An impact sensitivity assessment method of spacecraft based on virtual exterior wall

The impact sensitivity assessment of spacecraft is to obtain the probability of spacecraft encountering the OD/M(orbital debris or meteoroid),which is a prerequisite for survivability assessment of on-orbit spacecraft.An impact sensitivity assessment method of spacecraft based on virtual exterior wall was proposed to improve the computational efficiency.This method eliminates determination of the outermost surface elements of the spacecraft before generating the debris rays,which are assumed to originate from a non-concave virtual wall that completely wraps the spacecraft.The Dist Mesh method was adopted for the generating of the virtual wall to ensure its mesh quality.The influences of the sizes,mesh densities,shapes of the virtual wall on the efficiency and accuracy were considered to obtain the best combination of the size and mesh density of the wall and spacecraft.The results of this method were compared with those of S3DE(Survivability of Spacecraft in Space Debris Environment),BUMPER,MDPANTO,ESABASE2/Debris to verify the feasibility of the method.The PCHIP(Piecewise Cubic Hermite Interpolating Polynomial)was used to fit the size vs.flux relationship of the space debris to acquire the impact probability of OD/M with arbitrary size on the spacecraft.

THE SINGULAR LIMIT OF SECOND-GRADE FLUID EQUATIONS IN A 2D EXTERIOR DOMAIN

In this paper, we consider the second-grade fluid equations in a 2D exterior domain satisfying the non-slip boundary conditions. The second-grade fluid model is a wellknown non-Newtonian fluid model, with two parameters: α, which represents the length-scale,while ν > 0 corresponds to the viscosity. We prove that, as ν, α tend to zero, the solution of the second-grade fluid equations with suitable initial data converges to the one of Euler equations, provided that ν = o(α^(4/3)). Moreover, the convergent rate is obtained.

Experimental Study on Seismic Performance of SRUHSC⁃RC Frame Exterior Joints with Cyclic Loads

SRUHSC⁃RC(Steel Reinforced Ultra High Strength Concrete⁃Reinforced Concrete)structures are used extensively in super high⁃rise buildings.However,it has obvious brittleness.Wrapping structural steel inside is a good way to alleviate the brittleness problem.The purpose of this study is to investigate seismic behavior of SRUHSC⁃RC exterior joints on the basis of experimental results of eleven specimens under the reversed cyclic loading.The relationship among the force⁃displacement curve,ductility,energy dissipation property,strength degradation,stiffness degradation,the strains of steel bone and stirrup at the core area of the joint were analyzed based on the test results.It is shown that axial compression ratio and stirrup volumetric ratio have significant effects on the shear behavior of SRUHSC⁃RC frame exterior joints.The general requirement on the axial⁃load level and the amount of confinement stirrup for the joints in the design is suggested.

Measuring Exterior Housing Quality in Four Older-Urban Neighbourhoods in Windsor, Ontario

Four theoretically-deduced hypotheses about geographical and temporal variations in exterior housing quality within a neighbourhood are summarized as a renovation- or deterioration-of-self effect, a contagion-down-the-street effect, a distance-from-riverbank effect, and a distance-from core effect. These hypotheses are tested with data for the exterior conditions of hundreds of single- detached (-like) houses that have been individually surveyed twice with the same instrument in four older-urban neighbourhoods in Windsor, Ontario, Canada. Each surveyed house’s rated conditions of 12 exterior attributes are in particular utilized to calculate its overall exterior quality as a percentage above or below normal. Findings are that houses’ exteriors had average “normal” weathered conditions for Canada. Even so, overall exterior housing qualities in three neighbourhoods exemplified a hypothesized deterioration-of-self effect and proximity-to-core effect, as they had especially declined from their original survey to their resurvey for houses located near to a core such as downtown or a casino. In addition, the hypothesized distance-from-riverbank effect was observed in one neighbourhood where overall exterior housing quality linearly deteriorated with farther distance from a riverbank. Finally, overall exterior housing qualities had no observable contagion-down-the-street effect, and so, residents were not reacting positively or negatively to their neighbours’ maintenance and improvement of their homes’ exteriors. The practical implications of the study’s findings are discussed in the conclusion.

Interior and Exterior Differential Systems for Lie Algebroids

A theorem of Maurer-Cartan type for Lie algebroids is presented. Suppose that any vector subbundle of a Lie algebroid is called interior differential system (IDS) for that Lie algebroid. A theorem of Frobenius type is obtained. Extending the classical notion of exterior diffential system (EDS) to Lie algebroids, a theorem of Cartan type is obtained.

