Analytical solution of a multidimensional Langevin equation at high friction limits and probability passing over a two-dimensional saddle

The analytical solution of a multidimensional Langevin equation at the overdamping limit is obtained and the probability of particles passing over a two-dimensional saddle point is discussed. These results may break a path for studying further the fusion in superheavy elements synthesis.

Stability and Bifurcation Bahaviour of Electrostatic Torsional NEMS Varactor Influenced by Dispersion Forces

The influences of Casimir and van der Waals forces on the nano-electromechanical systems (NEMS) electrostatic torsional varactor are studied. A one degree of freedom, the torsional angle, is adopted, and the bifurcation behaviour of the NEMS torsional varactor is investigated. There are two bifurcation points, one of which is a Hopf bifurcation point and the other is an unstable saddle point. The phase portraits are also drawn, in which periodic orbits are around the Hopf bifurcation point, but the periodic orbit will break into a homoclinic orbit when meeting the unstable saddle point.

Dynamic Stability of Electrostatic Torsional Actuators with van Der Waals Effect

electrostatic torsional nano-electro-mechanical systems (NEMS) actuators is analyzed in the paper. The dependence of the critical tilting angle and voltage is investigated on the sizes of structure with the consideration of vdW effects. The pull-in phenomenon without the electrostatic torque is studied, and a critical pull-in gap is derived. A dimensionless equation of motion is presented, and the qualitative analysis of it shows that the equilibrium points of the corresponding autonomous system include center points, stable focus points, and unstable saddle points. The Hopf bifurcation points and fork bifurcation points also exist in the system. The phase portraits connecting these equilibrium points exhibit periodic orbits, heteroclinic orbits, as well as homoclinic orbits.

Dynamic Behaviour of Nanoscale Electrostatic Actuators

The dynamic behaviour for nanoscale electrostatic actuators is studied. A two Parameter mass-spring model is shown to exhibit a bifurcation from the case excluding an equilibrium point to the case including two equilibrium points as the geometrical dimensions of the device are altered. Stability analysis shows that one is a stable Hopf bifurcation point and the other is an unstable saddle point. In addition, we plot the diagram phases, which have periodic orbits around the Hopf point and a homoclinic orbit passing though the unstable saddle point.

Stability and bifurcation behaviour of electrostatic torsional NEMS varactor influenced by dispersion forces

The influences of Casimir and van der Waals forces on the nano-electromechanical systems (NEMS) electrostatic torsional varactor are studied. A one degree of freedom, the torsional angle, is adopted, and the bifurcation behaviour of the NEMS torsional varactor is investigated. There are two bifurcation points, one of which is a Hopf bifurcation point and the other is an unstable saddle point. The phase portraits are also drawn, in which periodic orbits are around the Hopf bifurcation point, but the periodic orbit will break into a homoclinic orbit when meeting the unstable saddle point.

On the topological bifurcation of flows around a rotating circular cylinder

Flow fields around a rotating circular cylinder in a uniform stream are computed using a low dimensional Galerkin method. Results show that the formation of a Fopple vortex pair behind a stationary circular cylinder is caused by the structural instability in the vicinity of the saddle located at the rear of the cylinder. For rotating cylinder a bifurcation diagram with the consideration of two parameters, Reynolds number Re and rotation parameter a, is built by a kinematic analysis of the steady flow fields.

An improvement on the theoretical model for the large-scale coherent structures in the outer region of a turbulent boundary layer

According to the experimental results, there exist large-scale coherent structures in the outer region of a turbulent boundary layer, which have been studied by many authors.As experimental results, Antonia (1990) showed the phase- aver aged streamlines and isovorticity lines of the large-scale coherent structures in a turbulent boundary layer for different Reynolds numbers. Based on the hydrodynamic stability theory, the 2-D theoretical model for the large-scale structures was proposed by Luo and Zhou, in which the eddy viscosity was defined as a complex function of the position in the normal direction. The theoretical results showed in ref. were in agreement with those in ref. However, there were two problems in the results. One is that in the experimental results, there were divergent focuses between two saddle points in the streamlines, but in the theoretical results, there were centers. The other is that the stretched parts of the isovorticity lines appear at the location of centers in the theoretical results, while in the experimental results they located somewhere between the focuses and saddle points. The reason is that the computations were based on a 2-D model.

