Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion

Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results.

THE CONSTITUTIVE RELATION OF CRACK-WEAKENED ROCK MASSES UNDER AXIAL-DIMENSIONAL UNLOADING

An accurate and efficient numerical method for solving the crack-crack interaction problem is presented. The method is mainly by means of the dislocation model, stress superposition principle and Chebyshev polynomial expansion of the pseudo-traction. This method can be applied to compute the stress intensity factors of multiple kinked cracks and multiple rows of periodic cracks as well as the overall strains of rock masses containing multiple kinked cracks under complex loads. Many complex computational examples are given. The dependence of the crack-crack interaction on the crack configuration, the geometrical and physical parameters, and loads pattern, is investigated. By comparison with numerical results under confining pressure unloading, it is shown that the crack-crack interaction under axial-dimensional unloading is weaker than those under confining pressure unloading. Numerical results for single faults and crossed faults show that the single faults are more unstable than the crossed faults. It is found from numerical results for different crack lengths and different crack spacing that the interaction among kinked cracks decreases with an increase in length of the kinked cracks and the crack spacing under axial-dimensional unloading.

Study on semi-active control of mega-sub controlled structure by MR damper subject to random wind loads

The recently proposed mega-sub controlled structure （MSCS）, a new type of structure associated with the design and construction of super-tall buildings, has attracted the attention of designers for use in enhancing the control effectiveness in mega-frame buildings. In this paper, a dynamic equation and method to assemble parameter matrixes for a mega-sub controlled structure under random wind loads is presented. Semi-active control using magnetorheological dampers for the MSCS under random wind loads is investigated, and is compared with a corresponding system without dampers. A parametric study of the relative stiffness ratio and relative mass ratio between the mega-frame and the substructures, as well as the additional column stiffness ratio that influences the response control effectiveness of the MSCS, is discussed. The studies reveal, for the first time, that different control mechanisms exist. The results indicate that the proposed structure employing semi-active control can offer an effective control mechanism. Guidelines for selecting parameters are provided based on the analytical study.

Brine-freeze-thaw Durability and Crack Density Model of Concrete in Salt Lake Region

The brine-freeze-thaw durability (defined as the durability under freeze-thaw cycles in Qinghai salt lake brine) of concrete (ordinary Portland cement concrete (OPC), high performance concrete (HPC-a), high performance concrete with steel fiber (HPC-b), and high performance concrete with high Young's modulus polyethylene fiber (HPC-c)) was systematically investigated by the relative dynamic elastic modulus, the relative mass, the appearance, the scanning electron microscopy, and the X-ray diffraction. In addition, the low-temperature physical and chemical corrosion mechanism and a crack density model after the modified relative dynamic elastic modulus being taken into consideration were proposed. The results show that the deterioration of OPC is the severest, followed by HPC-a, HPC-c and HPC-b. The admixture or the fiber is mixed into concrete, which can improve the brine-freeze-thaw durability of concrete. The critical mass growth of the failure of concrete is 3.7%. The cause of the deterioration of concrete under the brine-freeze-thaw cycles is physical and chemical corrosion, not freezing and thawing. The crack density model can effectively describe the deterioration evolution of concrete.

Relative Molecular Mass Distribution of BG Resins

Benzoguanamine formaldehyde (BG F) resins are a class of amino resins, which are important cross linking agents for epoxy, alkyol and acrylic resins, etc. The cross linking performance is the best one when the polymerization degree is 2 4. This paper discusses the effects of the pH value for polycondensation and the formaldehyde to benzoguanamine mole ratio in a methanol system, and compares the relative molecular mass distribution using the Flory statistics method.

Some new symmetric relations and prediction of left- and right-handed neutrino masses using Koide's relation

The masses of the three generations of charged leptons are known to completely satisfy Koide＇s mass relation,but the question remains of whether such a relation exists for neutrinos.In this paper,by considering the seesaw mechanism as the mechanism generating tiny neutrino masses,we show how neutrinos satisfy Koide＇s mass relation,on the basis of which we systematically give exact values of both left-and right-handed neutrino masses.