Control of exterior ballistic properties of spin-stabilized bullet by optimizing internal mass distribution

This paper introduces a novel approach for controlling the exterior ballistic properties of spin-stabilized bullets by optimizing their internal mass distributions. Specifically, the properties of interest are the bullets’ stability characteristics that are examined through dynamic and gyroscopic stability parameters.New analytical expressions for aerodynamic quantities are also derived to address the compressibility of air. These expressions are utilized in a bullet model that enables efficient computation of the stability parameters for a given mass distribution. The bullet model is used in the formulation of nonlinear optimization problems that provide optimal mass distributions with respect to given goals, i.e., desired stability characteristics. The bullet types investigated in this paper are a long range bullet and a limited range training bullet. In the optimization of the mass distribution of the long range bullet, the goal is that the bullet stays stable for as long as possible. The mass distribution of the training bullet is optimized such that the bullet is stable at launch but becomes unstable shortly afterwards. The global optimal solutions obtained with the new approach fulfill the desired stability characteristics better than currently used uniformly filled bullets. Overall, the optimization approach reveals a new goal focused philosophy for bullet design compared to current trial and error design practices.

EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC EQUATIONS IN EXTERIOR DOMAINS

This article deals with the degenerate parabolic equations in exterior domains and with inhomogeneous Dirichlet boundary conditions. We obtain that pc = （σ ＋ m ）n / （ n-σ- 2 ） is its critical exponent provided max{-1, [ （1- m ）n- 2] / （ n ＋ l ） } 〈 σ 〈 n- 2. This critical exponent is not the same as that for the corresponding equations with the boundary value 0, but is more closely tied to the critical exponent of the elliptic type degenerate equations. Futhermore, we demonstrate that if max（1, σ ＋ m） 〈 p 〈 pc, then every positive solution of the equations blows up in finite time; whereas for p 〉 pc, the equations admit global positive solutions for some boundary values and initial data. Meantime, we also demonstrate that its positive solutions blow up in finite time provided n〈σ＋2.

ON THE UNIQUENESS OF BOUNDARY INTEGRAL EQUATION FOR THE EXTERIOR HELMHOLTZ PROBLEM

From the point of view of energy analysis, the cause that the uniqueness of the boundary integral equation induced from the exterior Helmholtz problem does not hold is investigated in this paper. It is proved that the Sommerfeld's condition at the infinity is changed so that it is suitable not only for the radiative wave but also for the absorptive wave when we use the boundary integral equation to describe the exterior Helmholtz problem. There fore, the total energy of the system is conservative. The mathematical dealings to guarantee the uniqueness are discussed based upon this explanation.

FAST AND SLOW DECAY SOLUTIONS FOR SUPERCRITICAL FRACTIONAL ELLIPTIC PROBLEMS IN EXTERIOR DOMAINS

1 Introduction and Main Results We construct classic solutions of the following supercritical nonlinear fractional exterior problem.

THE COUPLING OF BOUNDARY ELEMENT AND FINITE ELEMENT METHODS FOR THE EXTERIOR NONSTATIONARY NAVIER-STOKES EQUATIONS

In this paper, we represent a new numerical method for solving the nonstationary Stokes equations in an unbounded domain. The technique consists in coupling the boundary integral and finite element methods. The variational formulation and well posedness of the coupling method are obtained. The convergence and optimal estimates for the approximation solution are provided.

LARCH BARK TANNIN ADHESIVE FOR EXTERIOR PARTICLEBOARD

The larch bark tannins were used to make adhesive for particleboard. The tanninadhesive in which 60% phcnol was replaced by tannin has 1 - 1 .5 month storage life and its cost is lower than that of PF resin. At the 10% and 9% rcsin solids content on dry wood chips, larch particleboard and poplar particleboard were made respectively. The physical properties of boards can meet the nccds of cxterior particleboard in German Standard DIN68763 V 100.

Experimental Studies on Seismic Behavior of Exterior SRUHSC Joints

To investigate the seismic behavior of the joints,six steel reinforced ultra high strength concrete( SRUHSC) frame exterior joints were tested. Three levels of axial compressive ratio varying from 0.25 to 0.45 were investigated to determine how this variable might influence the performance of the joints including failure mode,ductility,energy dissipation capacity,stiffness degradation,shear strength and shear deformation by the quasi-static cyclic test on SRUHSC exterior joints. This research program suggests that the design of joint should make full use of the joint panel deformation to dissipate energy of earthquake. It is tested that the value of 0.38 as a dividing point about the effect of axial compression ratio on the seismic performance of SRUHSC exterior joints should be taken into account in design. In addition,the increase of volumetric ratio of stirrup could possess the ductility for adequate response to unexpected strong earthquakes and a recommended value of minimum volumetric ratio of stirrup with high axial-load level is pointed out.

