Additional Free Parameters Research Articles

Equilibria of a solvable N-body problem and related properties of the N numbers xn at which the Jacobi polynomial of order N has the same value

The class of solvable N-body problems of “goldfish” type has been recently extended by including (the additional presence of) three-body forces. In this paper we show that the equilibria of some of these systems are simply related to the N roots xn of the polynomial equation (x)= w, where (x) is the Jacobi polynomial of order N, the parameters α and β are related to parameters of the N-body problem (which can be arbitrarily assigned) and w is an arbitrary number. By investigating the behavior of these solvable N-body systems in the infinitesimal neighborhood of these equilibria, the eigenvalues associated to certain N × N matrices explicitly given in terms of the N numbers xn (and of additional free parameters of the N-body problem) are explicitly identified. In some cases—corresponding to isochronous N-body problems—these findings have a Diophantine connotation, inasmuch as these eigenvalues are then rational numbers.

New solvable discrete-time many-body problem featuring several arbitrary parameters. II

A new solvable discrete-time many-body problem is identified. It extends a model treated in a previous paper by introducing in its equations of motion an additional free parameter. Hence, it features 6 parameters, 2 of which can be eliminated (say, replaced by unity) by appropriate rescalings. Assignments of these parameters are identified which entail that the many-body model is asymptotically isochronous, namely, that its generic solution—when the discrete-time variable ℓ diverges, ℓ → ∞—becomes completely periodic up to exponentially vanishing corrections, with a fixed period independent of the initial data.

Hermite G 1 rational spline motion of degree six

Applying geometric interpolation techniques to motion construction has many advantages, e.g., the parameterization is chosen automatically and the obtained rational motion is of the lowest possible degree. In this paper a G 1 Hermite rational spline motion of degree six is presented. An explicit solution of nonlinear equations that determine the spherical part of the motion is derived. Particular emphasis is placed on the construction of the translational part of the motion. Since the center trajectory is a G 1 continuous for an arbitrary choice of lengths of tangent vectors, additional free parameters are obtained, which are used to minimize particular energy functionals. Thenumerical examples provide an evidence that the obtained motions have nice shapes.

Improved robust model predictive control with guaranteed H2/H∞ performance for polytopic systems

This paper is concerned with model predictive control for polytopic systems subject to exogenous disturbance and [Formula: see text]/[Formula: see text] performance constraints. It is shown that a better characterization of [Formula: see text]/[Formula: see text] performance can be provided by introducing additional free parameters. Meanwhile, input constraints are ensured by using a dilated linear matrix inequality technique, so the utilization of actuator capability is improved. These two aspects bring extra degrees of freedom in optimizing control performance. Recursive feasibility and stability of the controller are proved. Numerical examples verify these properties.

Unified dark fluid with fast transition: Including entropic perturbations

In this paper, we investigate a unified dark fluid model with a fast transition and entropic perturbations. An effective sound speed is designated as an additional free model parameter when the entropic perturbations are included, and, if the entropic perturbations are zero, the effective sound speed will decrease to the adiabatic sound speed. In order to analyze the viability of the unified model, we calculate the squared Jeans wave number with the entropic perturbations. Furthermore, by using the Markov Chain Monte Carlo method, we perform a global fitting for the unified dark fluid model from the type Ia supernova Union 2.1, baryon acoustic oscillation, and the full information of the cosmic microwave background measurement given by the WMAP 7 yr data points. The constrained results favor a small effective sound speed. Compared to the cosmological constant and cold dark matter, it is found that the cosmic observations do not favor the phenomenon of a fast transition for the unified dark fluid model.

Perturbation theory for the non-linear halo power spectrum: the renormalized bias and halo bias

We revisit an analytical model to describe the halo-matter cross-power spectrum and the halo auto-power spectrum in the weakly nonlinear regime, by combining the perturbation theory (PT) for matter clustering, the local bias model, and the halo bias. Nonlinearities in the power spectra arise from the nonlinear clustering of matter as well as the nonlinear relation between the matter and halo density fields. By using the "renormalization" approach, we express the nonlinear power spectra by a sum of the two contributions: the nonlinear matter power spectrum with the effective linear bias parameter, and the higher-order PT spectra having the halo bias parameters as the coefficients. The halo auto-power spectrum includes the residual shot noise contamination that needs to be treated as additional free parameter. The term(s) of the higher-order PT spectra and the residual shot noise cause a scale-dependent bias function relative to the nonlinear matter power spectrum in the weakly nonlinear regime. We show that the model predictions are in good agreement with the spectra measured from a suit of high-resolution $N$-body simulations up to $k\simeq 0.2 h$/Mpc at $z=0.35$, for different halo mass bins.

