Simulation and comparison of several numerical algorithms for solving ballistic differential equations

Several numerical methods of differential equations and their applications in ballistic calculation are discussed for the purpose of simplification of the dynamic differential equations of projectile trajectory.Program simulations of Euler method,Heun method,lassic fourth-order Runge Kutta（RK4）method,ABM method and Hamming method are achieved based on Matlab.In addtion,the approximate solutions,local truncation errors and calculation time of the dynamic differential equations are obtained.By analyzing the simultaion results,the advantages and disadvantages of these methods are compared,which provides a basis for choice of ballistic calculation methods.

HIGH-ORDER RUNGE-KUTTA DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR 2-D RESONATOR PROBLEM

The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and it is explicit in the time domain. Consequently it is a best mixture of FEM and finite volume method （FVM）. RK-DGFEM can obtain local high-order accuracy by using high-order polynomial basis. Numerical experiments of transverse magnetic （TM） wave propagation in a 2-D resonator are performed. A high-order Lagrange polynomial basis is adopted. Numerical results agree well with analytical solution. And different order Lagrange interpolation polynomial basis impacts on simulation result accuracy are discussed. Computational results indicate that the accuracy is evidently improved when the order of interpolation basis is increased. Finally, L^2 errors of different order polynomial basis in RK-DGFEM are presented. Computational results show that L^2 error declines exponentially as the order of basis increases.

A Numerical Method for Calculating Transmission Coefficients Across Arbitrary Potential Barriers with High Accuracy

We report a new method for calculating transmission coefficients across arbitrary potential barriers based on the Runge-Kutta method. A numerical solution of the Schrodinger equation is calculated using the Runge-Kutta method,and a new model is established to analyze the numerical results to find the transmission coefficient. This technique is applied to various cases, such as parabolic potential barrier and double-barrier structures. Transmission probability with high precision is obtained and discussed. The tunnelling current density through a MOS structure is also explored and the result coincides with the Fowler-Nordheim model,which indicates the applicability of our method.

Preliminary Results on Hydrological and Hydrochemical Features of Kartamak Glacier Area in Mt. Muztag Ata

The variations of the meltwater runoff draining from Kartamak Glacier in Mt. Muztag Ata in China were studied by using the measured hydrological data from 1 June to 25 August 2003. The meltwater runoff is mainly affected by ambient temperature and precipitation. Meltwater and precipitation samples were collected from 10 to 23 August 2003. Their pH, EC (electric conductivity) and the major ions (Na^+, K^+, Ca^(2+), Mg^(2+), Cl^-, NO_3^-, SO_~4^(2-)) were determined. pH values showed a positive correlation with EC values for all samples. Meltwater samples were slightly alkaline. Sulfate and calcium were the dominant anion and cation in the measured ions, respectively. All the ion concentrations had inverse relationships with runoff or water level. In order to discuss the origins of dissolved chemical substances in the glacial meltwater, a principal component analysis was carried out. The results showed that water-rock interaction determined the ion components of the meltwater.

Novel High Performance Ziegler-Natta Catalyst for Ethylene Slurry Polymerization

A novel high performance MgCl2/TiCl4 catalyst with tetrabutyloxsilicane as electron donor was pre-pared for ethylene slurry polymerization process. The properties of the catalyst such as particle size distribution, catalytic activity, hydrogen responsibility and copolymerization performance were investigated and compared with commercial catalyst (imported catalyst). Copolymerization of ethylene and 1-butylene using the catalyst was stud-ied in a pilot plant. The composition, structure and property of the copolymer were characterized by 13C nuclear magnetic resonance (13C NMR) and gel permeation chromatography-Infrared (GPC-IR), and compared with those of the copolymer obtained from a commercial catalyst. In comparison with the commercial catalyst, the novel cata-lyst had a higher activity (up to 34.6 kg·g-1) and a better particle size distribution (PSD), and produced polymers having higher bulk density (up to 0.37 g·cm-3) with less fine resin. Meanwhile, the novel catalyst showed a higher hydrogen responsibility and better copolymerization performance. The results indicated that the copolymer obtained from the novel catalyst has a higher branch in the high molecular weight fraction and lower branch in the low mo-lecular weight fraction.

