Phenomenological Formula Research Articles

Time-resolved photoluminescence studies of annealed 1.3-μm GaInNAsSb quantum wells

Time-resolved photoluminescence (PL) was applied to study the dynamics of carrier recombination in GaInNAsSb quantum wells (QWs) emitting near 1.3 μm and annealed at various temperatures. It was observed that the annealing temperature has a strong influence on the PL decay time, and hence, it influences the optical quality of GaInNAsSb QWs. At low temperatures, the PL decay time exhibits energy dependence (i.e., the decay times change for different energies of emitted photons), which can be explained by the presence of localized states. This energy dependence of PL decay times was fitted by a phenomenological formula, and the average value of E0, which describes the energy distribution of localized states, was extracted from this fit and found to be smallest (E0 = 6 meV) for the QW annealed at 700°C. In addition, the value of PL decay time at the peak energy was compared for all samples. The longest PL decay time (600 ps) was observed for the sample annealed at 700°C. It means that based on the PL dynamics, the optimal annealing temperature for this QW is approximately 700°C.

Giant dipole resonance width and the universality of a fluctuation model including critical temperature

The universality of the critical-temperature-included fluctuation model (CTFM) in explaining the evolution of the giant dipole resonance (GDR) width as a function of angular momentum is examined in light of recent experimental data on ${}^{144}$Sm and ${}^{152}$Gd. We compare both data sets with the phenomenological formula based on the CTFM and the thermal shape fluctuation model (pTSFM). The CTFM describes both data sets reasonably well using the actual ground state GDR width (${\ensuremath{\Gamma}}_{0}$), whereas the pTSFM describes the ${}^{144}$Sm data well but is unable to explain the ${}^{152}$Gd data using a single value of ${\ensuremath{\Gamma}}_{0}$ for the two excitation energies. These interesting results clearly indicate that the phenomenological CTFM can be used universally to describe the evolution of the GDR width with both angular momentum and temperature in the entire mass region. Moreover, it should provide insights into the modification of the TSFM.

A simple approach for characterization of spring-type superlattice magnets using magneto-optical Kerr effect

A simple method for characterizing spring-type magnets is proposed by using a standard magneto-optical Kerr effect (MOKE) rig. As we previously reported, a spiral structure with parallel field (longitudinal) and normal field (transverse) components can easily develop in Laves-phase spring-type superlattice magnets once an external field is applied. Based on a phenomenological formula both longitudinal and transverse components in the exchange-springs can be probed simultaneously by MOKE. Out finding shows that not only the Kerr angle but the reflectivity change induced from transverse components can be used as good indicators for the formation of spiral structure in the spring-magnet.

Formula for the fine structure constant

An approach has been found to the Pauli problem which allows us to predict the experimental value of the fine structure constant in the form of a simple and symmetric formula giving accuracy to 12 significant digits. The phenomenological formula consists of a product of four geometric progressions so that the formal numerical representation of the factors consists only of occurrences of the numeral one. The formula gives impetus to the development of quantum electrodynamics.

Magnetic moment of constituent fermions in ground states with spontaneously broken translational invariance

Spontaneous symmetry breaking gives rise to a nonzero order parameter or a ground state expectation value (GEV) of the scalar field that generates energy gaps or constituent masses for the fermions via Yukawa interactions. There are several physical situations in which the order parameters or GEVs of the scalar field (and therefore constituent masses) can become space varying. This can change the definitions of several important physical operators. We investigate and rederive the generalized magnetic moment operator for ‘constituent’ fermions that arises from a space varying order parameter or GEV.We especially consider the high baryon density π0 condensed phase, in which chiral symmetry is spontaneously broken, with space varying expectation values of the σ and π0 fields. This phase has a spin polarized Fermi sea as the ground state. We show that there is indeed generated a macroscopic magnetization in this phase, contrary to what one would have found, if one just used a primitive phenomenological magnetic moment formula for explicit/current fermion masses. This is important in the context of neutron stars, as such a high density state may be responsible for very high magnetic fields in the dense core of neutron stars.