Constraints on neutrino mass and light degrees of freedom in extended cosmological parameter spaces

From a combination of probes including the cosmic microwave background (WMAP7+SPT), Hubble constant (HST), baryon acoustic oscillations (SDSS+2dFGRS), and supernova distances (Union2), we have explored the extent to which the constraints on the effective number of neutrinos and sum of neutrino masses are affected by our ignorance of other cosmological parameters, including the curvature of the universe, running of the spectral index, primordial helium abundance, evolving late-time dark energy, and early dark energy. In a combined analysis of the effective number of neutrinos and sum of neutrino masses, we find mild (2.2 sigma) preference for additional light degrees of freedom. However, the effective number of neutrinos is consistent with the canonical expectation of 3 massive neutrinos and no extra relativistic species to within 1 sigma when allowing for evolving dark energy and relaxing the strong inflation prior on the curvature and running. The agreement improves with the possibility of an early dark energy component, itself constrained to be less than 5% of the critical density (95% CL) in our expanded parameter space. In extensions of the standard cosmological model, the derived amplitude of linear matter fluctuations sigma_8 is found to closely agree with low-redshift cluster abundance measurements. The sum of neutrino masses is robust to assumptions of the effective number of neutrinos, late-time dark energy, curvature, and running at the level of 1.2 eV (95% CL). The upper bound degrades to 2.0 eV (95% CL) when further including the early dark energy density and primordial helium abundance as additional free parameters. Even in extended cosmological parameter spaces, Planck alone could determine the possible existence of extra relativistic species at 4 sigma confidence and constrain the sum of neutrino masses to 0.2 eV (68% CL).

MID-INFRARED DETERMINATION OF TOTAL INFRARED LUMINOSITY AND STAR FORMATION RATES OF LOCAL AND HIGH-REDSHIFT GALAXIES

We demonstrate estimating the total infrared luminosity, LIR, and star formation rates (SFRs) of star-forming galaxies at redshift 0 < z < 2.8 from single-band 24 micron observations, using local spectral energy distributions (SED) templates without introducing additional free parameters. Our method is based on characterizing the SEDs of galaxies as a function of their LIR surface density, which is motivated by the indications that the majority of IR luminous star-forming galaxies at 1 < z < 3 have extended star-forming regions, in contrast to the strongly nuclear concentrated, merger-induced starbursts in local luminous and ultraluminous IR galaxies. We validate our procedure for estimating LIR by comparing the resulting LIRs with those measured from far-IR observations at 0 < z < 2.8. AGNs were excluded using X-ray and 3.6-8.0 micron observations, which are generally available in deep cosmological survey fields. The Gaussian fits to the distribution of the discrepancies between the LIR measurements from single-band 24 micron and Herschel observations have sigma < 0.1 dex, with ~10% of objects disagreeing by more than 0.2 dex. Since the 24 micron estimates are based on SEDs for extended galaxies, this agreement suggests that ~90% of IR galaxies at high z are indeed much more physically extended than local counterparts of similar LIR, consistent with recent independent studies of the fractions of galaxies forming stars in the main-sequence and starburst modes, respectively. Because we have not introduced empirical corrections to enhance these estimates, in principle, our method should be applicable to lower luminosity galaxies. This will enable use of the 21 micron band of the Mid-Infrared Instrument (MIRI) on board the JWST to provide an extremely sensitive tracer of obscured SFR in individual star-forming galaxies across the peak of the cosmic star formation history.

Unified dark fluid with constant adiabatic sound speed: Including entropic perturbations

In this paper, we continue to study a unified dark fluid model with a constant adiabatic sound speed but with the entropic perturbations. When the entropic perturbations are included, an effective sound speed, which reduces to the adiabatic sound speed when the entropic perturbations are zero, has to be specified as an additional free model parameter. Because of the relations between the adiabatic sound speed and equations of state ${c}_{s,ad}^{2}(a)=w(a)\ensuremath{-}d\mathrm{ln}(1+w(a))/3d\mathrm{ln}a$, the equation of state can be determined up to an integration constant, in principle, when an adiabatic sound speed is given. Then there are two degrees of freedom to describe the linear perturbations for a fluid. Its microscale properties are characterized by its equations of state or adiabatic sound speed and an effective sound speed. We take the effective sound speed and adiabatic sound speed as free model parameters and then use the currently available cosmic observational data sets, which include type Ia supernova Union 2.1, baryon acoustic oscillation, and WMAP 7-yr data of cosmic background radiation, to constrain the possible entropic perturbations and the adiabatic sound speed via the Markov Chain Monte Carlo method. The results show that the cosmic observations favor a small effective sound speed ${c}_{s,\mathrm{eff}}^{2}={0.00155}_{\ensuremath{-}0.00155}^{+0.000319}$ in the $1\ensuremath{\sigma}$ region.

