Noether symmetry and conserved quantity for a Hamilton system with time delay

In this paper, the Noether symmetries and the conserved quantities for a Hamilton system with time delay are discussed. Firstly, the variational principles with time delay for the Hamilton system are given, and the Hamilton canonical equations with time delay are established. Secondly, according to the invariance of the function under the infinitesimal transformations of the group, the basic formulas for the variational of the Hamilton action with time delay are discussed,the definitions and the criteria of the Noether symmetric transformations and quasi-symmetric transformations with time delay are obtained, and the relationship between the Noether symmetry and the conserved quantity with time delay is studied. In addition, examples are given to illustrate the application of the results.     

Attainment of Emulsions with Liquid Crystal from Marigold Oil Using the Required HLB Method

Development of new formulations for topical use and cosmetic and pharmaceutical delivery agents has increased the complexity of emulsified systems. Liquid crystals, known since the nineteenth century are the third phase of an emulsion, being responsible for increasing its stability and the solubility of substances poorly soluble in water, or the oily phase, modulating the release of drugs imprisoned in its structure and promoting hydration of the skin surface. In the present work we developed oil/water emulsions, making use of Marigold oil (Calendula officinalis L) and ethoxylated fat alcohols as surfactant. The required HLB value for marigold oil was determined to be 6.0. The surfactants were associated in lipophilic/hydrophilic pairs. The lipophilic surfactants were Ceteth‐2 and Steareth‐2 and the hydrophilic surfactants were Steareth‐20, Ceteareth‐20, Ceteareth‐5, and Ceteth‐10. To identify the liquid crystalline phases, the emulsions were analyzed by polarized light microscopy. The physical stability was evaluated by rheology and zeta potential analysis. All emulsions presented lamellar liquid crystal structures. Results showed that this type of surfactant is able to produce liquid crystal in the system, with slight difference in appearance, influencing the physical stability, according to the methods applied.     

Permeability of microscale fibrous porous media using the lattice Boltzmann method

The permeabilities of microscale fibrous porous media were calculated using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Two models of the microscale fibrous porous media were constructed based on overlapping fibers (simple cubic, body-centered cubic). Arranging the fibers in skew positions yielded two additional models comprising non-overlapping fibers (skewed simple cubic, skewed body-centered cubic). As the fiber diameter increased, the fibers acted as granular inclusions. The effects of the overlapping fibers on the media permeability were investigated. The overlapping fibers yielded permeability values that were a factor of 2.5 larger than those obtained from non-overlapping fibers, but the effects of the fiber arrangement were negligible. Two correlations were obtained for the overlapping and non-overlapping fiber models, respectively. The effects of the rarefaction and slip flow are also discussed. As the Knudsen number increased, the dimensionless permeability increased; however, the increase differed depending on the fiber arrangement. In the slip flow regime, the fiber arrangement inside the porous media became an important factor.     

A Sharp Condition for the Ground State of Difference Equation

This note is concerned with a novel inequality condition for the existence of ground states of partial difference systems. Our result is potentially applicable to the estimation of eigenvalues of the loaded strings and nets.     

On the rate of convergence for central limit theorems of sojourn times of Gaussian fields

The aim of this paper is to control the rate of convergence for central limit theorems of sojourn times of Gaussian fields in both cases: the fixed and the moving level. Our main tools are the Malliavin calculus and the Stein method, developed by Nualart, Peccati and Nourdin. We also extend some results of Berman to the multidimensional case.     

Application of DEM modified with enlarged particle model to simulation of bead motion in a bead mill

We applied the discrete element method （DEM） of simulation modified by an enlarged particle model to simulate bead motion in a large bead mill. The stainless-steel bead mill has inner diameter of 102 mm and mill length of 198 mm. The bead diameter and filling ratio were fixed respectively at 0.5 mm and 85%. The agitator rotational speed was changed from 1863 to 3261 rpm. The bead motion was monitored experimentally using a high-speed video camera through a transparent mill body. For the simulation, enlarged particle sizes were set as 3-6 mm in diameter. With the DEM modified by the enlarged particle model, the motion of enlarged particles in a mill was simulated.The velocity data of the simulated enlarged particles were compared with those obtained in the experiment. The simulated velocity of the enlarged particles depends on the virtual frictional coefficient in the DEM model. The optimized value of the virtual frictional coefficient can be determined by considering the accumulated mean value. Results show that the velocity of the enlarged particles simulated increases with an increase in the optimum virtual frictional coefficient, but the simulated velocity agrees well with that determined experimentally by optimizing the virtual frictional coefficient in the simulation. The computing time in the simulation decreases with increased particle size.     

A new 4-D non-equilibrium fractional-order chaotic system and its circuit implementation

A new 4-D fractional-order chaotic system without equilibrium point is proposed in this paper. There is no chaotic behavior for its corresponding integer-order system. By computer simulations, we find complex dynamical behaviors in this system, and obtain that the lowest order for exhibiting a chaotic attractor is 3.2. We also design an electronic circuit to realize this 4-D fractional-order chaotic system and present some experiment results.     

In vitro metabolism study of Strychnos alkaloids using high‐performance liquid chromatography combined with hybrid ion trap/time‐of‐flight mass spectrometry

In this report, the in vitro metabolism of Strychnos alkaloids was investigated using liquid chromatography/high‐resolution mass spectrometry for the first time. Strychnine and brucine were selected as model compounds to determine the universal biotransformations of the Strychnos alkaloids in rat liver microsomes. The incubation mixtures were separated by a bidentate‐C₁₈ column, and then analyzed by on‐line ion trap/time‐of‐flight mass spectrometry. With the assistance of mass defect filtering technique, full‐scan accurate mass datasets were processed for the discovery of the related metabolites. The structural elucidations of these metabolites were achieved by comparing the changes in accurate molecular masses, calculating chemical component using Formula Predictor software and defining sites of biotransformation based upon accurate MSⁿ spectral information. As a result, 31 metabolites were identified, of which 26 metabolites were reported for the first time. These biotransformations included hydroxylation, N‐oxidation, epoxidation, methylation, dehydrogenation, de‐methoxylation, O‐demethylation, as well as hydrolysis reactions. Copyright © 2013 John Wiley & Sons, Ltd.     

A novel design of membrane mirror with small deformation and imaging performance analysis in infrared system

A method of diminishing the shape error of membrane mirror is proposed in this paper. The inner inflating pressure is considerably decreased by adopting the pre-shaped membrane. Small deformation of the membrane mirror with greatly reduced shape error is sequentially achieved. Primarily a finite element model of the above pre-shaped membrane is built on the basis of its mechanical properties. Then accurate shape data under different pressures can be acquired by iteratively calculating the node displacements of the model. Shape data are applicable to build up deformed reflecting surfaces for the simulative analysis in ZEMAX. Finally, ground-based imaging experiments of 4-bar targets and nature scene are conducted. Experiment results indicate that the MTF of the infrared system can reach to 0.3 at a high spatial resolution of 10l p/mm, and texture details of the nature scene are well-presented. The method can provide theoretical basis and technical support for the applications in lightweight optical components with ultra-large apertures.