The algebro-geometric solutions for Degasperis-Procesi hierarchy

Though completely integrable Camassa-Holm (CH) equation and Degasperis-Procesi (DP) equation are cast in the same peakon family, they possess the second- and third-order Lax operators, respectively. From the viewpoint of algebro-geometrical study, this difference lies in hyper-elliptic and non-hyper-elliptic curves. The non-hyper-elliptic curves lead to great difficulty in the construction of algebro-geometric solutions of the DP equation. In this paper, we derive the DP hierarchy with the help of Lenard recursion operators. Based on the characteristic polynomial of a Lax matrix for the DP hierarchy, we introduce a third order algebraic curve $\mathcal{K}_{r-2}$ with genus $r-2$, from which the associated Baker-Akhiezer functions, meromorphic function and Dubrovin-type equations are established. Furthermore, the theory of algebraic curve is applied to derive explicit representations of the theta function for the Baker-Akhiezer functions and the meromorphic function. In particular, the algebro-geometric solutions are obtained for all equations in the whole DP hierarchy.Comment: 65 pages. arXiv admin note: text overlap with arXiv:solv-int/9809004 by other author

Crashworthiness design of density-graded cellular metals

AbstractCrashworthiness of cellular metals with a linear density gradient was analyzed by using cell-based finite element models and shock models. Mechanisms of energy absorption and deformation of graded cellular metals were explored by shock wave propagation analysis. Results show that a positive density gradient is a good choice for protecting the impacting object because it can meet the crashworthiness requirements of high energy absorption, stable impact resistance and low peak stress

Strain-Induced Spin-Nematic State and Nematic Susceptibility Arising from 2×2 Fe Clusters in KFe_{0.8}Ag_{1.2}Te_{2}.

Spin nematics break spin-rotational symmetry while maintaining time-reversal symmetry, analogous to liquid crystal nematics that break spatial rotational symmetry while maintaining translational symmetry. Although several candidate spin nematics have been proposed, the identification and characterization of such a state remain challenging because the spin-nematic order parameter does not couple directly to experimental probes. KFe_{0.8}Ag_{1.2}Te_{2} (K_{5}Fe_{4}Ag_{6}Te_{10}, KFAT) is a local-moment magnet consisting of well-separated 2×2 Fe clusters, and in its ground state the clusters order magnetically, breaking both spin-rotational and time-reversal symmetries. Using uniform magnetic susceptibility and neutron scattering measurements, we find a small strain induces sizable spin anisotropy in the paramagnetic state of KFAT, manifestly breaking spin-rotational symmetry while retaining time-reversal symmetry, resulting in a strain-induced spin-nematic state in which the 2×2 clusters act as the spin analog of molecules in a liquid crystal nematic. The strain-induced spin anisotropy in KFAT allows us to probe its nematic susceptibility, revealing a divergentlike increase upon cooling, indicating the ordered ground state is driven by a spin-orbital entangled nematic order parameter

Dynamic response of elastic beam to a moving pulse: finite element analysis of critical velocity

Dynamic behaviour of a semi-infinite elastic beam subjected to a moving single sinusoidal pulse was investigated by using finite element method associated with dimensionless analysis. The typical features of the equivalent stress and beam deflection were presented. It is found that the average value of maximal equivalent stress in the beam reaches its maximum value when the velocity of moving pulse is closed to a critical velocity. The critical velocity decreases as the pulse duration increases. The material, structural and load parameters influencing the critical velocity were analysed. An empirical formula of the critical velocity with respect to the speed of elastic wave, the gyration radius of the cross-section and the pulse duration was obtained

Algebro-geometric Solutions for the Degasperis--Procesi Hierarchy

Though the completely integrable Camassa--Holm (CH) equation and Degasperis--Procesi (DP) equation are cast in the same peakon family, they possess the second- and third-order Lax operators, respectively. From the viewpoint of algebro-geometrical study, this difference lies in hyper-elliptic and non-hyper-elliptic curves. The non-hyper-elliptic curves lead to great difficulty in the construction of algebro-geometric solutions of the DP equation. In this paper, we derive the DP hierarchy with the help of Lenard recursion operators. Based on the characteristic polynomial of a Lax matrix for the DP hierarchy, we introduce a third order algebraic curve $\mathcal{K}_{r-2}$ with genus $r-2$, from which the associated Baker--Akhiezer functions, meromorphic function and Dubrovin-type equations are established. Furthermore, the theory of algebraic curve is applied to derive explicit representations of the theta function for the Baker--Akhiezer functions and the meromorphic function. In particular, the algebro-geometric solutions are obtained for all equations in the whole DP hierarchy

