Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal

Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.

Commissioning of a high-resolution collinear laser spectroscopy apparatus with a laser ablation ion source

Collinear laser spectroscopy is a powerful tool for studying the nuclear spins,electromagnetic moments,and charge radii of exotic nuclei.To study the nuclear properties of unstable nuclei at the Beijing Radioactive Ion-beam Facility(BRIF)and the future High Intensity Heavy-ion Accelerator Facility(HIAF),we developed a collinear laser spectroscopy apparatus integrated with an offline laser ablation ion source and a laser system.The overall performance of this state-of-the-art technique was evaluated,and the system was commissioned using a bunched stable ion beam.The high-resolution optical spectra for the 4s ^(2)S_(1/2)→4p^(2)P_(3/2)(D2)ionic transition of ^(40;42;44;48)Ca isotopes were successfully measured.The extracted isotope shifts relative to ^(40)Ca showed excellent agreement with the literature values.This system is now ready for use at radioactive ion beam facilities such as the BRIF and paves the way for the further development of higher-sensitivity collinear resonance ionization spectroscopy techniques.

Exact solutions of two semi-infinite collinear cracks in piezoelectric strip

Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface. Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable. The results can be reduced to the well-known solutions for a purely elastic material in the absence of an electric load. Moreover, when the distance between the two crack tips tends to infinity, analytic solutions of a semi-infinite crack in a piezoelectric strip can be obtained. Numerical examples are given to show the influence of the loaded crack length, the height of the strip, the distance between the two crack tips, and the applied mechanical/electric loads on the mechanical strain energy release rate. It is shown that the material is easier to fail when the distance between two crack tips becomes shorter, and the mechanical/electric loads have greater influence on the propagation of the left crack than those of the right one.

Identification of novel soybean oil content-related genes using QTL-based collinearity analysis from the collective soybean genome

Soybean is a global principal source of edible plant oil. As more soybean oil-related quantitative trait loci(QTLs) have been located in the collective genome, it is urgent to establish a classification system for these distributed QTLs. A collinear platform may be useful to characterize and identify relationships among QTLs as well as aid in novel gene discovery. In this study, the collinearity MCScan X algorithm and collective soybean genomic information were used to construct collinearity blocks, to which soybean oil-related QTLs were mapped. The results demonstrated that 666 collinearity blocks were detected in the soybean genome across 20 chromosomes, and 521 collinearity relationships existed in 231 of the 242 effective soybean oil-related QTLs. This included 214 inclusion relationships and 307 intersecting relationships. Among them, the collinearity among QTLs that are related to soybean oil content was shown on a maximum of seven chromosomes and minimum of one chromosome, with the majority of QTLs having collinearity on two chromosomes. Using overlapping hotspot regions in the soybean oil QTLs with collinearity, we mined for novel oil content-related genes. Overall, we identified 23 putatively functional genes associated with oil content in soybean and annotated them using a number of annotation databases. Our findings provide a valuable framework for elucidating evolutionary relationships between soybean oil-related QTLs and lay a foundation for functional marker-assisted breeding relating to soybean oil content.

THE BEHAVIOR OF TWO COLLINEAR CRACKS IN MAGNETO-ELECTRO-ELASTIC COMPOSITES UNDER ANTI-PLANE SHEAR STRESS LOADING

In this paper, the behavior of two collinear cracks in magneto-electro-elastic compos- ite material under anti-plane shear stress loading is studied by the Schmidt method for permeable electric boundary conditions. By using the Fourier transform, the problem can be solved with a set of triple integral equations in which the unknown variable is the jump of displacements across the crack surfaces. In solving the triple integral equations, the unknown variable is expanded in a series of Jacobi polynomials. Numerical solutions are obtained. It is shown that the stress feld is independent of the electric feld and the magnetic fux.

INVESTIGATION OF ANTI-PLANE SHEAR BEHAVIOR OF TWO COLLINEAR CRACKS IN PIEZOELECTRIC MATERIALS BY A NEW METHOD

In this paper, the interaction between two collinear cracks inpiezoelectric materials under anti-plane shear loading wasinvestigated for the impermeable crack face conditions. By using theFourier transform, the problem can be solved with two pairs of tripleintegral equations. These equations are solved using Schmidt'smethod. This process is quite different from that adopted previously.This makes it possible to understand the two collinear cracksinteraction in piezoelectric materials.

SINGULARITIES AND EXPLICIT SOLUTIONS OF COLLINEAR CRACK PROBLEM IN ANISOTROPIC MEDIA

The singularities of collinear cracks both in anisotropic single medium and at the interface of anisotropic bimaterials are studied by combining Stroh formalism and the analytic function method. The formulae for calculating the field potential and stress intensity factor (SIF) are obtained. It is found that the field potentials are explicitly related to material matrix L and the in-plane and anti-plane fields can be separately calculated when orthotropic bimaterials are considered.