Generalized Soft Wall model

We develop an exactly solvable generalization of the Soft Wall holographic model for the vector mesons. The generalization preserves the ultraviolet and infrared asymptotics of the Soft Wall model and contains an additional free parameter. This new parameter provides an arbitrary intercept in the Regge like spectrum of radial excitations and leads to a substantial modification of asymptotic expansion of the vector correlator at large momentum. The matching to the Operator Product Expansion from QCD allows to estimate the value of the new parameter which is shown to be in a good agreement with the phenomenology. In addition, the mass splitting between the vector and axial mesons arises naturally via the opposite sign of the introduced contribution to the intercept.

Analysis of level A in vitro–in vivo correlations for an extended‐release formulation with limited bioavailability

A two-stage, numerical deconvolution approach was employed to develop level A in vitro-in vivo correlations using data for three formulations of an extended-release oral dosage form. The in vitro dissolution data for all formulations exhibited near-complete dissolution within the time frame of the test. The pharmacokinetic concentration-time profiles for 16 subjects in a cross-over study demonstrated notably limited bioavailability for the slowest formulation. These data were used as the basis for the IVIVC model development. Two models were identified that satisfied the nominal requirements for a conclusive internal predictability of the IVIVC, provided that all three formulations were used as internal datasets. These were a simple linear model with absorption cut-off and a piecewise-linear variable absorption scale model. A subsequent cross-validation of the models' robustness indicated that neither model predicted satisfactorily the pharmacokinetic characteristics of all formulations in a conclusive manner. The piecewise-linear variable absorption scale model provided the most accurate results, particularly with respect to the prediction of the slowest formulation's pharmacokinetic metrics. But this latter model also involved additional free parameters compared with the simple linear model with absorption cut-off. It is argued that more complex IVIVC models with extra parameterization require comprehensive validation to ascertain the accuracy and robustness of the model. In order to achieve this, it is necessary to ensure a complete suite of supporting datasets for internal and external validation, irrespective of the mathematical approach used subsequently to develop the IVIVC.

Kinetic derivation of a quasi-hydrodynamic system of equations on the base of nonextensive statistics

- Applying the formalism of the Tsallis nonadditive statistical mechanics, a derivation of hydrodynamic and quasi-hydrodynamic equations is considered based on the generalized BGK kinetic equation. In particular, those equations are intended for construction of more appropriate macroscopic and mesoscopic models of transport systems related to the so-called anomalous systems where the corresponding phase space possesses a complicated (fractal) structure. The classic Boltzmann-Gibbs statistics (or Maxwell’s distribution of velocities in the case of kinetic theory) is violated in such systems and hence the additivity of extensive variables related to it does not hold either. The application of the approach developed in this paper does not change the structure of hydrodynamic and quasihydrodynamic equations, but the modified thermal and calorific state equations and also the transfer coefficients contain two additional free parameters, which are the parameter q of the non-additivity of the system and the fractional dimension D of the phase space. Along with the smoothing parameter t, these parameters can be determined empirically in each particular case from statistical or experimental data, which allows us to simulate the actual variable traffic situation within a continual approach both in regular and crisis cases.

Evaluation of a Modified Scheme for Shallow Convection: Implementation of CuP and Case Studies

Abstract A new treatment for shallow clouds has been introduced into the Weather Research and Forecasting Model (WRF). The new scheme, called the cumulus potential (CuP) scheme, replaces the ad hoc trigger function used in the Kain–Fritsch cumulus parameterization with a trigger function related to the distribution of temperature and humidity in the convective boundary layer via probability density functions (PDFs). An additional modification to the default version of WRF is the computation of a cumulus cloud fraction based on the time scales relevant for shallow cumuli. Results from three case studies over the U.S. Department of Energy’s Atmospheric Radiation Measurement (ARM) site in north-central Oklahoma are presented. These cases were selected because of the presence of shallow cumuli over the ARM site. The modified version of WRF does a much better job predicting the cloud fraction and the downwelling shortwave irradiance than control simulations utilizing the default Kain–Fritsch scheme. The modified scheme includes a number of additional free parameters, including the number and size of bins used to define the PDF, the minimum frequency of a bin within the PDF before that bin is considered for shallow clouds to form, and the critical cumulative frequency of bins required to trigger deep convection. A series of tests were undertaken to evaluate the sensitivity of the simulations to these parameters. Overall, the scheme was found to be relatively insensitive to each of the parameters.