Impact of Microstructure on Solar Radiation Transfer Within Sea Ice During Summer in the Arctic : A Model Sensitivity Study

The recent rapid changes in Arctic sea ice have occurred not only in ice thickness and extent, but also in the microstructure of ice. To understand the role of microstructure on partitioning of incident solar shortwave radiation within the ice and upper ocean, this study investigated the sensitivity of the optical properties of summer sea ice on ice microstructures such as the volume fraction, size, and vertical distribution of gas bubbles, brine pockets, and particulate matter (PM). The results show that gas bubbles are the predominant scatterers within sea ice. Their effects on the scattering coefficient and ice albedo are 5 and 20 times stronger respectively than the effect of brine pockets. Albedo and transmittance of ice decrease with higher concentration and larger size of PM particles. A 4-cm top layer of ice with high PM concentration (50 g/m(3)) results in a 10% increase in radiation absorption. The role of ice microstructure in the partitioning of radiation transfer is more important for seasonal than for multiyear ice, and more important for ponded than for snow-covered ice. Varying ice microstructure can obviously alter solar radiation transfer in the ice-ocean system, even with a constant ice thickness. Our results suggest that numerical models should take the variable microstructure of sea ice into account to improve model accuracy and to understand the interaction between internal variations in Arctic sea ice and the ocean, especially in summer.Peer reviewe

Admittance-based controller design for physical human-robot interaction in the constrained task space

In this article, an admittance-based controller for physical human-robot interaction (pHRI) is presented to perform the coordinated operation in the constrained task space. An admittance model and a soft saturation function are employed to generate a differentiable reference trajectory to ensure that the end-effector motion of the manipulator complies with the human operation and avoids collision with surroundings. Then, an adaptive neural network (NN) controller involving integral barrier Lyapunov function (IBLF) is designed to deal with tracking issues. Meanwhile, the controller can guarantee the end-effector of the manipulator limited in the constrained task space. A learning method based on the radial basis function NN (RBFNN) is involved in controller design to compensate for the dynamic uncertainties and improve tracking performance. The IBLF method is provided to prevent violations of the constrained task space. We prove that all states of the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB) by utilizing the Lyapunov stability principles. At last, the effectiveness of the proposed algorithm is verified on a Baxter robot experiment platform. Note to Practitioners-This work is motivated by the neglect of safety in existing controller design in physical human-robot interaction (pHRI), which exists in industry and services, such as assembly and medical care. It is considerably required in the controller design for rigorously handling constraints. Therefore, in this article, we propose a novel admittance-based human-robot interaction controller. The developed controller has the following functionalities: 1) ensuring reference trajectory remaining in the constrained task space: A differentiable reference trajectory is shaped by the desired admittance model and a soft saturation function; 2) solving uncertainties of robotic dynamics: A learning approach based on radial basis function neural network (RBFNN) is involved in controller design; and 3) ensuring the end-effector of the manipulator remaining in the constrained task space: different from other barrier Lyapunov function (BLF), integral BLF (IBLF) is proposed to constrain system output directly rather than tracking error, which may be more convenient for controller designers. The controller can be potentially applied in many areas. First, it can be used in the rehabilitation robot to avoid injuring the patient by limiting the motion. Second, it can ensure the end-effector of the industrial manipulator in a prescribed task region. In some industrial tasks, dangerous or damageable tools are mounted on the end-effector, and it will hurt humans and bring damage to the robot when the end-effector is out of the prescribed task region. Third, it may bring a new idea to the designed controller for avoiding collisions in pHRI when collisions occur in the prescribed trajectory of end-effector

Associations Between Home Dampness-related Indicators and Eczema among Preschool Children in Shanghai, China

AbstractIn recent years, prevalence of eczema has been increasing among preschool children in China. It's urgent to find associated factors. On basis of 13,335 questionnaires from parents or guardians for 4-6 year-old children (response rate 85.3%) in a cross-sectional study from April 2011 to April 2012 in Shanghai, the associations between home dampness related indicators and the prevalence of childhood eczema was investigated. There were 7.8%, 15.3%, 42.1%, 55.7%, and 30.7% of the surveyed residences who had visible mold spots, visible damp stains, damp clothing and/or bedding, water damage, condensation on window in winter, and moldy odor (six home dampness-related indicators), respectively. The prevalence of eczema (ever) and eczema (in the past 12 months) was 22.9% and 13.2%, respectively. These home dampness indicators had significant and strong associations with the increased risk of childhood eczema. With regard to the same indicators, the increased risk of eczema in girls was higher than in boys. Total numbers of home dampness-related indicators had notable dose-response relationships with the prevalence of childhood eczema. In conclusion, home dampness-related exposures are strong risk factors for childhood eczema