Self-consistent calculations of alpha-decay energies

On the basis of the self-consistent theory of finite Fermi systems, the energies of alphadecay chains were calculated for several new superheavy nuclei discovered recently in experiments of the Dubna-Livermore Collaboration headed by Yu.Ts. Oganessian. The approach in question is implemented on the basis of the generalized method of the density functional proposed by Fayans and his coauthors. The version used here relies on the functional DF3-a proposed recently for describing a wide array of nuclear data, including data on superheavy nuclei. A detailed comparison of the results obtained on this basis with the predictions of different approaches, including the self-consistent Skyrme-Hartree-Fock method, the micro-macro method in the version developed by Sobiczewski and his coauthors, and the phenomenological method of Liran and his coauthors, is performed. The resulting alpha-decay energies are used to calculate respective lifetimes with the aid of the phenomenological Parkhomenko-Sobiczewski formula.

High-shear drag reduction of surfactant solutions

Drag reducing surfactants produce micellar structures. Over critical shear stress, the break-up rate of these structures tends to be faster than the formation rate. An excess of counterions raises the critical shear stress, and enhances surfactant drag reduction up to higher shear in turbulent flow. We investigated this high-shear drag reduction for small circular cross-section tubes. The enhancement became saturated when the counterion to surfactant molar concentration ratio was higher than ten. This saturated condition allowed a 30% drag reduction for a wall shear stress of 103Pa (approximately 106s−1 shear rate) for a 1500ppm surfactant solution. The frictional drag of the tube flow was dependent on a Reynolds number at low shear and obeyed the friction formulas of a laminar pipe flow and a limiting drag reduction flow. Over critical shear stress, high shear decreased the drag reduction because of break-up of drag reducing micellar structures. This disappearance of the drag reduction was found to be a function of wall shear stress and independent of the tube diameters under saturated counterion-effect conditions. A phenomenological formula was introduced to describe the flow friction for these saturated counterion-effect conditions.

Diffraction gratings: An amazing phenomenon

Abstract The paper describes and explains the most surprising Woodʼs anomaly: the total absorption of a plane wave by a shallow metallic grating. After a numerical and experimental evidence of the total absorption, we develop a quantitative phenomenological theory. Assuming that the anomalies are caused by the excitation of surface plasmon polaritons on the grating surface, we use theorems on analytic functions of the complex variable for representing the amplitudes of the scattered waves accurately through a phenomenological formula. The original rigorous grating theory used for numerical computations is outlined and some practical applications of strong absorptions are presented.

Nuclear effective charge factor originating from covariant density functional theory

Guiding by the relativistic local density approximation, we explore a phenomenological formula for the coupling strength of Coulomb field to take into account the Coulomb exchange term effectively in the relativistic Hartree approximation. Its validity in finite nuclei is examined by comparing with the exact treatment of the Coulomb exchange energies in the relativistic Hartree-Fock-Bogoliubov approach. It is found that the exact Coulomb exchange energies can be reproduced by employing the phenomenological formula with the relative deviations less than 1% for semi-magic Ca, Ni, Sn, and Pb isotopes. Furthermore, we check the applicability of the phenomenological formula for the effective interactions in the relativistic Hartree approach by investigating the binding energy differences of mirror nuclei.

Erratum: Phenomenological formula of total reaction cross sections for low-energy systems [Phys. Rev. C86, 057603 (2012)

Received 13 December 2012DOI:https://doi.org/10.1103/PhysRevC.87.019901©2013 American Physical Society

Phenomenological formula of total reaction cross sections for low-energy systems

This Brief Report presents a phenomenological formula of total reaction cross sections for different reaction systems at low energies, taking into account the case of weakly bound nuclei as projectiles. To get this phenomenological formula, a large set of experimental data were collected and compared. Based on the experimental total reaction cross sections, three parameters were used to modify Wong's formula. The total reaction cross sections of different systems at low energies including weakly bound projectiles were reproduced using the modified formula.