Systematic calculation of fine structure in theαdecay of heavy odd-mass nuclei

The newly developed multichannel cluster model (MCCM) based on the coupled-channel Schrodinger equation with outgoing wave boundary conditions is extended to study the alpha-decay fine structure in heavy odd-A nuclei. More decay channels are considered for convergence in solving the coupled equations. Calculations are performed for 32 deformed nuclei with atomic numbers Z = 93-102. The branching ratios for various daughter states are well reproduced without any additional free parameters, and the calculated alpha-decay half-lives show good agreement with the experimental data. This indicates that the MCCM has universal applicability and equal validity regardless of even-even or odd-A alpha emitters.

Pair production of MSSM Higgs bosons in the nondecoupling region at the LHC

We consider the Higgs boson signals from pair production at the LHC within the framework of the MSSM in the non-decoupling (low-m_A) region. In light of the recent observation of a SM-like Higgs boson, we argue that the exploration for Higgs pair production at the LHC is a crucial next step to probe the MSSM Higgs sector. We emphasize that the production of H^\pm A^0 and H^{+}H^{-} depends only on the electroweak gauge couplings while all the leading Higgs production channels via gluon fusion, vector-boson fusion, and Higgsstrahlung depend on additional free Higgs sector parameters. In the non-decoupling region, the five MSSM Higgs bosons are all relatively light and pair production signals may be accessible. We find that at the 8 TeV LHC, a 5\sigma signal for H^\pm A^0, H^\pm h^0 -> \tau^{\pm}\nu b\bar b and H^{+}H^{-} -> \tau^{+}\nu \tau^{-}\nu are achievable with an integrated luminosity of 7 (11) fb^{-1} and 24 (48) fb^{-1}, respectively for m_A=95 (130) GeV. At the 14 TeV LHC, a 5\sigma signal for these two channels would require as little as 4 (7) fb^{-1} and 10 (19) fb^{-1}, respectively.

QCD diffractive mechanism of exclusive [formula omitted] pair production at high energies

We discuss new diffractive mechanism of central exclusive production of W+W− pairs in proton–proton collisions at the LHC. We include diagrams with intermediate virtual Higgs boson as well as quark box diagrams. Several observables related to this process are calculated. Predictions for the total cross section and differential distributions in W-boson rapidity and transverse momentum as well as WW invariant mass are presented. We also show results for different polarization states of the final W± bosons. We compare the contribution of the γγ→W+W− mechanism considered in the literature with the contribution of the diffractive mechanism through the gg→W+W− subprocess for the different observables. The phase space integrated diffractive contribution when separated is only a small fraction of fb compared to 115.4 fb of the γγ-contribution without absorption. The latter contribution dominates at small four-momentum transfers squared in the proton lines and in a broad range of W+W− invariant masses. This offers a possibility of efficient searches for anomalous triple-boson (γWW) and quartic-boson (γγWW) couplings and testing models beyond the Standard Model. We discuss shortly also the pp→ppγγ process, where the box contribution is very similar to that for W+W− and compare our results with recent CDF data. Nice agreement has been achieved without additional free parameters.

Infrared excess around nearby red giant branch stars and Reimers law (Corrigendum)