Theoretical investigation of micropolar fluid flow between two porous disks

The steady, laminar, incompressible and two dimensional micropolar flow between two porous disks was investigated using optimal homotopy asymptotic method(OHAM) and fourth order Runge–Kutta numerical method. Comparison between OHAM and numerical method shows that OHAM is an exact and high efficient method for solving these kinds of problems. The results are presented to study the velocity and rotation profiles for different physical parameters such as Reynolds number, vortex viscosity parameter, spin gradient viscosity and microinertia density parameter. As an important outcome, the magnitude of the microrotation increases with an increase in the values of injection velocity while it decreases by increasing the values of suction velocity.

Active set truncated-Newton algorithm for simultaneous optimization of distillation column

An active set truncated-Newton algorithm (ASTNA) is proposed to solve the large-scale bound constrained sub-problems. The global convergence of the algorithm is obtained and two groups of numerical experiments are made for the various large-scale problems of varying size. The comparison results between ASTNA and the subspace limited memory quasi-Newton algorithm and between the modified augmented Lagrange multiplier methods combined with ASTNA and the modified barrier function method show the stability and effectiveness of ASTNA for simultaneous optimization of distillation column.

Low-Storage Runge-Kutta Method for Simulating Time-Dependent Quantum Dynamics

A wide range of quantum systems are time-invariant and the corresponding dynamics is dic- tated by linear differential equations with constant coefficients. Although simple in math- ematical concept, the integration of these equations is usually complicated in practice for complex systems, where both the computational time and the memory storage become limit- ing factors. For this reason, low-storage Runge-Kutta methods become increasingly popular for the time integration. This work suggests a series of s-stage sth-order explicit Runge- Kutta methods specific for autonomous linear equations, which only requires two times of the memory storage for the state vector. We also introduce a 13-stage eighth-order scheme for autonomous linear equations, which has optimized stability region and is reduced to a fifth-order method for general equations. These methods exhibit significant performance improvements over the previous general-purpose low-stage schemes. As an example, we ap- ply the integrator to simulate the non-Markovian exciton dynamics in a 15-site linear chain consisting of perylene-bisimide derivatives.

Study on the distribution of active centers in novel low Ti-loading MgCl2-supported Ziegler-Natta catalyst

Novel MgCl2-supported Ziegler-Natta (Z-N) catalysts prepared using a new one-pot ball milling method can effectively control the amounts of Ti-loading in the catalysts. Complex GPC data on polypropylene synthesized by these novel catalysts were analyzed using the method of fitting the molecular weight distribution (MWD) curves with a multiple Flory-Schulz function. It was found that multiple active centers exist in these novel catalysts. Detailed study of the effects of the Ti-loadings in the catalysts on the distribution of the active centers showed that the Ti-loadings in the novel MgCl2-supported Z-N catalysts might affect the proportion of each type of active centers; and might be the main factor responsible for the effect of the Ti-loadings on the microstructure, the molecular weight and molecular weight distribution width of the resultant polymer, the catalytic activity and polymerization kinetics.

Comparison of modelled-and remote sensing-derived daily snow line altitudes at Ulugh Muztagh,northern Tibetan Plateau

