Conformal Invariance and Conserved Quantity for?the?Nonholonomic System of Chetaev’s Type

In this paper the definition of conformal invariance and determining equation for the holonomic system which correspond to a nonholonomic system of Chetaev’s type are provided. Conformal factor expression is deduced through relationship between a system’s conformal invariance and Lie symmetry. The necessary and sufficient condition that the system’s conformal invariance would be Lie symmetry under transformations by the infinitesimal one-parameter transformation group is obtained. The conformal invariance of weak and strong Lie symmetry for the nonholonomic system of Chetaev’s type is given using restriction equations and additional restriction equations. And the system’s corresponding conserved quantity is derived with the aid of a structure equation that gauge function satisfied. Lastly, an example is taken to illustrate the application of the result.     

Study on autonomous navigation based on pulsar timing model

The basic principle of pulsar timing model was introduced, and the general relativistic corrections were analyzed when pulse time of arrival (TOA) was transferred to coordinate TOA at the Solar System Barycentre. Based on the shifting, an iterative method of autonomous position determination for spacecraft was developed. Accordingly, the linear form of the position offset equation was evolved. Using the initial estimated value of spacecraft’s position as the input of pulsar timing equation, through calculation of the offset between measured or transferred and predicted TOA, the position offset can be solved by Least Squares. At last, the main error sources including modeling error and parameters error were discussed. Supported by the National Defence Laboratory Foundation of China (Grant No. 9140C3601010901) and Science Foundation of Shaanxi Province (Grant No. 2007F12) and the Technology Specialism Foundation of Shaanxi Education Department of Shaanxi Province (Grant No. 07JK332), and the Innovative Research Plan of Xi’an University of Technology (Grant No. 105-210714)     

Quantum threshold group signature

In most situations, the signer is generally a single person. However, when the message is written on behalf of an organization, a valid message may require the approval or consent of several persons. Threshold signature is a solution to this problem. Generally speaking, as an authority which can be trusted by all members does not exist, a threshold signature scheme without a trusted party appears more attractive. Following some ideas of the classical Shamir’s threshold signature scheme, a quantum threshold group signature one is proposed. In the proposed scheme, only t or more of n persons in the group can generate the group signature and any t − 1 or fewer ones cannot do that. In the verification phase, any t or more of n signature receivers can verify the message and any t − 1 or fewer receivers cannot verify the validity of the signature. Supported by the National Basic Research Program of China (973 Program)(Grant No. 2007CB311100), the National High-Technology Research and Development Program of China (Grant Nos. 2006AA01Z419 and 2006AA01Z440), the Major Research Plan of the National Natural Science Foundation of China (Grant No. 90604023), the Scientific Research Common Program of Beijing Municipal Commission of Education (Grant No. KM200810005004), the Scientific Research Foundation for the Youth of Beijing University of Technology (Grant No. 97007016200701), the Doctoral Scientific Research Activation Foundation of Beijing University of Technology (Grant No. 52007016200702), the ISN Open Foundation, and the National Laboratory for Modern Communications Science Foundation of China (Grant No. 9140C1101010601)     

Ambient noise near the sea-route

Ambient noise data measured in an experiment conducted in shallow water near a sea-route were analyzed. It was observed that, at low frequency, the horizontal correlation has an obvious difference from that predicted by the classical ambient noise model. The theoretical analyses show that this phenomenon is caused by wind noise together with the discrete shipping noise nearby. An ambient noise model was proposed to include the effects caused by both the noise sources. Data measured at different times verify that the proposed model can be used to forecast the ambient noise field in shallow water near the sea-route. Supported by the National Natural Science Foundation of China (Grant No. 10734100), the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. KZCX1-YW-12-2), the National Basic Research Program of China (Grant No. 2007CB209603), and the Open Foundation of China National Petroleum Corporation Key Laboratory (Grant No. GPKL0804)     

A Rigorous Treatment of Energy Extraction from a Rotating Black Hole

The Cauchy problem is considered for the scalar wave equation in the Kerr geometry. We prove that by choosing a suitable wave packet as initial data, one can extract energy from the black hole, thereby putting supperradiance, the wave analogue of the Penrose process, into a rigorous mathematical framework. We quantify the maximal energy gain. We also compute the infinitesimal change of mass and angular momentum of the black hole, in agreement with Christodoulou’s result for the Penrose process. The main mathematical tool is our previously derived integral representation of the wave propagator. Research supported in part by the Deutsche Forschungsgemeinschaft. Research supported by NSERC grant # RGPIN 105490-2004. Research supported in part by the Humboldt Foundation and the National Science Foundation, Grant No. DMS-0603754. Research supported in part by the NSF, Grant No. 33-585-7510-2-30.     

