A two-parameter multiple shooting method and its application to the natural vibrations of non-prismatic multi-segment beams

This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved.A novel approach is applied to the analysis of the natural vibrations of Euler-Bernoulli beams.The proposed algorithm,named as two-parameter multiple shooting method,is a new powerful numerical tool for calculating the natural frequencies and modes of multi-segment prismatic and non-prismatic beams with different boundary conditions.The impact of the axial force and additional point masses is also taken into account.Due to the fact that the method is based directly on the fourth-order ordinary differential equation,the structures do not have to be divided into many small elements to obtain an accurate enough solution,even though the geometry is very complex.To verify the proposed method,three different examples are considered,i.e.,a three-segment non-prismatic beam,a prismatic column subject to non-uniformly distributed compressive loads,and a two-segment beam with an additional point mass.Numerical analyses are carried out with the software MATHEMATICA.The results are compared with the solutions computed by the commercial finite element program SOFiSTiK.Good agreement is achieved,which confirms the correctness and high effectiveness of the formulated algorithm.

Efficient Micropropagation of Chestnut Hybrids(Castanea spp.)Using Modified Woody Plant Medium and Zeatin Riboside

The chestnuts genus(Castanea spp.)is comprised of economically important trees native to the Northern hemisphere that are used as food and hardwood timber.Here,a very efficient method for micropropagation of European×Japanese chestnut hybrids(Castanea sativa×C.crenata)is described.Woody Plant Medium was used as the basal medium.In vitro shoots of four rootstock cultivars were micropropagated without shoot-tip necrosis on multiplication medium containing 5.7 or 11.4μmol·L^(−1)zeatin riboside,and were rooted on rooting medium containing 2.46μmol·L^(−1)indolebutyric acid.Monthly shootmultiplication rates for each cultivarwere 2–5 folds.In vitro rooting percentages for four cultivars were 87%for‘Maraval’,67%for‘Marigoule’,93%for‘Marsol’,and 97%for‘Précoce Migoule’.Within a 5 week period,80%–95%of rooted shoots were successfully acclimated under high humidity conditions after they were planted in either soil or rockwool.

Micropropagation of Curcuma Sp., a Threatened Medicinal Plant

A rapid and improved micropropagation protocol was developed for Curcuma sp., a threatened and high value medicinal plant, using main bud sprout and top of rhizome sprout as explants. Stepwise optimization of different plant is to change the growth regulator, reduce the level of macro-nutrition and add humate. The present study has created multiple shoot and root induction and plantlet in vitro culture, transfers the plantlet to ex vitro. The M2 medium (MS’s macronutrition 1/4, MS’s micronutrition + Morel’s vitamine + coconut milk 10% + sucrose 25 g/l + humate 1.0 ml/l + agar 7.5 g/l + 2,4D 0.5 mg/l + BAP1.0 mg/l + TDZ 1.0 mg/l) is the highest ratio of callus induction. The TA3 medium (MS’s macronutrition 1/4 + MS’s micronutrition + Morel’s vitamin+ coconut milk 10% + sucrose 25g/l + humate 2.0 ml/l + 2,4 D 0.5 mg/l + Kinetin 2.0 mg/l + TDZ 1.0 mg/l + BAP 1.0 mg/l2 + NAA 2.0 mg/l + activated carbon 2.0 g/l) is able to create buds and regeneration multiple bud for Curcuma sp. TA3 medium adding IAA 2 mg/l and IBA 0.5 mg/l has resulted in the highest indices of quantity, healthy shoot and large diameter of roots. A large number of healthy plantlets are induced by the medium of MS’s macronutrients 1/2, MS’s micronutrients full, Morel’s vitamin, humate 3 g/l, coconut milk 150 ml/l, activated carbon 3 g/l, composition phytohormone: IAA 2 mg/l + BAP 2 mg/l + TDZ 0.5 mg/l. Further studies should focus on optimizing the humate concentration for these species of Zingiberaceae. The duration of the research is from 5/2015 to 4/2016 at Faculty of Agriculture and Forestry, Tay Nguyen University, Vietnam.

LONG-TERM RIGOROUS NUMERICAL INTEGRATION OF NAVIER-STOKES EQUATION BY NEWTON-GMRES ITERATION

The recent result of an orbit continuation algorithm has provided a rigorous method for long-term numerical integration of an orbit on the unstable manifold of a periodic solution.This algorithm is matrix-free and employs a combination of the Newton-Raphson method and the Krylov subspace method.Moreover,the algorithm adopts a multiple shooting method to address the problem of orbital instability due to long-term numerical integration.The algorithm is described through computing the extension of unstable manifold of a recomputed Nagata′s lowerbranch steady solution of plane Couette flow,which is an example of an exact coherent state that has recently been studied in subcritical transition to turbulence.

基于在线轨迹优化的运载火箭可重构制导方法

In order to improve the safety and reliability of a launch vehicle, we present a reconfigurable guidance method based on online trajectory optimization for thrust decrease at the ascending stage of the launch vehicle in this paper. We used a multiple shooting method to convert the optimal control problem into a nonlinear programming(NLP) problem. Finally, we used the interior point method to solve the NLP problem. The simulation results show that the method can effectively adapt to thrust decreases by 5% and 10%. This reconfigurable guidance method based on online planning is proposed to realize launch missions under the condition of power descent, thus verifying the feasibility of the method.

Effects of plant growth regulators on the rapid proliferation of shoots and root induction in the Chinese traditional medicinal plant Atractylodes macrocephala

We developed an efficient plant regeneration protocol for rapidly propagating Atractylodes macrocephala Koidz,an important traditional Chinese medicinal plant,via shoot organogenesis.Shoot multiplication was induced on Murashige-Skoog(MS)medium supplemented with various concentrations of N-phenyl-N-1,2,3-thidiazol-5-ylurea(TDZ),6-benzylaminopurine(BA)andα-naphthaleneacetic acid(NAA).Rooting was induced on half-strength MS medium supplemented with NAA and indolebutyric acid(IBA).The maximum mean number of shoots(5.61)was obtained from a single explant by the combined effect of 1.08μmol/L NAA and 2.25μmol/L TDZ.The longest roots and a minimum number of roots were produced when they were cultured in a medium without plant growth regulators.The shortest roots and the largest number of roots were observed in the medium supplemented with 2.7μmol/L NAA.