Discrepancies between Observational Data and Theoretical Forecast in Single Field Slow Roll Inflation

The PLANCK collaboration has determined, or greatly constrained, values for the spectral parameters of the CMB radiation, namely the spectral index n_s, its running α_s, the running of the running β_s, using a growing body of measurements of CMB anisotropies by the Planck satellite and other missions. These values do not follow the hierarchy of sizes predicted by single field, slow roll inflationary theory, and are thus difficult to fit for such inflation models. In this work we present first a study of 49 single field, slow roll inflationary potentials in which we assess the likelyhood of these models fitting the spectral parameters to their currently most accurate determination given by the PLANCK collaboration. We check numerically with a MATLAB program the spectral parameters that each model can yield for a very broad, comprehensive list of possible parameter and field values. The comparison of spectral parameter values supported by the models with their determinations by the PLANCK collaboration leads to the conclusion that the data provided by PLANCK2015 TT+lowP and PLANCK2015 TT,TE,EE+lowP taking into account the running of the running disfavours 40 of the 49 models with confidence level at least 92.8 %. Next, we discuss the reliability of the current computations of these spectral parameters. We identify a bias in the method of determination of the spectral parameters by least residue parameter fitting (using MCMC or any other scheme) currently used to reconstruct the power spectrum of scalar perturbations. This bias can explain the observed contradiction between theory and observations. Its removal is computationally costly, but necessary in order to compare the forecasts of single field, slow roll theories with observations.     

Classical versus non-classical behaviour of incommensurate systems from secondary order parameter susceptibility

A relation between the susceptibility of secondary order parameters (polarization, elastic strain, etc.) and the soliton density n_s in incommensurate systems is derived from phenomenological considerations. It is argued, that this relation allows to distinguish between classical and nonclassical behaviour of n_s. Present experimental findings support the idea, that the classical theory is essentially correct for three-dimensional systems.     

A New Unified Dark Fluid Model and Its Cosmic Constraint

In this paper, we propose a new unified dark fluid (UDF) model with equation of state (EoS) w(a)=?α/(β a ^?n +1), which includes the generalized Chaplygin gas model (gGg) as its special case, where α, β and n are three positive numbers. It is clear that this model reduces to the gCg model with EoS w(a)=?B _s /(B _s +(1?B _s )a ^?3(1+α)), when α=1, β=(1?B _s )/B _s and n=3(1+α). By combination the cold dark matter and the cosmological constant, one can coin a EoS of unified dark fluid in the form of w(a)=?1/(1+(1?Ω_Λ)a ^?3/Ω_Λ). With this observations, our proposed EoS provides a possible deviation from ΛCDM model when the model parameters α and n deviate from 1 and 3 respectively. By using the currently available cosmic observations from type Ia supernovae (SN Ia) Union2.1, baryon acoustic oscillation (BAO) and cosmic microwave background radiation (CMB), we test the viability of this model and detect the possible devotion from the ΛCDM model. The results show that the new UDF model fits the cosmic observation as well as that of the ΛCDM model and no deviation is found from the ΛCDM model in 3σ confidence level. However, our new UDF model can give a non-zero sound speed, as a contrast, which is zero for the ΛCDM model. We expect the large structure formation information can distinct the new UDF model from the ΛCDM model.     

Excitation of rubidium atoms by electron impact

An analytic central potential containing two adjustable parameters is used to generate wave functions for the ground and excited states of the rubidium atom. The two parameters are chosen so that the potential reproduces accurately known values of optical oscillator strengths for the 5s?np (n≧5) transitions. Using the Born approximation, we calculate generalized oscillator strengths and integrated cross sections up to 5 keV for the 5s?np excitations. Reasonable agreement with experimental data is obtained.     

Tuning and validation of hadronic event generator for R value measurements in the tau-charm region

To measure the R value in an energy scan experiment with e⁺e^- collisions, precise calculation of initial state radiation is required in the event generators. We present an event generator for this consideration, which incorporates initial state radiation effects up to second order accuracy. The radiative correction factor is calculated using the totally hadronic Born cross section. The measured exclusive processes are generated according to their cross sections, while the unknown processes are generated using the LUND Area Law model, and its parameters are tuned with data collected at √s=3.65 GeV. The optimized values are validated with data in the range √s=2.2324-3.671 GeV. These optimized parameters are universally valid for event generation below the DD threshold.     