(Abridged) The spectral energy distributions of a well-defined sample of 54 RGB stars are constructed, and fitted with the dust radiative transfer model DUSTY. The central stars are modeled by MARCS model atmospheres. In a first step, the best-fit MARCS model is derived, determining the effective temperature. In a second step, models with a finite dust optical depth are fitted and it is determined whether the reduction in chi2 in such models with one additional free parameter is statistically significant. 23 stars are found to have a significant infrared excess, which is interpreted as mass loss. The dust optical depths are translated into mass-loss rates assuming a typical expansion velocity of 10 km/s and a dust-to-gas ratio of 0.005. The mass-loss rates are compared to those derived for luminous stars in globular clusters, by fitting both the infrared excess, as in the present paper, and the chromospheric lines. There is excellent agreement between these values and the mass-loss rates derived from the chromospheric activity. There is a systematic difference with the literature mass-loss rates derived from modeling the infrared excess, and this has been traced to technical details on how the DUSTY radiative transfer model is run. If the present results are combined with those from modeling the chromospheric emission lines, we obtain the fits Log Mdot = (1.0 +- 0.3) Log L + (-12.0 +- 0.9) and Log Mdot = (0.6 +- 0.2) Log (LR/M) + (-11.9 +- 0.9). The predictions of these mass-loss rate formula are tested against the RGB mass loss determination in NGC 6791. Using a scaling factor of (8 +- 5), both relations can fit this value. That the scaling factor is larger than unity suggests that the expansion velocity and/or dust-to-gas ratio, or even the dust opacities, are different from the values adopted.

Reconstruction of total solar irradiance 1974–2009

Context: The study of variations in total solar irradiance (TSI) is important for understanding how the Sun affects the Earth's climate. Aims: Full-disk continuum images and magnetograms are now available for three full solar cycles. We investigate how modelled TSI compares with direct observations by building a consistent modelled TSI dataset. The model, based only on changes in the photospheric magnetic flux can then be tested on rotational, cyclical and secular timescales. Methods: We use Kitt Peak and SoHO/MDI continuum images and magnetograms in the SATIRE-S model to reconstruct TSI over cycles 21-23. To maximise independence from TSI composites, SORCE/TIM TSI data are used to fix the one free parameter of the model. We compare and combine the separate data sources for the model to estimate an uncertainty on the reconstruction and prevent any additional free parameters entering the model. Results: The reconstruction supports the PMOD composite as being the best historical record of TSI observations, although on timescales of the solar rotation the IRMB composite provides somewhat better agreement. Further to this, the model is able to account for 92% of TSI variations from 1978 to 2009 in the PMOD composite and over 96% during cycle 23. The reconstruction also displays an inter-cycle, secular decline of 0.20 (+0.12 / -0.09) Wm-2 between cycle 23 minima, in agreement with the PMOD composite. Conclusions: SATIRE-S is able to recreate TSI observations on all timescales of a day and longer over 31 years from 1978. This is strong evidence that changes in photospheric magnetic flux alone are responsible for almost all solar irradiance variations over the last three solar cycles.

Infrared excess around nearby red giant branch stars and Reimers law

Context. Mass loss is one of the fundamental properties of asymptotic giant branch (AGB) stars, but for stars with initial masses below ∼1 M� , the mass loss on the first red giant branch (RGB) actually dominates mass loss on the AGB. Nevertheless, mass loss on the RGB is still often parameterised by a simple Reimers law in stellar evolution models. Aims. We study the infrared excess and mass loss of a sample of nearby RGB stars with reliably measured Hipparcos parallaxes and compare the mass loss to that derived for luminous stars in clusters. Methods. The spectral energy distributions of a well-defined sample of 54 RGB stars are constructed, and fitted with the dust radiative transfer model DUSTY. The central stars are modelled by MARCS model atmospheres. In a first step, the best-fit MARCS model is derived, basically determining the effective temperature. In a second step, models with a finite dust optical depth are fitted and it is determined whether the reduction in χ 2 in such models with one additional free parameter is statistically significant. Results. Among the 54 stars, 23 stars are found to have a significant infrared excess, which is interpreted as mass loss. The most

A new method for constructing exact solutions to three-dimensional Navier-Stokes and Euler equations

Formulas are derived that make it possible to construct new exact solutions for three-dimensional stationary and nonstationary Navier-Stokes and Euler equations using simpler solutions to the respective two-dimensional equations. The formulas contain from two to five additional free parameters, which are not present in the initial solutions to the two-dimensional equations. It is important that these formulas do not contain quadratures in the steady-state case. We consider some examples of constructing new three-dimensional exact solutions to the Navier-Stokes equations using the derived formulas. The results are used to solve some problems of the hydrodynamics of a viscous incompressible liquid. Examples of thenonuniqueness of solutions to steady-state problems are given. Some three-dimensional solutions to the Navier-Stokes equations are constructed using nonviscous solutions to the Euler equations. Two classes of new exact solutions to the Grad-Shafranov equation that contain functional arbitrariness are specified. Note that, in this study, a new method for constructing exact solutions is applied that can be useful for analyzing other nonlinear physical models and phenomena. Several physical and physicochemical systems where this method can be used are considered.