First-principle study on the electronic structure of stressed CrSi<Subscript>2</Subscript>

The electronic structure of stressed CrSi₂ was calculated using the first-principle methods based on plane-wave pseudo-potential theory. The calculated results showed that, under the uniaxial compression, the energy level of CrSi₂ shifted toward high energy and its energy gap became wider with the increasing uniaxial stress, while the gap became narrower under the negative uniaxial stress. When the negative uniaxial stress was up to −18.5 GPa, CrSi₂ was converted into a direct-gap semiconductor with the band gap of 0.32 eV. Supported by the National Natural Science Foundation of China (Grant No. 60566001), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20050657003), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China (Grant No. (2005)383), the Program for the Excellent Young Talents of Guizhou Province (Grant No. 20050528), the Specialized Nomarch Research Fund for the Excellent Science and Technology and Education Talent’s Projects of Guizhou Province, Scientific and Technological Projects for the Returned Overseas Chinese Scholars, the Guizhou Province (Grant No. (2004)03), and the Top Talent’s Scientific Research Project of Organization Department of Guizhou Province     

Quantum corrections for Boltzmann equation

We present the lowest order quantum correction to the semiclassical Boltzmann distribution function, and the equation satisfied by this correction is given. Our equation for the quantum correction is obtained from the conventional quantum Boltzmann equation by explicitly expressing the Planck constant in the gradient approximation, and the quantum Wigner distribution function is expanded in powers of Planck constant, too. The negative quantum correlation in the Wigner distribution function which is just the quantum correction terms is naturally singled out, thus obviating the need for the Husimi’s coarse grain averaging that is usually done to remove the negative quantum part of the Wigner distribution function. We also discuss the classical limit of quantum thermodynamic entropy in the above framework. Supported by the National Natural Science Foundation of China (Grant No. 10404037) and the Scientific Research Fund of GUCAS (Grant No. 055101BM03)     

Turbulence. 2. Pfaff’s systems in turbulence models

Based on the classification of dynamic coordinates presented in Part 1 of this work and analogy with the classical systems constrained by nonholonomic coupling, Pfaff’s systems of turbulent dynamics are constructed. A method of constructing trajectory bundles for particles forming a vortex sheet is described. Thermodynamic interpretation of Pfaff’s coefficients is suggested.     

Factors affecting the superconductivity in the process of depositing Nd1.85Ce0.15CuO4-δ by the pulsed electron deposition technique

On SrTiO₃ single crystal substrate, by using the pulsed electron deposition technique, the high-quality electron doped Nd_1.85Ce_0.15CuO_4−δ superconducting film was successfully fabricated. After careful study on the R-T curves of the obtained samples deposited with different substrate temperatures, thicknesses, annealing methods and pulse frequencies, the effects of them on the superconductivity of the films were found, and the reasons were also analyzed. Additionally, by using the same model of the pulsed laser deposition technique, the relation between the target-to-substrate distance and the deposition pressure was drawn out as a quantitative one. Supported by the Key Project of Zhejiang Provincial Natural Science Foundation (Grant No. Z605131), the ‘100 Talents Project’ of Chinese Academy of Sciences, the Creative Research Group of National Natural Science Foundation of China (Grant No. 60321001) and the National Natural Science Foundation of China (Grant No. 60571029)     

Improvement of the relative entropy based protein folding method

The “relative entropy” has been used as a minimization function to predict the tertiary structure of a protein backbone, and good results have been obtained. However, in our previous work, the ensemble average of the contact potential was estimated by an approximate calculation. In order to improve the theoretical integrity of the relative-entropy-based method, a new theoretical calculation method of the ensemble average of the contact potential was presented in this work, which is based on the thermodynamic perturbation theory. Tests of the improved algorithm were performed on twelve small proteins. The root mean square deviations of the predicted versus the native structures from Protein Data Bank range from 0.40 to 0.60 nm. Compared with the previous approximate values, the average prediction accuracy is improved by 0.04 nm. Contributed equally to this work Supported by the National Natural Science Foundation of China (Grant No. 30670497), the Beijing Natural Science Foundation (Grant No. 5072002), and the Specialized Research Foundation for the Doctoral Program of Higher Education (Grant No. 200800050003)     

