Narrow Results

The nucleon has been used as a laboratory to investigate its own spin structure and quantum chromodynamics. New experimental data on nucleon spin structure at low to intermediate momentum transfers combined with existing high momentum transfer data offer a comprehensive picture of the transition region from the confinement regime of the theory to its asymptotic freedom regime. Insight for some aspects of the theory is gained by exploring lower moments of spin structure functions and their corresponding sum rules (i.e. the Gerasimov–Drell–Hearn, Bjorken and Burkhardt–Cottingham). These moments are expressed in terms of an operator-product expansion using quark and gluon degrees of freedom at moderately large momentum transfers. The sum rules are verified to good accuracy assuming that no singular behavior of the structure functions is present at very high excitation energies. The higher-twist contributions have been examined through the moments evolution as the momentum transfer varies from higher to lower values. Furthermore, QCD-inspired low-energy effective theories, which explicitly include chiral symmetry breaking, are tested at low momentum transfers. The validity of these theories is further examined as the momentum transfer increases to moderate values. It is found that chiral perturbation calculations agree reasonably well with the first moment of the spin structure function g₁ at momentum transfer of 0.1 GeV² but fail to reproduce the neutron data in the case of the generalized polarizability δ_LT.

The moments $〈r^m〉$ of the spherical three-parameter Fermi distribution (3pF) are presented for $m=1$ to 8 as a function of the parameter $w$, the half-density radius $c$ and the diffuseness parameter $a$ through the introduced parameter $\beta =\pi a/c$, which can be applied to study the neutron skin in neutron rich nuclei. The general expression of the moment can be written as the combination of integrals $I_n(k,w)$ with $k=c/a$. The errors of the analytic moments $〈r^m〉$ are estimated with the typical values of the parameters in 3pF compared with the numerical results.

A theoretical comparison has been made for some calcium isotopes (${}_{20}$Ca) which are even–even nuclei and have the atomic mass (Z = 20) with its previous experimental data. Theoretical calculations of some ${}_{20}$Ca isotopes (A = 42, 44, 46, 48, 50, 52) adopted by the shell model theory were performed to calculate the transition rate B(E2), theoretical intrinsic quadruple moments ($Q_{0\mathrm{\text{Th}}})$ and theoretical deformation parameters (${\beta }_2$, $\delta {)}_{\mathrm{\text{Th}}}$ were calculated by two methods by using different effective interactions for each isotope such as, su3fp, fpbm, fprkb, fpd6, kb3. Through code NuShellX@MSU, the single-body density matrix was calculated. The effects of the core polarization were neglected by adopting various effective charges that were employed, effective charges of conventional (Con-E), effective charges of standard (St-E) and effective charges of Bohr and Mottelson (B-M-E) which were calculated. The theoretical values of the B(E2)_Th, the $Q_{0\mathrm{\text{Th}}}$ and the (${\beta }_2$, $\delta {)}_{\mathrm{\text{Th}}}$ were then compared with the previous experimental data where values of the transition rate B(E2)_Th, theoretical intrinsic quadrupole moments $Q_{0\mathrm{\text{Th}}}$ and theoretical deformation parameter (${\beta }_2$, $\delta {)}_{\mathrm{\text{Th}}}$, using the fpbm, the fpd6 and the kb3 interactions were the best.

Nucleon structure study is one of the most important research areas in modern physics and has challenged us for decades. Spin has played an essential role and often brought surprises and puzzles to the investigation of the nucleon structure and the strong interaction. New experimental data on nucleon spin structure at low to intermediate momentum transfers combined with existing high momentum transfer data offer a comprehensive picture in the strong region of the interaction and of the transition region from the strong to the asymptotic-free region. Insight into some aspects of the theory for the strong interaction, Quantum Chromodynamics (QCD), is gained by exploring lower moments of spin structure functions and their corresponding sum rules (i.e., the Bjorken, Burkhardt–Cottingham, Gerasimov–Drell–Hearn (GDH), and the generalized GDH). These moments are expressed in terms of an operator-product expansion using quark and gluon degrees of freedom at moderately large momentum transfers. The higher-twist contributions have been examined through the evolution of these moments as the momentum transfer varies from higher to lower values. Furthermore, QCD-inspired low-energy effective theories, which explicitly include chiral symmetry breaking, are tested at low momentum transfers. The validity of these theories is further examined as the momentum transfer increases to moderate values. It is found that chiral perturbation theory calculations agree reasonably well with the first moment of the spin structure function g₁ at low momentum transfer of 0.05–0.1 GeV² but fail to reproduce some of the higher moments, noticeably, the neutron data in the case of the generalized polarizability δ_LT. The Burkhardt–Cottingham sum rule has been verified with good accuracy in a wide range of Q² assuming that no singular behavior of the structure functions is present at very high excitation energies.

The cello suites of Johann Sebastian Bach exhibit several types of power-law scaling, the best examples of which can be considered fractal in nature. This article examines scaling with respect to the characteristics of melodic interval and its derivative, melodic moment. A new and effective method for pitch-related analysis is described and then applied to a selection of the 36 pieces that comprise the six cello suites.

A new type of iterated function systems is constructed based on different weights, and it is proved that this type of iterated function systems generates a class of bivariate continuous functions whose graphs are the fractal interpolation surfaces passing through the given interpolation points. Considering the influences of the fractal interpolation functions on different weights and basic functions, we give the corresponding error estimation formula. Finally, the calculation formula for the integral moments of this class of bivariate fractal interpolation functions is given.

The blended wing body (BWB) is the hottest one of the aerodynamic shapes of next generation airliner because of its' high lift-drag ratio, but there are still some flaws that cut down its aerodynamical performance. One of the most harmful flaws is the low efficiency of elevator and direction rudder, this makes the BWB hard to be controlled. In this paper, we proposed a new control method to solve this problem by morphing wing—that is, to control the BWB only by changing its wing shape but without any rudder. The pitching moments, rolling moments and yawing moments are plotted versus the parameters section and the wing shape in figures and are discussed in the paper. The result shows that the morphing wing can control the moments of BWB more precisely and in wider range. The pitching moments, rolling moments and yawing moments increases or decreases linearly or almost linearly, with the value of the selected parameters. These results show that using morphing wing is an excellent aerodynamic control way for a BWB craft.

Some aspects of long surface waves are considered. Special attention is focused on the existence of conservation laws for this physical system and related problems.

The nucleon spin structure has been an active, exciting and intriguing subject of interest for the last three decades. Recent experimental data on nucleon spin structure at low to intermediate momentum transfers provide new information in the confinement regime and the transition region from the confinement regime to the asymptotic freedom regime. New insight is gained by exploring moments of spin structure functions and their corresponding sum rules (i.e. the generalized Gerasimov-Drell-Hearn, Burkhardt-Cottingham and Bjorken). The Burkhardt-Cottingham sum rule is verified to good accuracy. The spin structure moments data are compared with Chiral Perturbation Theory calculations at low momentum transfers. It is found that chiral perturbation calculations agree reasonably well with the first moment of the spin structure function g₁ at momentum transfer of 0.05 to 0.1 GeV² but fail to reproduce the neutron data in the case of the generalized polarizability δ_LT (the δ_LT puzzle). New data have been taken on the neutron (³He), the proton and the deuteron at very low Q² down to 0.02 GeV². They will provide benchmark tests of Chiral dynamics in the kinematic region where the Chiral Perturbation theory is expected to work.