The ice cap Ulugh Muztagh in the central Kunlun Shan at the northern fringe of the Tibetan Plateau is a very isolated region with arid cold conditions. No observational, meteorological or glaciological ground truth data is available. Using the Moderate-resolution Imaging Spectroradiometer(MODIS) Level 1 radiance Swath Data(MOD02QKM) with a spatial resolution of 250 m, transient snow lines during the months of July to September in 2001 to 2014 are derived. Results are used to calibrate the physical based Coupled Snowpack and Ice surface energy and Mass balance model(COSIMA). The model runs on a representative detail region of Ulugh Muztagh(UM) on a digital elevation model with the same spatial resolution as the MODIS bands. In the absence of field observations, the model is driven solely by dynamically downscaled global analysis data from the High Asia Refined analysis(HAR). We compare remote sensing derived and modelled mean regional transient snow line altitudes in the course of consecutive summer seasons in 2008 to 2010. The resulting snow line altitude(SLA) and annual equilibrium line altitude(ELA) proxy of both methods coincide very well in their interannual variability in accordance with interannual variability of climatic conditions. Since SLAs of both methods do notconsistently agree on a daily basis a usage of remote sensing derived SLAs for model calibration in the absence of field observation data is only limitedly feasible for daily analysis. ELA approximation using the highest SLA at the end of ablation period may not be applied to UM because the negative winter mass balance(MB) is not reflected in the summer SLA. The study reveals moderate negative MB for UM throughout the modelling period. The mean regional MB of UM accounts for-523±410 mm w.e. a-1 in the modelling period. Hence UM seems not to belong to the area of the ‘Karakorum anomaly' comprising a region of positive mass balances in recent years which has its centre presumably in the Western Kunlun Shan.

Jemaa el-Fnaa Public Square： A Cultural and Literary Source in Ben Jelloun＇s The Sand Child and The Sacred Night

The purpose of this article is to analyze the significance of a special space, which has a particular meaning in Tahar Ben Jelloun＇s work： the public square of Jemaa el-Fnaa, Marrakesh＇s Medina Quarter. For Tahar Ben Jelloun, the well-known French Maghrebian writer, the process of writing begins with the emergence of creative evidence in speech. It is the matrix of his writing. Thus, an oral perspective is sketched out, a whole game of fleeting narratives told in the public square. This space is an ideal one that draws its elements from orality and contributes to the preservation of traditional knowledge and the implementation of common values participating in a collective memory. How does Ben Jelloun seize the voices that already exist in the real Public Square in order to engage them in his narrative？ A closer examination of the text enables us to unpick the process of Ben Jelloun＇s narrative strategies. In the public square, the picture that emerges is that two essential elements reveal the organization of the narrative： the cultural source and the literary source.

Preparation of graphene/MgCl_2-supported Ti-based Ziegler-Natta catalysts by the coagglomeration method and their application in ethylene polymerization

We report a facile coagglomeration method for preparing graphene (G)/MgCl2‐supported Ti‐based Ziegler‐Natta catalysts. The effects of graphene feed ratio on catalyst morphology and ethylene polymerization behavior were examined. The synthesized catalyst exhibited very high activity for ethylene polymerization. The resultant polyethylene (PE)/G nanocomposites showed a layered morphology, and the graphene fillers were well dispersed in the PE matrix. In addition, the thermal stability and mechanical properties of PE were significantly enhanced with the introduction of a very small amount of G fillers (0.05 wt%). This work provides a facile approach to the production o fhigh‐performance PE.

Light-Induced Hofstadter's Butterfly Spectrum in Optical Lattices

We propose a scheme to create an effective magnetic field, which can be perceived by cold neutral atoms in a two-dimensional optical lattice, with a laser field with a space-dependent phase and a conventional laser field acting on A-type three-level atoms. When the dimensionless parameter a, being the ratio of flux through a lattice cell to one flux quantum, is rational, the energy spectrum shows a fractal band structure, which is so-called Hofstadter＇s butterfly.