Effects of the mid-air collision on sand saltation

As to the fact that the effects of saltating particles’ mid-air collision on the sand transport rate are often neglected in the current theoretical models describing sand saltation movement, expressions to calculate velocity diversity of saltating particles after mid-air collision are presented through collision theory of hard ball in this paper. Then, the theoretical model of the wind blown sand movement at the steady state, taking account of coupled interaction between saltation particles and wind, is combined with the model of the mid-air collision probability to calculate the saltating particles’ mass flux at heights, the sand transport rate, and further, their changing rules. The comparison of the results with those when the mid-air collision is not considered suggests that the mass flux at heights and the sand transport rate in this paper are less, and much closer, respectively, to the corresponding experimental values. The difference between the sand mass fluxes without and with consideration of mid-air collision increases at first, and then decreases as the height increases, exhibiting the stratified characteristics. Supported by the Key Project of National Natural Science Foundation of China (Grant No. 10532040), the National Natural Science Foundation of China (Grant Nos. 40571018 and 10772073), the New Century Outstanding Talent of the Ministry of Education of China, and the Science Fund of the Ministry of Education of China for PhD Program (Grant No. 20060730014)     

Morphological study of atherosclerotic plaque and its application in vulnerability evaluation

The relationships between the morphological characteristics and the vulnerability of atherosclerotic plaque were analyzed theoretically and several suggestions were proposed to evaluate the plaque vulnerability. Validated by animal experiments and clinical studies, the theoretical results were confirmed. Supported by the National Natural Science Foundation of China (Grant Nos. 10302016 and 60402023), the National Basic Research Program of China (973 Program)(Grant No. 2006CB503803), and the National Hi-Tech Research and Development Program of China (863 Program) (Grant No. 2007AA02Z448)     

Peculiarities of the ignition of propane-air premixed flows by CO2 laser radiation

Results of an experimental study of the ignition dynamics of propane-air premixed flows under pulsed-periodic laser irradiation are reported. Ignition of homogeneous flows emanating into free atmosphere is considered. A comparative analysis of experimental and predicted delay times for the ignition for a medium at rest is given. This work was supported by the President of the Russian Federation (Grant No. NSh-8597. 2006.1), by the Russian Foundation for Basic Research (Grant No. 05-01-00560) and by the Presidium of the Russian Academy of Sciences (under the Program “Fundamental Problems in Magnetoplasma Aerodynamics”).     

Quantum secure direct communication over the collective amplitude damping channel

An efficient quantum secure direct communication protocol is presented over the amplitude damping channel. The protocol encodes logical bits in two-qubit noiseless states, and so it can function over a quantum channel subjected to collective amplitude damping. The feature of this protocol is that the sender encodes the secret directly on the quantum states, the receiver decodes the secret by performing determinate measurements, and there is no basis mismatch. The transmission’s safety is ensured by the nonorthogonality of the noiseless states traveling forward and backward on the quantum channel. Moreover, we construct the efficient quantum circuits to implement channel encoding and information encoding by means of primitive operations in quantum computation. Supported by the National Natural Science Foundation of China (Grant Nos. 60873191 and 60821001), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 200800131016), the Natural Science Foundation of Beijing (Grant No. 4072020), the National Laboratory for Modern Communications Science Foundation of China (Grant No. 9140C1101010601), and the ISN Open Foundation     

First-principles calculations on the electronic structure and optical properties of BaSi<Subscript>2</Subscript>

The electronic structure, densities of states and optical properties of the stable orthorhombic BaSi₂ have been calculated using the first-principle density function theory and pseudopotential method. The results show that BaSi₂ is an indirect semiconductor with the band gap of 1.086 eV, the valence bands of BaSi₂ are mainly composed of Si 3p, 3s and Ba 5d, and the conduction bands are mainly composed of Ba 6s, 5d as well as Si 3p. The static dielectric function ɛ ₁(0) is 11.17, the reflectivity n ₀ is 3.35, and the biggest peak of the absorption coefficient is 2.15×10₅ cm⁻¹. Supported by the National Natural Science Foundation of China (Grant Nos. 60566001 and 60766002), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20050657003), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China (Grant No. (2005)383), the Specialized Fund of Nomarch for Excellent Talent of Science and Technology of Guizhou Province (Grant No. Z053114), the Scientific and Technological Projects for the Returned Overseas of Guizhou Province (Grant No. (2004)03), and the Top Talent’s Scientific Research Project of Organization Department of Guizhou Province (Grant No. Z053123)     