Transition energy and dipole oscillator strength of 1s23d-1s2 nf transitions for Sc18+ ion

The transition energies of the 1s²3d-1s² nf (4?n?9) transitions and fine structure splittings of 1s² nf (n?9) states for Sc¹⁸⁺ ion are calculated with the full-core plus correlation method. The quantum defect of 1s² nf series is determined by the single-channel quantum defect theory. The energies of any highly excited states with n?10 for this series can be reliably predicted using the quantum defect as function of energy. Three alternative forms of the dipole oscillator strengths for the 1s²3d-1s² nf (n?9) transitions of Sc¹⁸⁺ ion are calculated with the transition energies and wave functions obtained above. Combining the quantum defect theory with the discrete oscillator strengths, the discrete oscillator strengths for 1s²3d-1s² nf (n > 9) transitions and the oscillator strengths densities corresponding to the bound-free transitions are obtained.     

Composition law of cardinal ordering permutations

In this paper the theorems that determine composition laws both cardinal ordering permutations and their inverses are proven. So, the relative position of points in an hs-periodic orbit is completely known as well as which order those points are visited, no matter how the hs-periodic orbit emerges, be it through a period doubling cascade (s=2ⁿ) of as the h-periodic orbit or a primary window (like saddle-node bifurcation cascade with h=2ⁿ) or a secondary window (the birth of an s-periodic window inside the h-periodic one). Certainly, period doubling cascade orbits are particular cases with h=2 and s=2ⁿ. Both composition laws are also shown in algorithmic way for easy use.     

On the dynamic conductivity for an electron-impurity system

The correlation function formula for the dynamic conductivity of a system of non-interacting electrons in the field of impurities is analyzed in terms of proper connected diagrams. By selecting those diagrams appropriate in the region of weak coupling and low impurity concentration, a set of coupled equations for the energy broadening γ (ω, ε, n_s) and the energy shift Δ(ω, ε, n_s) is derived, where both γ and Δ depend on the frequency ω of a probing field, the energy ε of the electron, and the concentration, n_g, of impurities. With the assumption of a finite range potential, these equations are solved. It is found that γ (ω, n_s) is smaller than that extrapolated value which the conventional expression γ₀ for the low-concentration collision frequency would predict, in the entire region studied, that the difference γ₀-γ becomes appreciable when the ratio of the average time between scatterings, τ_c, to the average duration of a scattering, τ_d, is 100 or less, that γ (ω, n_s) decreases monotonically from its static value γ (0, n_s), and becomes vanishingly small in the region ω≈1/τ_d, and that in the static limit (ω=0), γ=γ₀[1?(2/π) (γ₀τ_d)+…], that the energy shift Δ is positive, and increases from 0 and reach a peak of magnitude γ₀ as ω is raised from 0. By using the γ and Δ obtained, the dynamic conductivity σ(ω, n_s) for degenerated electrons is calculated. The deviation, σ-σ₀, from the conventional expression σ₀=(?i) (n_ee²/M) [ω-iΓ₀]^?1, (n_e]=number density of electrons), for 0°K, is appreciable when the ratio τ_c/τ_d is 100 or less. The field-term correction, which arises from the modification of the scattering due to the probing field, is found to be negligible in the entire region studied.     

Neutron irradiation effects on I–V characteristics of Au/n-GaAs Schottky diodes

Diodes are one of the most important and widely used components of electronic circuits. These devices can be damaged especially when they are used in radiation fields whose effects depend on radiation type and energy. To investigate these effects, the Au/n-GaAs type Schottky diodes have been irradiated by neutrons emitted from a ²⁵²Cf source which provides neutrons at an average energy of 2.14 MeV. The diode parameters barrier height (Φ_b0), ideality factor (n) and series resistance (R_s) have been obtained from forward current–voltage (I–V) characteristics before and after irradiation and the results are discussed.     

Glauber Dynamics for the Mean-Field Potts Model

We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with q??3 states and show that it undergoes a critical slowdown at an inverse-temperature ?? _s (q) strictly lower than the critical ?? _c (q) for uniqueness of the thermodynamic limit. The dynamical critical ?? _s (q) is the spinodal point marking the onset of metastability. We prove that when ??<?? _s (q) the mixing time is asymptotically C(??,q)nlogn and the dynamics exhibits the cutoff phenomena, a sharp transition in mixing, with a window of order n. At ??=?? _s (q) the dynamics no longer exhibits cutoff and its mixing obeys a power-law of order n ^4/3. For ??>?? _s (q) the mixing time is exponentially large in n. Furthermore, as ?????? _s with n, the mixing time interpolates smoothly from subcritical to critical behavior, with the latter reached at a scaling window of O(n ^?2/3) around ?? _s . These results form the first complete analysis of mixing around the critical dynamical temperature??including the critical power law??for a model with a first order phase transition.     