Control and data acquisition system for collinear laser spectroscopy experiments

A control and data acquisition system was implemented for the recently developed collinear laser spectroscopy setup.This system is dedicated to data recording,storage,processing,monitoring of the beam intensity and energy,and visualization of various spectra.In comparison to the conventional resonance nuclear reaction system,the key technique is the precise synchronization of the detected counts with the actual scanning voltage(or probing laser frequency).The functions of the system were tested by measuring the hyperfine structure spectra of stable calcium(e.g.,^(40)Ca^(+))and radioactive potassium(e.g.,^(38)K)in the bunched and continuous modes,respectively.This system will be routinely applied and further improved in subsequent laser spectroscopy experiments on unstable isotopes at the Beijing Radioactive Ion-beam Facility(BRIF).

Collinear holographic data storage technologies

In the era of information explosion,the demand of data storage is increased dramatically.Holographic data storage technology is one of the most promising next-generation data storage technologies due to its high storage density,fast data transfer rate,long data life time and less energy consumption.Collinear holographic data storage technology is the typical solution of the holographic data storage technology which owns a more compact,compatible and practical system.This paper gives a brief review of holographic data storage,introduces collinear holographic data storage technology and discusses phase modulation technology being used in the holographic data storage system to achieve higher storage density and higher data transfer rate.

Strip-coalesced interior zone model for two unequal collinear cracks weakening piezoelectric media

In this paper, a mathematical strip-saturation model is proposed for a poled transversely isotropic piezoelectric plate weakened by two impermeable unequal-collinear hairline straight cracks. Remotely applied in-plane unidirectional electromechanical loads open the cracks in mode-I such that the saturation zone developed at the interior tips of cracks gets coalesced. The developed saturation zones are arrested by distributing over their rims in-plane normal cohesive electrical displacement. The problem is solved using the Stroh formalism and the complex variable technique. The expressions are derived for the stress intensity factors （SIFs）, the lengths of the saturation zones developed, the crack opening displacement （COD）, and the energy release rate. An illustrative numerical case study is presented for the poled PZT-5H ceramic to investigate the effect of prescribed electromechanical loads on parameters affecting crack arrest. Also, the effect of different lengths of cracks on the SIFs and the local energy release rate （LERR） has been studied. The results obtained are graphically presented and analyzed.

A CLASS OF COLLINEAR SCALING ALGORITHMS FOR UNCONSTRAINED OPTIMIZATON

A Class of Collinear Scaling Algorithms for Unconstrained Optimization. An appealing approach to the solution of nonlinear optimization problems based on conic models of the objective function has been in troduced by Davidon (1980). It leads to a broad class of algorithms which can be considered to generalize the existing quasi-Newton methods. One particular member of this class has been deeply discussed by Sorensen (1980), who has proved some interesting theoretical properties. In this paper, we generalize Sorensen’s technique to Spedicato three-parameter family of variable-metric updates. Furthermore, we point out that the collinear scaling three- parameter family is essentially equivalent to the Spedicato three-parameter family. In addition, numerical expriments have been carried out to compare some colliner scaling algorithms with a straightforward implementation of the BFGS quasi-Newton method.

Collinear micro-shear-bands model for grain-size and precipitate-size effects on the yield strength

Numerous experimental evidences show that the grain size may significantly alter the yield strength of metals.Similarly,innickel-based superalloys,the precipitate size also influences their yield strength.Then,how to describe such two kinds of size effects on the yield strength is a very practical challenge.In this study,according to experimental observations,a collinear micro-shear-bands model is proposed to explore these size effects on metal materials’yield strength.An analytical solution for the simple model is derived.It reveals that the yield strength is a function of average grain-size or precipitate-size,which is able to reasonably explain size effects on yield strength.The typical example validation shows that the new relationship is not only able to precisely describe the grain-size effect in some cases,but also able to theoretically address the unexplained Hall-Petch relationship between theprecipitate size and the yield strength of nickel-based superalloys.

Interaction between collinear periodic cracks in an infinite piezoelectric body

The problem of collinear periodic cracks in an infinite piezoelectric body is studied. Effect of saturation strips at the crack-tips is taken into account. By means of the Stroh formalism and the conformal mapping technique, the general periodic solutions for collinear cracks are obtained. The stress intensity factors and the size of saturation strips are derived analytically, and their dependencies on the ratio of the periodicity on the half-length of the crack are analyzed in detail. Numerical results show the following two facts. （1） When h/l 〉 4.0, the stress intensity factors become almost identical to those of a single crack in an infinite piezoelectric body. This indicates that the interaction between cracks can be ignored in establishing the criterion for the crack initiation in this case. （2） The speed of the saturation strip size of periodic cracks approaching that of a single crack depends on the electric load applied at infinity. In general, a large electric load at infinity is associated with a slow approaching speed.