Phenomenological formula for alpha-decay half-lives

A phenomenological formula is presented for the partial half-life from the Q value for α decay. It is constructed in a conventional way by considering the penetrability of a charged particle in a spherical Coulomb potential. Parameters in the formula are fixed because they are determined by physical constants except for the following three adjustable parameters: the product of the collision frequency of an α particle and the formation probability, N; the distance between the charge radius and the radius of an inner point of the Coulomb barrier, r 0; and the odd-mass hindrance, h 0. The values obtained for the three adjustable parameters are reasonable, in contrast with those of conventional models such as the Viola–Seaborg formula. The root-mean-square deviations from experimental partial half-lives for even–even, odd-A, and odd–odd nuclei are 0.344, 0.740, and 0.940 (in log10), respectively. The obtained formula gives half-lives that are two or three times longer than those obtained using the Viola–Seaborg formula in the superheavy nuclear mass region.

ENDPOINT OF rp PROCESS USING RELATIVISTIC MEAN FIELD APPROACH AND A NEW MASS FORMULA

Densities from relativistic mean field calculations are applied to construct the optical potential and, hence calculate the endpoint of the rapid proton capture (rp) process. Mass values are taken from a new phenomenological mass formula. Endpoints are calculated for different temperature-density profiles of various X-ray bursters. We find that the rp process can produce significant quantities of nuclei upto around mass 95. Our results differ from existing works to some extent.

A simple approach to the polytypism in SiC

A simple approach to the polytypism in SiC is proposed on the basis of phenomenological energy formula incorporating electrostatic interactions between interatomic bond charges and between ionic charges. The versatility of our approach is confirmed by calculating the energy differences among 3C (zinc blende), 6H, 4H and 2H (wurtzite) structures with/without vacancy. When the ionicity fi=0.232 for SiC is employed, the calculated respective energy differences ΔE for 6H, 4H, and 2H are very small such as 0.18meV/atom, 0.27meV/atom, and 5.7meV/atom where the energy origin is the energy for the most stable 3C. Furthermore, it is found that vacancy formation stabilizes 4H– or 6H–SiC. This is because the vacancy formation reduces the interatomic bond charges to destabilize 3C–SiC. These results are consistent with our previous ab initio calculations and experimental findings where 3C appears at low temperatures while 6H and 4H for SiC are favored at high temperatures enhancing vacancy formation. Our simple approach is also applied to the polytypism in SiC with impurities.

Modeling ductile fracture in metals involving two populations of voids – influence of continuous nucleation of secondary voids upon growth and coalescence of primary voids

This paper is devoted to the study of the influence of the nucleation of small, secondary voids upon the growth and coalescence of large, primary cavities in porous ductile metals. For this purpose, a simple model is considered: a hollow sphere subjected to hydrostatic loading whereby the central hole simulates a large, primary void, and the presence of secondary voids in the surrounding matrix is accounted for by the Gurson–Tvergaard–Needleman homogenized model for plastic porous materials. Continuous nucleation of small voids in the matrix is described by the straightforward phenomenological formula proposed by Pineau and Joly. Initially, the problem is solved analytically, then numerically when a non-uniform distribution of secondary voids develops in the matrix. These elements are used to define a simplified model in which only a small number of internal parameters describe the growth of primary voids coupled with the nucleation, growth and coalescence of secondary voids. Comparisons between the results derived from this simplified model and those obtained through the numerical computations are used to demonstrate the accuracy of the proposed model.

Relativistic channeling of a linearly polarized laser pulse in overdense plasma

AbstractWe investigated a dynamic procedure for relativistic channeling by a linearly polarized ultraintense laser pulse in overdense plasma, subsequently determining a phenomenological formula for the channel-digging speed. Channeling of the linearly polarized pulse usually results in a sharp-cut (non-adiabatic) pulse front, since the pulse is continuously reflected on the transparency-opacity interface during the channeling process. Using the novel formula for the channel-digging speed, it was possible to analytically predict where such a sharp-cut occurs longitudinally.