Molecular nanocluster fluorescence in microwave infrared-radiation fields

The paper considers a donor-acceptor nanocluster fluorescing in a microwave infrared radiation field. It is assumed that the nanocluster consists of two dipole-dipole interacting organic molecules. It is shown that the fluorescence process of the nanocluster occurs if the donor molecule contains a substructure of identical diatomic pairwise interacting bonds of dipoles (an IR antenna). This antenna is capable of accumulating vibrational energy as a sum of collective vibrational quanta (excimols). The acceptor molecule has no permanent dipole moment and cannot be excited by microwave IR radiation. This molecule is polarized in the dipole moment field of the donor IR antenna and can receive energy accumulated in the IR antenna of the donor molecule. If the acceptor molecule has an electronically excited state in the long-wavelength visible region of its absorption spectrum, then after receiving energy equal to the energy of this state from the donor antenna, the electronic excitation of the acceptor molecule and its fluorescence is possible. As an example, the fluorescence of a nanocluster is considered whose donor molecule has a C _n H_2n IR antenna. The acceptor molecule is aromatic and the external infrared frequency, 1.1 × 10¹⁴ s^?1, is equal to the frequency of the excimol in the donor infrared antenna.     

Isometric immersions of pseudo-Riemannian space forms

In this paper we study local isometric immersions f:M_sⁿ(K)→N_s+q²ⁿ⁻¹(c) of a time-like n-submanifold M_sⁿ(K) with constant sectional curvature K and index s into a pseudo-Riemannian space form N_s+q²ⁿ⁻¹(c) with constant sectional curvature c and index s+q, where q≥0, 1≤s≤n−1 and K≠c. We first prove the existence of Chebyshev coordinates of a time-like submanifold M_sⁿ(K) in certain conditions. Afterwards, we generalize the classical Bäcklund theorem for space-like (or time-like) submanifolds in N_n−1²ⁿ⁻¹(c) and N₁²ⁿ⁻¹(c). Finally as an application, in the Chebyshev coordinates, we use the Bäcklund theorem to give a Bäcklund transformation and a permutability formula between the generalized sine-Laplace equation and the generalized sinh-Laplace equation.     

Measurements of optical parameters of phantom solution and bulk animal tissues in vitro at 650 nm

Optical parameters of bulk animal tissue in vitro, including absorption coefficient (μ_a), reduced scattering coefficient (μ′_s) or scattering coefficient (μ_s), total attenuation coefficient (μ_t), anisotropy factor (g) and refractive index (n) are measured at wavelength of 650 nm. Clinical Intralipid-10% is diluted in distilled water into different concentrations to use as tissue phantoms. Four types of animal tissues in vitro are studied. The relationships among the optical parameters are analyzed systemically. For animal tissues, μ_a, μ′_s or μ_s and n rely on muscle fiber orientations. μ_s and μ_t range from 10 to 20 mm⁻¹, μ_a from 10⁻² to 10⁻³ mm⁻¹ and g from 0.95 to 0.99.     

Natural frequencies of simply supported circular plates

Although the problem of finding the natural frequencies of free vibration of a simply supported circular plate has a straightforward solution, very few numerical results are available in the literature. In the present work accurate (six significant figure) non-dimensional frequency parameters (λ²) are given for all values of n + s ? 10, where n and s are the numbers of nodal diameters and internal nodal circles, respectively, and for Poisson's ratios 0, 0·1, …, 0·5. Simplified formulas for determining additional values of λ² for large s are derived by the use of asymptotic expansions.     

First-principles calculation of the energy of compressed calcium

The energy of a calcium crystal with a simple cubic lattice as a function of the ratio (t/U) between two internal parameters of the Hubbard model has been calculated using the Hubbard model for the s bands, equations of motion, and direct algebraic method. The electronic spectra have been calculated for the 4s band of the crystal in two principal symmetry directions of the first Brillouin zone. The calculations have been performed at temperatures T ₁ = 0 K and T ₂ = 1000 K. All calculations have been carried out for different interaction energies U of s electrons, one angle, and their different concentrations n in the range 0 ≤ n ≤ 2. The calculations have demonstrated that the dependences of the energy and electronic spectra in this compressed state are very smooth. The occupation of the Ca 4s band is in good agreement with the results of the pioneering calculations of compressed Ca (and a number of other metals), which were carried out by Gandel’man and his colleagues in the Wigner-Seitz spherical cell approximation. It has been shown that the performed analysis accurately reproduces the data obtained on the superconductivity in terms of the Bardeen-Cooper-Schrieffer theory if the 4s band is half-occupied.     