Interferences in photo-detached electron spectra from a non-collinear tri-atomic anion

The electron flux oscillations in photo-detachment of a non-collinear tri-atomic anion have been studied by taking each atom of the system as a coherent source of detached-electron wave. These electron waves traversing along three different trajectories result in a quantum interference. An analytical expression of detached-electron flux is evaluated for various detached-electron energies and for different geometrical shapes of the system. The results show that the electron flux distributions exhibit molecular shape-induced oscillatory structures. These oscillations are explained using the semi- classical closed-orbit theory; the outgoing electron waves produced from one center are propagated in the vicinity of the sources at other centers. It is also observed that in a particular case our non-collinear tri-atomic system reduces to the collinear tri-atomic system recently published.

Improved semi-analytical computation of center manifolds near collinear libration points

In the framework of the circular restricted three-body problem, the center manifolds associated with collinear libration points contain all the bounded orbits moving around these points. Semianalytical computation of the center manifolds and the associated canonical transformation are valuable tools for exploring the design space of libration point missions. This paper deals with the refinement of reduction to the center manifold procedure. In order to reduce the amount of calculation needed and avoid repetitive computation of the Poisson bracket, a modified method is presented. By using a polynomial optimization technique, the coordinate transformation is conducted more efficiently. In addition, an alternative way to do the canonical coordinate transformation is discussed, which complements the classical approach. Numerical simulation confirms that more accurate and efficient numerical exploration of the center manifold is made possible by using the refined method.

First fundamental problems of anisotropic elastic plane weakened by periodic collinear cracks

Using the method of complex functions, we discuss the first fundamental problems of an anisotropic infinite elastic plane weakened by periodic collinear cracks and with periodic boundary loads on both sides of the cracks. This problem was considered by Cai [Engineering Fracture Mechanics 46（1）, 133-142 （1993）]. However, the previous method is imperfect. Therefore, the results are incorrect. Here, we revise the method and give a correct solution.

The dynamic behavior of two collinear cracks in magneto-electro-elastic composites under harmonic anti-plane shear waves

The dynamic behavior of two collinear cracks in magneto-electro-elastic composites under harmonic anti-plane shear waves is studied using the Schmidt method for the permeable crack surface conditions. By using the Fourier transform, the problem can be solved with a set of triple integral equations in which the unknown variable is the jump of the displacements across the crack surfaces. In solving the triple integral equations, the jump of the displacements across the crack surface is expanded in a series of Jacobi polynomials. It can be obtained that the stress field is independent of the electric field and the magnetic flux.

Short Term Forecasting Performances of Classical VAR and Sims-Zha Bayesian VAR Models for Time Series with Collinear Variables and Correlated Error Terms

Forecasts can either be short term, medium term or long term. In this work we considered short term forecast because of the problem of limited data or time series data that is often encounter in time series analysis. This simulation study considered the performances of the classical VAR and Sims-Zha Bayesian VAR for short term series at different levels of collinearity and correlated error terms. The results from 10,000 iteration revealed that the BVAR models are excellent for time series length of T=8 for all levels of collinearity while the classical VAR is effective for time series length of T=16 for all collinearity levels except when ρ = -0.9 and ρ = -0.95. We therefore recommended that for effective short term forecasting, the time series length, forecasting horizon and the collinearity level should be considered.

Motion modeling and formation form analysis of spacecraft near collinear libration points

To meet the increasing research demand for deep space exploration,especially for the second libration point (L2) conditional periodic orbit (Halo orbit) in the Sun-Earth system,the methods to get analytical Halo orbit and differential-correction Halo orbit were described firstly,and the corresponding orbits accuracy was analyzed.Then,based on the results of third-order and differential-correction Halo orbits,the formation form was studied.Analysis was carried out to discuss the influence of system amplitude,initial phase,and phase difference on the formation form,as well as that of initial orbit values on form accuracy.Finally,some simulation results demonstrate the validity of the proposed methods.

Frequency dependence of quantum path interference in non-collinear high-order harmonic generation

High-order harmonic generation（HHG） driven by two non-collinear beams including a fundamental and its weak second harmonic is numerically studied. The interference of harmonics from adjacent electron quantum paths is found to be dependent on the relative delay of the driving pulse, and the dependences are different for different harmonic orders.This frequency dependence of the interference is attributed to the spatial frequency chirp in the HHG beam resulting from the harmonic dipole phase, which in turn provides a potential way to gain an insight into the generation of high-order harmonics. As an example, the intensity dependent dipole phase coefficient α is retrieved from the interference fringe.