Numerical study of bifurcation solutions of spherical Taylor-Couette flow

The steady bifurcation flows in a spherical gap (gap ratio sigma=0.18) with rotating inner and stationary outer spheres are simulated numerically for Re(c1)less than or equal to Re less than or equal to 1 500 by solving steady axisymmetric incompressible Navier-Stokes equations using a finite difference method. The simulation shows that there exist two steady stable flows with 1 or 2 vortices per hemisphere for 775 less than or equal to Re less than or equal to 1 220 and three steady stable flows with 0, 1, or 2 vortices for 1 220saddle point in the meridional plane at higher Re number and its role in the formation of two-vortex flow are analyzed.

Parameter-transformation relations for traveling-wave solutions of kdv-burgers equation

 Burgers suggested that the main properties of free-turbulence in the boundless area without basic flow might be understood with the aid of the following equation, which was much simpler than those of fluid dynamics, 更多还原

WANNIER LOCALIZATION IN GAAS/GAALAS SUPERLATTICES UNDER ELECTRIC-FIELD

We have studied the Wannier-Stark effect in GaAs/GaAlAs short-period superlattices under applied electric field perpendicular to the layers by room- and low-temperature photocurrent measurements. The changes in the transition intensities with biasing are well fitted to a theoretical calculation based on the finite Kronig-Penney model on which the potential of an applied electric field is superposed. With increasing electric field, the 0h peak grows to a maximum while the -1h and +1h peaks monotonousely decrease. By a comparison of the spectra measured at different temperatures, the two peaks in the room temperature photocurrent spectra at relatively low electric field (1.0 X 10(4) V/cm) are identified to be caused by the Wannier localization effect instead of saddle-point excitons.

Structures and vibrational spectra of C-2 and LaC2+ clusters

C-2 and LaC2+ were studied using Hartree-Fock(HF), B3LYP (Becke 3-paremeter-Lee-Yang-Parr) density functional method, second-order Moller-Plesset perturbation (MP2) and coupled cluster singles and doubles with non-iterative triples(CCSD(T)) methods. The basis set employed was LANL1DZ. Geometries, vibrational frequencies and other quantities were reported. The results showed that for C-2, all the methods performed well for low spin state (singlet), while only HF and B3LYP remained so for high spin state (triplet). For LaC2+, four isomers were presented and fully optimized. The results suggested that linear isomers with C-infinity v and D-infinity h symmetries were predicted to be saddle points on the energy surface for all the methods, while for isomers with C-2 upsilon and C-s symmetries, they were local minima except C-2 upsilon at B3LYP level, and were isoenergetic at HF, MP2 and CCSD(T) levels, near isoenergetic at B3LYP level. From the differences between HOMO and LUMO, it is also known that the isomers with C-2 upsilon and C-s symmetries offer the largest values and therefore correspond to the most stable structure. For La-C bond lengths, B3LYP gives the shortest, the order is B3LYP