On the quantum density of states and partitioning an integer

This paper exploits the connection between the quantum many-particle density of states and the partitioning of an integer in number theory. For N bosons in a one-dimensional harmonic oscillator potential, it is well known that the asymptotic (N→∞) density of states is identical to the Hardy-Ramanujan formula for the partitions p(n), of a number n into a sum of integers. We show that the same statistical mechanics technique for the density of states of bosons in a power-law spectrum yields the partitioning formula for p^s(n), the latter being the number of partitions of n into a sum of sth powers of a set of integers. By making an appropriate modification of the statistical technique, we are also able to obtain d^s(n) for distinct partitions. We find that the distinct square partitions d²(n) show pronounced oscillations as a function of n about the smooth curve derived by us. The origin of these oscillations from the quantum point of view is discussed. After deriving the Erdos-Lehner formula for restricted partitions for the s=1 case, we use the modified technique to obtain a new formula for distinct restricted partitions.     

Axisymmetric fluid-dominated wave in fluid-filled plastic pipes: Loading effects of surrounding elastic medium

Axisymmetric (n = 0) waves that propagate at low frequencies are of practical interest in the application of acoustic techniques for the detection of leaks in fluid-filled pipelines. A general expression for the fluid-dominated (s = 1) wavenumber is presented in a thin-walled fluid-filled pipe surrounded by an elastic medium. In this paper the analysis is extended to investigate the loading effects of surrounding medium on the low-frequency propagation characteristics of the s = 1 wave. The analytical model is subsequently applied to MDPE water pipes surrounding by three media, namely an air, water and soil. It is used to demonstrate explicitly the loading effects of surrounding medium, acting as a combination of mass, stiffness and radiation damping on the s = 1 wavenumber. Good agreement is achieved between the measurements and predictions. The theory with experimental validations provides the basis for improving acoustic leak detection methods in fluid-filled pipe systems.     

Study of the iterations of a mapping associated to a spin glass model

We study the iterations of the mapping $$\mathcal{N}[F(s)] = \frac{{(F(s))^2 - (F(0))^2 }}{s} + (F(0))^2 ,$$ with the constraintsF(1)=1,F(s)=∑a _nsⁿ,a _n≧0, and find that, except ifF(s)≡s,N[F(s)] approaches either 0 or 1 for |s|<1 ask→∞.     

Dielectronic recombination rate coefficients for Fe23+ ion

The dielectronic recombination rate coefficients are explicitly calculated for the Li-like ion Fe²³⁺, which recombines with the continuum electron to form Fe²²⁺. Both 1s²2s and 1s²2p initial states are treated for the temperature range 1～8 keV. The rate coefficients are obtained from a direct evaluation of the Auger and radiative transition probabilities which are calculated from nonrelativistic Hartree-Fock wave functions. The L-shell electron excitation with Δn≠0 is found to be the dominant transition, while the 2s→2p excitation with Δn = 0 contributes approx. 10–25% of the Δn≠0 value. The K-shell excitation effect is about 1～30% in the temperature range considered, and the cascade effect is estimated to be a reduction in the rate of about 14%.     

Lattice model calculation of hugoniot curves and the grüneisen parameter at high pressure for the alkali halides

A seven parameter shell model of the interatomic forces in the NaCl lattice is used to make a detailed lattice dynamics calculation at arbitrary volume, for fourteen alkali halides. The calculated normal mode spectrum gives an explicit vibrational contribution to the pressure and the elastic constants in the quasiharmonic approximation. The seven parameters are chosen to fit low pressure ultrasonic data and the low and high frequency dielectric constants. Prediction of the Grüneisen parameter γ, (?lnγ/?lnV), and δ_s = (?1/βB_s)(dB_s/dT) are in reasonable agreement with experiment. The calculated γ decreases monotonically with volume. Calculated Hugoniots are in good agreement with experiment for NaCl, NaBr and NaI, and in fair agreement for LiBr, LiI and NaF.