Community detection based on the “clumpiness” matrix in complex networks

The “clumpiness” matrix of a network is used to develop a method to identify its community structure. A “projection space” is constructed from the eigenvectors of the clumpiness matrix and a border line is defined using some kind of angular distance in this space. The community structure of the network is identified using this borderline and/or hierarchical clustering methods. The performance of our algorithm is tested on some computer-generated and real-world networks. The accuracy of the results is checked using normalized mutual information. The effect of community size heterogeneity on the accuracy of the method is also discussed.     

The inverse problem in the case of bound states

We investigate the inverse problem for bound states in the D = 3 dimensional space. The potential is assumed to be local and spherically symmetric. The present method is based on relationships connecting the moments of the ground state density to the lowest energy of each state of angular momentum ?. The reconstruction of the density ρ(r) from its moments is achieved by means of the series expansion of its Fourier transform F(q). The large q-behavior is described by Padé approximants. The accuracy of the solution depends on the number of known moments. The uniqueness is achieved if this number is infinite. In practice, however, an accuracy better than 1% is obtained with a set of about 15 levels.The method is tested on a simple example, and applied to three different spectra.     

QCD at finite temperature

Quantum chromodynamics is studied at finite temperatures and densities using the temperature Green functions method. For the Green functions the renormalized Schwinger-Dyson equations are obtained and their qualitative properties are discussed. The equality of the renormalization constants for the equations obtained at T, μ ≠ 0 with those for quantum field theory is pointed out. General properties of the gluon polarization tensor are investigated at T, μ ≠ 0. The temperature Green functions are calculated within the one-loop approximation using both relativistic and axial gauges. The fulfilment of the Slavnov-Taylor identities is verified. The asymptotic behaviour of the polarization tensor at T, μ ≠ 0 is established and the excitation spectrum of quark-gluon plasma is found. Both Fermi and Bose excitations are considered and the gauge invariance of the spectra is demonstrated. The renormalization group extension of the dispersion laws into the regions of high temperatures and densities is presented. The exact representation of the thermodynamical potential in QCD is found in terms of the temperature Green functions. For the quark-gluon plasma the thermodynamical potential is calculated with the g³-term taken into account. The equation of state of the hot quark-gluon plasma is found and its properties are discussed. The complete evolutional diagram of the hadronic matter is outlined. The phase curve asymptotics, which put bounds on the quark-gluon plasma domain, are found for the two limiting cases (μ = 0, T → T₀; T = 0, μ → μ₀). The phase transition of the hot quark-gluon plasma placed in external Abelian field is studied. The instability of such plasma has been found and the program of its stabilization is indicated. The infrared behaviour of the non-Abelian gauge theory is studied for finite temperatures when power divergencies are essential. The propagator of transverse gluons is shown to be singular for momenta |p| ˜ g²T and this cannot be avoided by summing the simplest bubble chains. The infrared asymptotic behaviour of the tree-gluon vertex is found and the results obtained are checked using the Slavnov-Taylor identities. The Green functions asymptotics found indicate either an instability of the quark-gluon plasma in the infrared momentum domain or the inconsistency of the perturbational methods. A non-perturbative approach to the infrared problem in QCD is developed within the axial gauge. The closed equations for the structure functions that determine the gluon polarization tensor are obtained by using the Slavnov-Taylor identities to found approximately the three-gluon vertex. It is shown that the solution of the equations obtained by iterations does not remove the infrared singularity from the temperature Green functions. The nonperturbative solution of such equations is discussed.     

Simple generalization of Kramers theory to finite barrier height in spatial diffusion regime

Motivated by the escape process at low reduced barrier heights (measured in units of $k_{B}T$) is still a stationary one, the Kramers theoretical method in spatial diffusion regime should be applicable to this process. The Kramers theory is generalized to finite barrier height in a simple manner. The integration constant is redetermined by introducing metastable equilibrium state concept and continuous condition of the probability at the joint point of the potential barrier and potential well. The parabolic barrier with local frequency is replaced by a parabolic barrier with nonlocal frequency. The modified Kramers theory is confirmed by a cubic potential case. The maximal relative error in the spatial diffusion regime is less than 3% for the applied parameters.     

The Knudsen Ion Layer Problem in the Theory of the Collisionless Sheath

The interaction of a partially ionized continuum gas with a negatively charged electrode is investigated theoretically. It is supposed that l_d ? 1, where l_d is the Debye length, l is the mean-free-path. The self-consistent solution is given for two cases: l_I ? l and l_I ～ l, l_I is the effective ionisation length. The matched asymptotic expansions method is used. The Bohm sheath criterion is shown to be satisfied automatically in the considered cases.     