Changes in visibility with PM_(2.5) composition and relative humidity at a background site in the Pearl River Delta region

In fall–winter, 2007–2013, visibility and light scattering coefficients（b sp） were measured along with PM_（2.5）mass concentrations and chemical compositions at a background site in the Pearl River Delta（PRD） region. The daily average visibility increased significantly（p 〈 0.01） at a rate of 1.1 km/year, yet its median stabilized at ~13 km. No haze days occurred when the 24-hr mean PM_（2.5）mass concentration was below 75 μg/m^3. By multiple linear regression on the chemical budget of particle scattering coefficient（b sp）, we obtained site-specific mass scattering efficiency（MSE） values of 6.5 ± 0.2, 2.6 ± 0.3, 2.4 ± 0.7 and 7.3 ± 1.2 m2/g,respectively, for organic matter（OM）, ammonium sulfate（AS）, ammonium nitrate（AN） and sea salt（SS）. The reconstructed light extinction coefficient（b ext） based on the Interagency Monitoring of Protected Visual Environments（IMPROVE） algorithm with our site-specific MSE revealed that OM, AS, AN, SS and light-absorbing carbon（LAC） on average contributed 45.9% ± 1.6%,25.6% ± 1.2%, 12.0% ± 0.7%, 11.2% ± 0.9% and 5.4% ± 0.3% to light extinction, respectively.Averaged b ext displayed a significant reduction rate of 14.1/Mm·year（p 〈 0.05）; this rate would be 82% higher if it were not counteracted by increasing relative humidity（RH） and hygroscopic growth factor（f（RH）） at rates of 2.5% and 0.16/year-1（p 〈 0.01）, respectively, during the fall–winter, 2007–2013. This growth of RH and f（RH） partly offsets the positive effects of lowered AS in improving visibility, and aggravated the negative effects of increasing AN to impair visibility.

Age structure of a lizard along an elevational gradient reveals nonlinear lifespan patterns with altitude

Lifespan is one of the main components of life history.Shorter lifespans can be expected in marginal habitats.However,in the case of ectotherms,lifespan typically increases with altitude,even though temperature-one of the main factors to determine ectotherms'life history-declines with elevation.This pattern can be explained by the fact that a shorter activity time favors survival.In this study,we analyzed how lifespan and other life-history traits of the lizard Psammodromus algirus vary along a 2,200 m elevational gradient in Sierra Nevada(SE Spain).Populations at inter-mediate altitudes(1,200-1,700 m),corresponding to the optimal habitat for this species,had the shortest lifespans,whereas populations inhabiting marginal habitats(at both low and at high altitudes)lived longest.Therefore,this lizard did not follow the typical pattern of ectotherms,as it also lived longer at the lower limit of its distribution,nor did it show a longer lifespan in areas with optimal habitats.These results might be explained by a complex combination of different gradients along the mountain,namely that activity time decreases with altitude whereas food availability increases.This could explain why lifespan was maximum at both high(limited activity time)and low(limited food availability)altitudes,resulting in similar lifespans in areas with contrasting environmental conditions.Our findings also indicated that reproductive investment and body condition increase with elevation,suggesting that alpine populations are locally adapted.

A new parametric equation of state and quark stars

It is still a matter of debate to understand the equation of state of cold matter with supra-nuclear density in compact stars because of unknown non-perturbative strong interaction between quarks. Nevertheless, it is speculated from an astrophysical view point that quark clusters could form in cold quark matter due to strong coupling at realistic baryon densities. Although it is hard to calculate this conjectured matter from first principles, one can expect that the inter-cluster interaction will share some general features with the nucleon- nucleon interaction successfully depicted by various models. We adopt a two-Gaussian component soft-core potential with these general features and show that quark clusters can form stable simple cubic crystal structure if we assume that the wave function of quark clusters have a Gaussian form. With this parametrization, the Tolman-Oppenheimer-Volkoff equation is solved with reasonably constrained parameter space to give massradius relations of crystalline solid quark stars. With baryon number densities truncated at 2n0 at surface and the range of the interaction fixed at 2 fm we can reproduce similar mass-radius relations to that obtained with bag model equations of state. The maximum mass ranges from - 0.5M⊙ to 〉 ～ 3M⊙. The recently measured high pulsar mass （〉～ 2M⊙） is then used to constrain the parameters of this simple interaction potential.