A Study of Kumtag Desert:Progresses and Achievements

The Kumtag Desert, the fourth largest sand desert covered mainly by mobile dunes and shifting sands, had remained as the last untouched natural desert to be fully investigated in a scientific way. Therefore,＂Integrated Scientific Expedition of the Kumtag Desert Programme＂was listed as one of nine key research programmes of China National Science and Technology Basic Research Programmes in December, 2006. The expedition team carried out two large-scale and multidisciplinary scientific expeditions from June 2007 to December 2009, to the Kumtag Desert and collected more than 20 sets of field samples and ground observations. Finally, the expedition team completed not only systematic and integrated scientific expedition of the Kumtag Desert and filled in the gap of the last unexplored desert in China, but also gained fruitful research results in many scientific research subjects. These research results included that：（i） A unique aeolian landform unit, sand-gravel-moraine, developed in the Kumtag Desert, was defined and named for the first time, and the morphologic characteristics of feather-like longitudinal sand dune and its formation process are initially proved;（ii） Two sources and mineral element composition of the surface sedimentation of the Kumtag Desert was determined, and the characteristics of the desert sedimentation and stratum chronology of the Later Cenozoic Era was illustrated;（iii） The chronology of the paleo-aeolian sand was essentially determined and the formation courses and evolution process of the desert was illustrated;（iv） The thorough investigations of water system distribution, hydrology,chemical characteristics of water of the Kumtag Desert were made and six Water System Evolution Maps of the Kumtag Desert were compiled from the Later Cenozoic Era to the contemporary age;（v） The types, formation processes and distribution of soil in the Kumtag Desert were fully determined;（vi）An all-direction, all-weather, full-coverage desert meteorology observation was established and the characteristics and trend of climate change of the Kumtag Desert and nearby districts were adequately illustrated;（vii） It is the first time that the distribution areas of six plant species, including Tamarix taklamakanensis, Tamarix albiflonum, Agriophyllum lateriflorum etc., were catalogued in the Desert;（viii） The varieties, population, quantity and distribution of the wild animal such as the Bactrian Camel （Camelus ferus Przewalski）, are now documented;And （ix） it is the first time that the ecological services and economic function subdivision zones of the Kumtag Desert were classified;the Framework of the Great Dunhuang Special Ecological-Economic Zone was proposed to realize the sustainable development strategy in population, resources, environment, ecology and economics in the Kumtag Desert and nearby districts.

在理想和现实之间——评吴奎南的《遮羞布》

"伟大的作家要么是丈夫,要么是情人.……在艺术中,正如在生活中,丈夫和情人不可或缺.当一个人被迫在他们之间做出取舍的时候,那真是天大的憾事."桑格塔在上个世纪六十年代《纽约时报·书评》中的《加缪的〈日记〉》如是说.刚刚故去的当前美国声名卓著的"新知识分子"和被誉为"美国公众的良心"的苏珊·桑格塔,是美国"现有的目光最敏锐的论文家".……

The discovery of the oldest rocks in the Kuluketage area and its geological implications

The basement rocks in the Kuluketage area are composed predominately of tonalite-trondhjemite-granodiorite rocks, and occured mainly in Xinger and Korla. U-Pb dating of TTG gneiss near Korla yielded a late Neoarchean weighted mean 207Pb/206Pb age of 2.65 Ga, which is the oldest published age for the TTG rocks in the Kuluketage area and thus suggests that Archean terrane in the area was formed in the late Neoarchean. The Korla gneiss is much younger than the TTG rocks in the northern Altyn Tagh, eastern Tarim Craton, indicating that the oldest terrane of the Tarim Craton was exposed probably in the northern Altyn Tagh. Until late Neoarchean, the Tarim continent extends to the Kuluketage area and finally had generated a relatively large uniform Archean basement within the craton. Zircon Hf isotopic analyses of the TTG gneiss give low εHf(t) values (-5 to 1) with Paleoarchean to Mesoarchean two-stage model ages (TDM2) between 3.0 and 3.3 Ga, suggesting that the basement rocks in the northern Tarim Craton were derived dominately from partial melting of Paleoarchean to Mesoarchean juvenile crustal material. The Hf model ages, therefore, indicate that no continent crust older than 3.3 Ga existed in the Kuluketage area.