Magnetic inhomogeneity of lanthanum manganites single crystals

The magnetic inhomogeneity of the single crystals of La_1−xD_xMnO₃, where D=Ca, Sr, Ba, is studied. The Curie temperature distribution function is found. The form of this function is shown to depend on whether the mean value of the divalent element concentration is close to the “optimal” concentration (≈1/3) or not. The standard deviation for Curie temperature is evaluated. The correlation between the distribution coefficient for divalent elements and the standard deviation is established.     

高峰值功率脉冲激光与石英光纤耦合的空气击穿问题

 研究了15 MW峰值功率脉冲激光与600 μm芯径石英光纤耦合中存在的空气击穿现象。对聚焦区域的空气击穿现象进行了理论和实验研究,测得空气击穿阈值为0.79×10⁹ W/cm²。测得固体介质的激光损伤阈值为2.12×10⁹ W/cm²,与理论计算结果相符。提出了七合一光纤耦合器用于解决空气击穿的办法,实验测得7根光纤并束的耦合效率为67.21%。结果表明光纤耦合器可有效解决15 MW峰值功率脉冲激光与600 μm芯径石英光纤的耦合。     

钨磷酸盐非晶铜离子导体的结构与电性能

本文给出了当CuI含量为30mol%时CuI-Cu₂O-WO₃-P₂O₅系统的玻璃形成区。测量了样品的交流电导率,得出了电导率随WO₃含量变化规律。采用红外光谱、阻抗谱、径向分布函数(RDF)和扫描电子显微镜(SEM)等测试手段研究了该系统材料的结构,讨论了电学性能与结构的相互关系。 关键词：     

Schwinger Effect in a Robertson-Walker Space-Time

The problem of particle creation from vacuum in a flat Robertson-Walker space-time in the presence of a varying electric field is studied. The Klein Gordon equation is exactly solved when the scale factor is a(η)=A+Btanh(λη). The canonical method based on Bogoliubov transformation is applied. The pair creation probability and the density number of created particles are calculated. The particular case of radiation dominated universe is considered where the total probability is written as a Schwinger-like series. It is shown that the electric field amplifies gravitational particle creation.     

Brueckner G matrix for a planar slab of nuclear matter

The equation for the Brueckner G matrix is investigated for planar-slab geometry. A method for calculating the G matrix for a planar slab of nuclear matter is developed for a separable form of NN interaction. Actually, the separable version of the Paris NN potential is used. The singlet ¹ S ₀ and the triplet ³ S ₁–³ D ₁ channel are considered. The present analysis relies on the mixed momentum-coordinate representation, where use is made of the momentum representation in the slab plane and of the coordinate representation in the orthogonal direction. The full two-particle Hilbert space is broken down into the model subspace, where the two-particle propagator is considered exactly, and the complementary subspace, where the local-potential approximation is used, which was proposed previously for calculating the effective pairing potential. Specific calculations are performed for the case where the model subspace is constructed on the basis of negative-energy single-particle states. The G matrix is parametrically dependent on the total two-particle energy E and the total momentum P _⊥ in the slab plane. Since the G matrix is assumed to be further used to calculate the Landau-Migdal amplitude, the total two-particle energy is fixed at the value E=2μ, where μ is the chemical potential of the system under investigation. The calculations are performed predominantly for P _⊥=0. The role of nonzero values of P _⊥ is assessed. The resulting G matrix is found to depend greatly on μ in the surface region.     

Investigation on the optical and electrical properties of MMTG crystal: A Lewis base adduct

The growth of nonlinear optical single crystal of manganese mercury thiocyanate glycol monomethyl ether (MMTG), a Lewis base adduct of manganese mercury thiocyanate (MMTC), is reported. MMTG crystallizes in orthorhombic structure with Pca2₁ space group. The optical band gap energy of the sample is found to be 3.5 eV. The sample is thermally stable up to 145 °C. The grown crystal is characterized by photoluminescence, dielectric, dc conductivity, photoconductivity and SEM studies. From the photoluminescence study, the suitability of the material for blue and green light generation is confirmed. The electric and dielectric response of the grown crystal is studied as a function of temperature and the results are discussed. The dc activation energy of the sample is found to be 0.048 eV.     

HT-6M托卡马克等离子体紫外-可见谱

利用光学多道分析仪(OMA)拍摄了HT-6M托卡马克等离子体近紫外可见谱.系统分析了杂质行为,给出了主要杂质碳和氧的朝内的通量,在简化模型下计算了碳氧的化学溅射率,并由此得出碳氧杂质产生机制和可能的循环途径.结果表明,氧杂质在循环途径中起关键性的作用,控制氧杂质尤其重要.     

Hierarchical neutrinos and supersymmetric inflation

A moderate extension of MSSM based on a left-right symmetric gauge group, within which hybrid inflation is `naturally' realized, is discussed. The μ problem is solved via a Peccei-Quinn symmetry. Light neutrinos acquire hierarchical masses by the seesaw mechanism. They are taken from the small angle MSW resolution of the solar neutrino puzzle and the SuperKamiokande data. The range of parameters consistent with maximal ν<sub>μ</sub>−ν<sub>τ</sub> mixing and the gravitino constraint is determined. The baryon asymmetry of the universe is generated through a primordial leptogenesis. The subrange of parameters, where the baryogenesis constraint is also met, is specified. The required values of parameters are more or less `natural'.     