悬索桥隧道式锚碇与围岩系统的破坏模式研究

The anchorages are unparalleled structures only in a suspension bridge, and as main bearing facilities, play an important role in connecting the superstructures and the ground. The tunnel anchorage, as one alternative type of the anchorages, has more advantages over its counterpart, the gravity anchorage. With the tunnel anchorages adopted, not only can surface excavation be reduced to protect the environment, and natural condition of the rock be utilized and potential bearing capacity of surrounding rock be mobilized to save engineering cost, but also the technological predominance of auxiliary engineering measures, such as prestressed concrete, anchoring piles, rock anchors and collar beam between the two separated anchorages, can be easily cooperated to work together harmoniously under the circumstances of poor rock quality. There are plentiful high mountains and deep canyons in west part of China, and long-span bridge construction is inevitably encountered in order to realize leapfrogging development of the transportation infrastructure. Western mountainous areas usually possess the conditions for constructing tunnel anchorages, and therefore, the tunnel anchorages, which are conformed to the conception of resource conservative and sustainable society, extremely have application and popularization value in western underdeveloped region. The scientific and technological problem about the design, construction and operation of tunnel anchorages should be further investigated. Combining the engineering of western tunnel anchorages for the Balinghe Suspension Bridge, this paper probed into the survey method and in-situ test method for tunnel anchorages, scientific rock quality evaluation of surrounding rock to provide reasonable physical and mechanical parameters for design, construction and operation of tunnel anchorages, bearing capacity estimation for tunnel anchorage, deformation prediction of the anchorage-rockmass system, tunnel-anchorage slope stability analysis and the evaluation of excavation stability and degree of safety of the anchorage tunnel. The following outcomes were obtained: 1. Materials of tunnel anchorages of suspension bridge built (and in progress) at home and abroad were systematically sorted out, with the engineering geological condition and geomechanical property of surrounding rock around the anchorage tunnel, the design size of anchorages and the construction method of anchorage tunnel paid more emphasis on, to unveil the internal relationship between the engineering geological conditions of surrounding rock and the design size and axis angle of anchorages and provide references for future design, construction and study of tunnel anchorages. 2. Physical and mechanical parameters were recommended based on three domestic and foreign methods of rock quality evaluation. 3. In-situ tests, adopting the back-thrust method, of two kinds of reduced scale model, 1/30 and 1/20, for the tunnel anchorages were conducted in the declining exploration drift with rock mass at the test depth being the same as surrounding rock around real anchorages, and reliable field rockmass displacement data were acquired. Attenuation relation between the increment of distance from the anchorage and the decrement of rockmass displacement under maximum test load, and influential scope suffered by anchorage load were obtained. 4. Using similarity theory, the magnitude of real anchorage and rockmass displacement under design load and degree of safety of the anchorage system were deduced. Furthermore, inversion analysis to deformation modulus of slightly weathered dolomite rock, the surrounding rock of anchorage tunnel, was performed by the means of numerical simulation. 5. The influential law of the geometrical size to the limit bearing capacity of tunnel anchorage was studied. 6. Based on engineering geological survey data, accounting for the combination of strata layer and adverse discontinuities, the failure patterns of tunnel anchorage slope were divided into three modes: sliding of splay saddle pier slope, superficial-layer slippage, and deep-layer slippage. Using virtual work principle and taking anchorage load in account, the stability of the three kinds of failure patterns were analyzed in detail. 7. The step-by-step excavation of anchorage tunnel, the numerical overload and the staged decrement of rock strength parameters were numerically simulated to evaluate the excavation stability of surrounding rock around anchorage tunnel, the overload performance of tunnel anchorage, and the safety margin of strength parameters of the surrounding rock.