Biostratigraphic correlation of the Ordovician black shales in Tarim Basin and its peripheral regions

Ordovician black shales are widely distributed in the Tarim Basin and its peripheral regions,and some of them may serve as potential hydrocarbon source rocks.The present study of the Ordovician graptolite fauna from these shales,together with the yielded conodonts and chitinozoans etc.,permits a refined correlation of the rocks.Based mainly on a new collecting of the graptolites and a study of the faunas in Kalpin and Kuruktag regions,and the successful identification of the new graptolite material from a few drill cores within the basin,we are able to update our knowledge of the Ordovician in the regions,and draw some conclusions:(1) The most widespread distribution of the black shales in the Tarim Basin and its peripheral regions,which correspond to the Nemagraptus gracilis Zone,may be related to a global sea-level rise during this time interval.(2) Black shales of Ordovician occur most frequently and extensively in the Kuruktag(also spelled as Quruq Tagh) region in east-ern Tianshan Mountains,spanning Tremadocian to mid-Katian(D.spiniferus Zone) temporally and extending southeastwards into Manjiaer Depression.The black shales of the D.spiniferus Zone may even extend into the central Tarim Basin.(3) Three different bio-and litho-facies belts(Bachu:carbonate platform and reef belt;Kalpin-Aksu:marginal platform and upper slope belt;Wushi:slope belt) are recognized in the northwestern Tarim Basin.(4) The internationally well-correlated Saergan black shale,which has been considered to possess high potential for hydrocarbon source rock,may possess a restricted distribution in the Kalpin and Aksu areas.

Feathered sand ridges in the Kumtagh Desert and their position in the classification system

Feathered sand ridges in the northeastern Kumtagh Desert in China cover an area of 4016 km 2 and consist of crescent sand ridges and interridge tongue-shaped dunes.Differences in grain size,mineral composition and albedo between crescent sand ridges and tongue-shaped dunes,and between windward and leeward slopes of tongue-shaped dunes,result in their feathery appearance in aerial and satellite imagery.Measurements of the sand drift potential in the region show that the sand-moving wind for feathered sand ridges can be divided into three sectors;i.e.north-northeasterly,easterly and east-northeasterly sectors roughly corresponding to the southeast,northwest and southwest slip faces.Our findings suggests that the crescent sand ridges resulting from the connection of barchan dunes along the prevailing wind direction are longitudinal dune ridges rather than transverse ones.Tongue-shaped dunes and quasi-dune shapes have obvious distinctions and are new transverse dune types.According to McKee's dune shape classification,the feathered sand ridges are not a deformation dune type but a complex one.According to Wu's dune morphological and genetic classification,they are not dune ridges or compound dune ridges that form under the action of unidirectional winds or two winds intersecting at an acute angle,but are complex dune ridges that form under the action of three winds intersecting at an acute angle.

Predictor homotopy analysis method for nanofluid flow through expanding or contracting gaps with permeable walls

In this paper a definitely new analytical technique, predictor homotopy analysis method （PHAM）, is employed to solve the problem of two-dimensional nanofluid flow through expanding or contracting gaps with permeable walls. Moreover, comparison of the PHAM results with numerical results obtained by the shooting method coupled with a Runge- Kutta integration method as well as previously published study results demonstrates high accuracy for this technique. The fluid in the channel is water containing different nanoparticles： silver, copper, copper oxide, titanium oxide, and aluminum oxide. The effects of the nanoparticle volume fraction, Reynolds number, wall expansion ratio, and different types of nanoparticles on the flow are discussed.

A study of nonlinear biochemical reaction model

The present study deals with the introduction of an alteration in Legendre wavelets method by availing of the Picard iteration method for system of differential equations and named it Legendre wavelet-Picard method （LWPM）. Convergence of the proposed method is also discussed. In order to check the competence of the proposed method, basic enzyme kinetics is considered. Systems of nonlinear ordinary differential equations are formed from the considered enzyme-substrate reaction. The results obtained by the proposed LWPM are compared with the numerical results obtained from Runge-Kutta method of order four （RK-4）. Numerical results and those obtained by LWPM are in excellent conformance, which would be explained by the help of table and figures. The proposed method is easy and simple to implement as compared to the other existing analytical methods used for solving systems of differential equations arising in biology, physics and engineering.