Fedosov Deformation Quantization as a BRST Theory

The relationship is established between the Fedosov deformation quantization of a general symplectic manifold and the BFV-BRST quantization of constrained dynamical systems. The original symplectic manifold ℳ is presented as a second class constrained surface in the fibre bundle ?^* _ρℳ which is a certain modification of a usual cotangent bundle equipped with a natural symplectic structure. The second class system is converted into the first class one by continuation of the constraints into the extended manifold, being a direct sum of ?^* _ρℳ and the tangent bundle Tℳ. This extended manifold is equipped with a nontrivial Poisson bracket which naturally involves two basic ingredients of Fedosov geometry: the symplectic structure and the symplectic connection. The constructed first class constrained theory, being equivalent to the original symplectic manifold, is quantized through the BFV-BRST procedure. The existence theorem is proven for the quantum BRST charge and the quantum BRST invariant observables. The adjoint action of the quantum BRST charge is identified with the Abelian Fedosov connection while any observable, being proven to be a unique BRST invariant continuation for the values defined in the original symplectic manifold, is identified with the Fedosov flat section of the Weyl bundle. The Fedosov fibrewise star multiplication is thus recognized as a conventional product of the quantum BRST invariant observables. Received: 28 April 2000 / Accepted: 6 December 2000     

Co-dopant affect on the structural,electrical and magnetic properties of zirconium and copper co-substituted Ni0.75Zn0.25Fe2O4 spinel ferrites synthesized by sol-gel method

The zirconium and copper co-substituted Ni_0.75Zn_0.25Zr_xCu_xFe_2-2xO₄ (where x?=?0.05, 0.1, 0.15, 0.2) ferrites have been prepared by sol-gel auto-combustion method. The XRD patterns provide the evidence of single phase cubic spinel structure. The theoretical and experimental lattice parameters have resemblance with increase dopant concentration. The sintered density and porosity show the opposite trend with dopant concentration. The FT-IR spectrum of prepared samples reveal cubic spinel with $Fd\overline{3}m$($O_h^7$) space group. The wave numbers of tetrahedral and octahedral sites show agnate trend. The dielectric constant and loss factors decreased with increasing dopant concentration. The saturation magnetization and net magnetic moment have the identical trend with increasing dopant concentration. The coercive field is decreased with increasing dopant concentration. The Y–K angles are increased with increasing dopant concentration. The Q-factor in prepared samples, exhibit narrower frequency bands with increasing frequency.     

Linear amplifier via the displaced Fock states superposition

The linear amplifier with the superposition of displaced Fock states (DFS’s) as an input field is discussed. The s-parameterized characteristic function (CF) of linear amplifier for the superposition of two DFS’s is considered. Several quantum statistical expectation values for the output of linear amplifier are evaluated once the time dependent CF has been computed. The Glauber secondorder coherence function is calculated. The squeezing properties of the output field are studied. The s-ordered quasiprobability distribution function (QDF) for the output of linear amplifier driven by DFS’s superposition is investigated. The phase properties of the superposition of DFS’s are studied. The s-parameterized phase distribution, obtained by integrating the s-parameterized QDF over radial variable is illustrated.     

Carbon diffusion between the volume and surface of (100) molybdenum

The diffusion of carbon atoms between the volume and the surface of (100) molybdenum is directly studied at temperatures between 1400 and 2000 K (i.e., at process temperatures) for the first time. The balance of carbon atoms in the system is determined. The difference in the activation energies of carbon dissolution and precipitation, ΔE=E s 1-E1s, is found for the case when the diffusion fluxes of dissolved and precipitated carbon atoms are in equilibrium. This difference defines the enrichment of the surface by carbon relative to the bulk. The experimentally found activation energy of carbon dissolution is Es1=3.9 eV. The activation energy of carbon precipitation is estimated at E 1 s=1.9 eV. The latter value is close to the energy of bulk diffusion of carbon in molybdenum.     

Relativistic study of the reaction pp → dπ: Formalism and comparison with experiment at Tp = 578 MeV

A detailed relativistic calculation of pp → πd is presented. The leading graph is the exchange of a nucleon and a pion. The πN amplitudes, including off-shell information, are input, together with relativistic dpn and πNN vertex functions. The dominant nucleon spectator term is calculated without uncontrolled approximations, and the relativistic pion antiparticle contribution is evaluated. The single nucleon exchange diagram is added. Higher order rescattering is treated by initial and final state distortion factors. All amplitudes and spin observables are calculated and a detailed comparison with the measured data at 578 MeV is made. The remaining observed discrepancies are traced to the pp spin-triplet waves.