塔里木盆地塔北、塔中地区早古生代白云岩形成机理

In Tarim Basin, extensive carbonates of Lower Paleozoic occur, in which thick Cambrian and Lower Ordovician dolostones are widespread and show a potential perspective in hydrocarbon exploration. So they are viewed as an important target for exploration. Tarim Basin is a poly phase composite basin, which underwent multiphase tectonic modification and volcanic activities; these exerted significant influences on the basin-fills and basin fluid evolution, thereby the diagenetic history, particularly on the deep-buried Lower Paleozoic dolostones. Referring to the classification of dolomite texture proposed by Gregg & Sibley (1984) and Sibley & Gregg (1987). In view of crystal size, crystal shape, crystal surface and contact relation, eight genetic textures of dolomite crystals are identified, based on careful petrographic examinatoins. These textures include: 1) micritic dolomite; 2) relict mimetic dolomite; 3)finely crystalline, planar-e(s), floating dolomite; 4)finely crystalline, planar-e(s) dolomite; 5) finely-coarse crystalline, nonplanar-a dolomite; 6)coarse crystalline, nonplanar saddle dolomite; 7) finely-medium crystalline, planar-e(s) dolomite cement; 8) coarse crystalline, nonplanar saddle dolomite cement, in which the former six textures occurs as in matrix, the latter two in the cements. Detailed geochemistry analysis is carried out on the basis of genetic textures of dolomite and related minerals such as quartz and calcite. The result showed that the calcite has the highest average content in Sr, which can be sorted into two groups; micritic dolomite has the highest average content in Sr among all kinds of dolomites; the REE patterns of all kinds of dolomites is similar to those of marine limestone samples. Saddle dolomite cement has δ13C values from -2.44‰ to 1.27‰ PDB, and δ18O values from -13.01‰ to -5.12‰ PDB, which partially overlap with those of matrix dolomite (δ13C values from -2.83‰ to 2.01‰ PDB, δ18O values from -10.63‰ to -0.85‰ PDB). Saddle dolomite cement has 87Sr/86Sr ratios from 0.7086 to 0.7104, which totally overlap with those of matrix dolomite (0.7084 ~ 0.7116). Compared with saddle dolomite derived from other basins all over the world, the saddle dolomites of Tarim Basin have similar δ13C, δ18O and 87Sr/86Sr ratios values with those of matrix dolomite. This scenario reflects the unusual geological setting and special dolomitizing liquid of Tarim Basin. The values of δ18O, δ13C and 87Sr/86Sr ratios of calcite also can be sorted out two groups, which may been resulted from the one stage of extensive uplift of Tarim Basin from Mesozoic to Cenozoic. Fluid inclusion microthermometry data of the diagenetic mineral indicates that matrix dolomite has relatively low homogenization temperatures (Th) of 80～105oC and salinities of 12.3％ (wt% NaCl equivalent); saddle dolomite has highest Th values, which concentrate in 120～160oC and salinities of 13.5～23.7％ (wt% NaCl equivalent); quartz has relatively low Th of 135～155oC and salinities of 17.8～22.5％ (wt% NaCl equivalent); calcite has relatively low Th of 121～159.5oC and salinities of 1.4～17.5％ (wt% NaCl equivalent). These data suggest that the saddle dolomites could have formed in thermal brine fluids. Based on comprehensive petrographical study, detailed geochemistry and fluid inclusion microthermometry analysis on Lower Paleozoic dolomite of Tarim Basin, three types of dolomitisation mechanism are proposed: Penecontemporaneous dolomitisation (Sabkha dolomitisation & Reflux dolomitisation); Burial dolomitisation (shallow-intermediate burial dolomitisation & Deep burial dolomitisation ); Hydrothermal cannibalized dolomitisation. In view of host-specified occurrences of hydrothermal dolomite, the low abundance of saddle dolomite and high geochemical similarities between saddle dolomite and host dolomite, as well as highest Th and high salinities , the hydrothermal dolomite in Tarim Basin is thus unique, which could have been precipitated in modified fluid in the host dolomite through intraformational thermal fluid cannibalization of Mg ions from the host. This scenario is different from the cases that large scale dolomitizing fluid migration took place along the fluid pathways where abundant saddle dolomite precipitated. Detailed observations on 180 petrographic and 60 casting thin sections show original pores in Lower Paleozoic dolomite were almost died out by complicated diagenetic process after a long time geologic evolution. On the other hand, deep-buried dolomite reservoirs is formed by tectonic and hydrothermal reforming on initial dolomites. Therefore, the distribution of structure-controlled hydrothermal dolomite reservoirs is predicted in Tabei and Tazhong Area of Tarim Basin based on the geophysical data.