SU-E-T-248: An Extended Generalized Equivalent Uniform Dose Accounting for Dose-Range Dependency of Radio-Biological Parameters.

Introducing an extended, phenomenological, generalized equivalent uniform dose (eEUD) that incorporates multiple volume-effect parameters for different dose-ranges. The generalized EUD (gEUD) was introduced as an estimate of the EUD that incorporates a single, tissue-specific parameter - the volume-effect-parameter (VEP) 'a'. As a purely phenomenological concept, its radio-biological equivalency to a given inhomogeneous dose distribution is not a priori clear and mechanistic models based on radio-biological parameters are assumed to better resemble the underlying biology. However, for normal organs mechanistic models are hard to derive, since the structural organization of the tissue plays a significant role. Consequently, phenomenological approaches might be especially useful in order to describe dose-response for normal tissues. However, the single parameter used to estimate the gEUD may not suffice in accurately representing more complex biological effects that have been discussed in the literature. For instance, radio-biological parameters and hence the effects of fractionation are known to be dose-range dependent. Therefore, we propose an extended phenomenological eEUD formula that incorporates multiple VEPs accounting for dose-range dependency. The eEUD introduced is a piecewise polynomial expansion of the gEUD formula. In general, it allows for an arbitrary number of VEPs, each valid for a certain dose-range. We proved that the formula fulfills required mathematical and physical criteria such as invertibility of the underlying dose-effect and continuity in dose. Furthermore, it contains the gEUD as a special case, if all VEPs are equal to 'a' from the gEUD model. The eEUD is a concept that expands the gEUD such that it can theoretically represent dose-range dependent effects. Its practicality, however, remains to be shown. As a next step, this will be done by estimating the eEUD from patient data using maximum-likelihood based NTCP modelling in the same way it is commonly done for the gEUD.

Can the Dean number Alone Characterize Flow Similarity in Differently Bent Tubes?

Although flows of fluids in curved channels belong to a classical problem of fluid dynamics, most publications are restricted to investigations of flows in tube coils, or in single bends. This paper presents experimental and numerical (CFD) results concerning Newtonian flows in a set of multiple S-type bends of various orientations. Investigations were conducted for a wide range of Re values (0–3500) and for a significant curvature ratio lying between 0.05 and 0.29, which corresponds to De value falling within the range 0.02–1200. A coiled tube was also examined and treated as the reference geometry. It was shown, that despite a completely different velocity pattern, the nonlinear dependence of normalized flow resistance of wavy tubes and coiled tube of the same curvature ratio overlap within a significant range of De. A novel, close phenomenological formula to estimate the nonlinear flow resistance of tortuous tube in a wide range of De was proposed and compared with those in the literature. The conditions were also determined in which the De might be the only dimensionless group that characterizes such flows.

Design Principle Study of High Efficiency Compact Fluorescent Lamps

Design rules for small power T2 and T3 compact fluorescent lamps (CFLs) with power ranging from 5 to 23 W were investigated to develop high efficiency lamps. The relationships between light performance, electrical characteristics and tube design were studied. Phenomenological formulas of light efficacy were deduced from the experimental data. Calculations based on the design formulas are compared with the measured data for several brands and powers of lamps to verify the validity of the design formulas. The calculations fit well with the measured data. Maps relating light efficacy, lamp power and lamp geometry were created from the phenomenological formulas. The maximum light efficacy curves produced provide guidance for the development of high efficacy CFL lamps.

NEUTRON RICH NUCLEI IN A NEW BINDING ENERGY FORMULA AND THE ASTROPHYSICAL r-PROCESS

Neutron rich nuclei has been studied with a new phenomenological mass formula. Predictions of different mass formulas for the location of the neutron drip line are compared with those from the present calculation. The implications of the new mass formula for r-process nucleosynthesis are discussed. It is found that though the neutron drip line obtained from this formula differs substantially from other formulas, the r-process abundance upto mass 200 are unlikely to be significantly different. The errors inherent in the mass formula are found to play an insignificant role beyond mass A = 80.