Threshold proxy quantum signature scheme with threshold shared verification

A threshold proxy quantum signature scheme with threshold shared verification is proposed. An original signer could authorize a group as its proxy signers. Then only t or more of n persons in the proxy group can generate the proxy signature on behalf of the original signer and any t − 1 or fewer ones cannot do that. When the proxy signature needs to be verified, any t or more of n persons belonging to the verification group can verify the message and any t − 1 or fewer ones cannot verify the validity of the proxy signature. Supported by the National Basic Research Program of China (973 Program)(Grant No. 2007CB311100), the National High-Technology Research and Development Program of China (Grant Nos. 2006AA01Z419 and 20060101Z4015), the Major Research Plan of the National Natural Science Foundation of China (Grant No. 90604023), the Scientific Research Common Program of Beijing Municipal Commission of Education (Grant No. KM200810005004), the Scientific Research Foundation for the Youth of Beijing University of Technology (Grant No. 97007016200701), the Doctoral Scientific Research Activation Foundation of Beijing University of Technology (Grant No. 52007016200702), and the National Laboratory for Modern Communications Science Foundation of China (Grant No. 9140C1101010601)     

Remote Preparation of a Two-Particle Entangled State via Two Tripartite <Emphasis Type="Italic">W</Emphasis> Entangled States

We present a scheme for remotely preparing a general two-particle entangled state via two tripartite W entangled states of different amplitudes. In this scheme one sender and two remote receivers are involved. The sender can help either one of the receivers to remotely reconstruct the original state with the aid of the other receiver’s two single-particle orthogonal measurements. It is shown that by means of the method of the positive operator-valued measurement, our remote state preparation scheme can be achieved probabilistically. This project supported by the National Key Basic Research and Development Program of China under Grant No. 2006CB921604 and the National Natural Science Foundation of China under Grant Nos. 60578050 and 10434060.     

An efficient quantum secret sharing protocol with orthogonal product states

An efficient quantum secret sharing protocol with orthogonal product states in the 33 Hilbert space is presented. The particles in the orthogonal product states form two particle sequences. One sequence is sent to Bob and the other is sent to Charlie after rearranging the particle orders. With the help of Alice, Bob and Charlie make the corresponding local measurement to obtain the information of the or- thogonal product states prepared. This protocol has many distinct features such as great capacity and high efficiency.     

The elasto-damage theory of the components assembling model

The potential energy in materials is well approximated by pair functional which is composed of pair potentials and embedding energy. During calculating material potential energy, the orientational component and the volumetric component are derived respectively from pair potentials and embedding energy. The sum of energy of all these two kinds of components is the material potential. No matter how microstructures change, damage or fracture, at the most level, they are all the changing and breaking atomic bonds. As an abstract of atomic bonds, these components change their stiffness during damaging. Material constitutive equations have been formulated by means of assembling all components’ response functions. This material model is called the component assembling model. Theoretical analysis and numerical computing indicate that the proposed model has the capacity of reproducing some results satisfactorily, with the advantages of great conceptual simplicity, physical explicitness, and intrinsic induced anisotropy, etc. Supported by the National Natural Science Foundation of China (Grant Nos. 10572140 and 10232050) and the Ministry of Science and Technology Foundation (Grant No. 2002CB412706)     

Quasi-variational principles of single flexible body dynamics and their applications

The reasons for studying single flexible body dynamics are that on one hand, it is the basis of flexible multi-body dynamics. If the theory of the single flexible body dynamics has been deeply studied, the theory of flexible multi-body dynamics will be researched easily. On the other hand, it has its unique and important applications. Quasi-variational principle of non-conservative single flexible body dynamics is established under the cross-link of particle rigid body mechanics and deformable body mechanics. Taking the interceptor as an example, this paper has explained the physical meaning of the quasi-stationary value condition of the quasi-variational principle in non-conservative single flexible body dynamics. Taking the launch of rocket as an example, it has illustrated the features of “one force for two effects” in a single flexible body dynamics. With an example of the extending flexible beam coupled with the spacecraft attitude, it has shown the transition from the single flexible body dynamics to the flexible multi-body dynamics. Finally, a number of related problems are discussed. Supported by the National Natural Science Foundation of China (Grant No. 10272034), the Doctoral Education Foundation (Grant No. 20060217020), and the Natural Science Foundation of Harbin Engineering University (Grant No. HEUF04003)