Three dimensional simulation of electromagnetic railgun's exterior ballistics

In order to evaluate the electromagnetic railgun＇ s practical combat capability as well as its tactic application prospects, a three dimensional simulation model of electromagnetic railgun＇ s exterior ballistics is presented. On the hypothesis of the Earth＇ s being round and ignoring the influ- ence of rotation, the railgun＇ s atmospheric environment and its motion equations are established by the Simulink Module of Matlab. And the railgun＇ s characteristics of exterior ballistic under different muzzle energy and emission inclinations are discussed. Results show that its incomparable superiori- ty in improving range and lethality to conventional artillery under the same launch condition based on railgun＇ s range and variation of velocities. It is useful for the efficacy evaluation of railgun＇ s combat capability and its practical applications in fields such as ground war, missile interception and so on.

Fitting on elements of exterior orientation utilizing SPOT-5 raw data file

In traditional pattern, the calculation of elements of exterior orientation is to calculate the elements of image forming moment by using fundamental ground control points. Utilizing satellite raw data file directly, which holds abundant information and using the numerical analysis methods of modern mathematics, the parameter equations about each element of exterior orientation are adjused and the elements of image forming moment under some precision are calculated.

LOW MACH NUMBER LIMIT ON EXTERIOR DOMAINS

This paper is concerned with the low Mach number limit for the compressible Navier-Stokes equations in an exterior domain. We present here an approach based on Strichartz estimate defined on a non trapping exterior domain and we will be able to show the compactness and strong convergence of the velocity vector field.

BOUNDARY INTEGRAL FORMULAS FOR ELASTIC PLANE PROBLEM OF EXTERIOR CIRCULAR DOMAIN

After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress function and making use of some formulas in Fourier series and the convolutions, the boundary integral formula of the stress function is derived further. Then the stress function can be obtained directly by the integration of the stress function and its normal derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function is convenient to be used for solving the elastic plane problem of exterior circular domain.

Finding vibrations of inclined cable structures by approximately solving governing equations for exterior matrix

In this paper, how to compute the eigenfrequencies of the structures composed of a series of inclined cables is shown. The physics of an inclined cable can be complicated, so solving the differential equations even approximately is difficult. However, rather than solving the system of 4 first-order equations governing the dynamics of each cable, the governing equations are instead converted to a set of equations that the exterior matrix satisfies. Therefore, the exterior matrix method （EMM） is used without solving the original governing equations. Even though this produces a system of 6 first-order equations, the simple asymptotic techniques to find the first three terms of the perturbative solution can be used. The solutions can then be assembled to produce a 6 x 6 exterior matrix for a cable section. The matrices for each cable in the structure are multiplied together, along with the exterior matrices for each joint. The roots of the product give us the eigenfrequencies of the system.

DISCRETENESS OF THE EXTERIOR TRANSMISSION EIGENVALUES

In this paper we consider a kind of exterior transmission problem in which the refractive index n（x） is a piecewise positive constant. Through establishing an equivalent boundary integral system, we obtain that the set of exterior transmission eigenvalues is a discrete set. Furthermore, we prove that there does not exist a transmission eigenvalue under some conditions.

Parameters of Exterior Ballistic Feature Points Extraction in Radar Measurement Data by EMD

The problem of measuring exterior ballistic feature points is always difficult to solve and it is essentiale on exterior ballistic measurement.By analysis of radar reflection characteristics and non-stationary echo signals of exterior ballistic feature points,the echo data of exterior ballistic feature points is measured by using the continuous wave radar.The parameters of feature points are extracted by the empirical mode decomposition method(EMD)of Hilbert-Huang transform(HHT)spectrum analysis technique.The radar echo signal model and EMD extraction model are established to analyze the exterior ballistic mutation point detection and EMD extraction method of aliasing echo signal.Typical feature point parameters of exterior ballistic in rocket flight tests are carried out and the effectiveness of the method is verified.A new method of measuring the parameters of exterior ballistic feature point is therefore presented.

GLOBAL EXISTENCE FOR THE NONHOMOGENEOUS QUASILINEAR WAVE EQUATION WITH A LOCALIZED WEAKLY NONLINEAR DISSIPATION IN EXTERIOR DOMAINS

It is proved that the global existence for the nonhomogeneous quasilinear wave equation with a localized weakly nonlinear dissipation in exterior domains.