–Leffler 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 36:165–178, 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) Mittag–Leffler functions, and establish a direct correspondence with the familiar sums of exponentials used in PK

Fractional dynamics pharmacokinetics–pharmacodynamic 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 pharmacokinetics–pharmacodynamic (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

Spin chemistry investigation of peculiarities of photoinduced electron transfer in donor-acceptor linked system

Photoinduced intramolecular electron transfer in linked systems, (R,S)- and (S,S)-naproxen-N-methylpyrrolidine dyads, has been studied by means of spin chemistry methods [magnetic field effect and chemically induced dynamic nuclear polarization (CIDNP)]. The relative yield of the triplet state of the dyads in different magnetic field has been measured, and dependences of the high-field CIDNP of the N-methylpyrrolidine fragment on solvent polarity have been investigated. However, both (S,S)- and (R,S)-enantiomers demonstrate almost identical CIDNP effects for the entire range of polarity. It has been demonstrated that the main peculiarities of photoprocesses in this linked system are connected with the participation of singlet exciplex alongside with photoinduced intramolecular electron transfer in chromophore excited state quenching.This work was supported by the grants 08-03-00372 and 11-03-01104 of the Russian Foundation for Basic Research, and the grant of Priority Programs of the Russian Academy of Sciences, nr. 5.1.5.Magin, I.; Polyakov, N.; Khramtsova, E.; Kruppa, A.; Stepanov, A.; Purtov, P.; Leshina, T.... (2011). Spin chemistry investigation of peculiarities of photoinduced electron transfer in donor-acceptor linked system. Applied Magnetic Resonance. 41(2-4):205-220. https://doi.org/10.1007/s00723-011-0288-3S205220412-4J.S. Park, E. Karnas, K. Ohkubo, P. Chen, K.M. Kadish, S. Fukuzumi, C.W. Bielawski, T.W. Hudnall, V.M. Lynch, J.L. Sessler, Science 329, 1324–1327 (2010)S.Y. Reece, D.G. Nocera, Annu. Rev. Biochem. 78, 673–699 (2009)M.S. Afanasyeva, M.B. Taraban, P.A. Purtov, T.V. Leshina, C.B. Grissom, J. Am. Chem. Soc. 128, 8651–8658 (2006)M.A. Fox, M. Chanon, in Photoinduced Electron Transfer. C: Photoinduced Electron Transfer Reactions: Organic Substrates (Elsevier, New York, 1988), p. 754P.J. Hayball, R.L. Nation, F. Bochner, Chirality 4, 484–487 (1992)N. Suesa, M.F. Fernandez, M. Gutierrez, M.J. Rufat, E. Rotllan, L. Calvo, D. Mauleon, G. Carganico, Chirality 5, 589–595 (1993)A.M. Evans, J. Clin. Pharmacol. 36, 7–15 (1996)Y. Inoue, T. Wada, S. Asaoka, H. Sato, J.-P. Pete, Chem Commun. 4, 251–259 (2000)T. Yorozu, K. Hayashi, M. Irie, J. Am. Chem. Soc. 103, 5480–5548 (1981)N.J. Turro, in Modern Molecular Photochemistry (Benjamin/Cummings, San Francisco, 1978)K.M. Salikhov, Y.N. Molin, R.Z. Sagdeev, A.L. Buchachenko, in Spin Polarization and Magnetic Field Effects in Radical Reactions (Akademiai Kiado, Budapest, 1984), p. 419E.A. Weiss, M.A. Ratner, M.R. Wasielewski, J. Phys. Chem. A 107, 3639–3647 (2003)A.S. Lukas, P.J. Bushard, E.A. Weiss, M.R. Wasielewski, J. Am. Chem. Soc. 125, 3921–3930 (2003)R. Nakagaki, K. Mutai, M. Hiramatsu, H. Tukada, S. Nakakura, Can. J. Chem. 66, 1989–1996 (1988)M.C. Jim′enez, U. Pischel, M.A. Miranda, J. Photochem. Photobiol. C Photochem. Rev. 8, 128–142 (2007)S. Abad, U. Pischel, M.A. Miranda, Photochem. Photobiol. Sci. 4, 69–74 (2005)U. Pischel, S. Abad, L.R. Domingo, F. Bosca, M.A. Miranda, Angew. Chem. Int. Ed. 42, 2531–2534 (2003)G.L. Closs, R.J. Miller, J. Am. Chem. Soc. 101, 1639–1641 (1979)G.L. Closs, R.J. Miller, J. Am. Chem. Soc. 103, 3586–3588 (1981)M. Goez, Chem. Phys. Lett. 188, 451–456 (1992)I.F. Molokov, Y.P. Tsentalovich, A.V. Yurkovskaya, R.Z. Sagdeev, J. Photochem. Photobiol. A 110, 159–165 (1997)U. Pischel, S. Abad, M.A. Miranda, Chem. Commun. 9, 1088–1089 (2003)H. Hayashi, S. Nagakura, Bull. Chem. Soc. Jpn. 57, 322–328 (1984)Y. Sakaguchi, H. Hayashi, S. Nagakura, Bull. Chem. Soc. Jpn. 53, 39–42 (1980)H. Yonemura, H. Nakamura, T. Matsuo, Chem. Phys. Lett. 155, 157–161 (1989)N. Hata, M. Hokawa, Chem. Lett. 10, 507–510 (1981)M. Shiotani, L. Sjoeqvist, A. Lund, S. Lunell, L. Eriksson, M.B. Huang, J. Phys. Chem. 94, 8081–8090 (1990)E. Schaffner, H. Fischer, J. Phys. Chem. 100, 1657–1665 (1996)Y. Mori, Y. Sakaguchi, H. Hayashi, Chem. Phys. Lett. 286, 446–451 (1998)I.M. Magin, A.I. Kruppa, P.A. Purtov, Chem. Phys. 365, 80–84 (2009)K.K. Barnes, Electrochemical Reactions in Nonaqueous Systems (M. Dekker, New York, 1970), p. 560J. Bargon, J. Am. Chem. Soc. 99, 8350–8351 (1977)M. Goez, I. Frisch, J. Phys. Chem. A 106, 8079–8084 (2002)A.K. Chibisov, Russ. Chem. Rev. 50, 615–629 (1981)J. Goodman, K. Peters, J. Am. Chem. Soc. 107, 1441–1442 (1985)H. Cao, Y. Fujiwara, T. Haino, Y. Fukazawa, C.-H. Tung, Y. Tanimoto, Bull. Chem. Soc. Jpn. 69, 2801–2813 (1996)P.A. Purtov, A.B. Doktorov, Chem. Phys. 178, 47–65 (1993)A.I. Kruppa, O.I. Mikhailovskaya, T.V. Leshina, Chem. Phys. Lett. 147, 65–71 (1988)M.E. Michel-Beyerle, R. Haberkorn, W. Bube, E. Steffens, H. Schröder, H.J. Neusser, E.W. Schlag, H. Seidlitz, Chem. Phys. 17, 139–145 (1976)K. Schulten, H. Staerk, A. Weller, H.-J. Werner, B. Nickel, Z. Phys. Chem. 101, 371–390 (1976)K. Gnadig, K.B. Eisenthal, Chem. Phys. Lett. 46, 339–342 (1977)T. Nishimura, N. Nakashima, N. Mataga, Chem. Phys. Lett. 46, 334–338 (1977)M.G. Kuzmin, I.V. Soboleva, E.V. Dolotova, D.N. Dogadkin, High Eng. Chem. 39, 86–96 (2005