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Energy spectra for decaying 2D turbulence in a bounded domain   总被引:1,自引:0,他引:1  
We use results derived in the framework of the replica approach to study the liquid-glass thermodynamic transition. The main results are derived without using replicas and applied to the study of the Lennard-Jones binary mixture introduced by Kob and Andersen. We find that there is a phase transition due to the entropy crisis. We compute both analytically and numerically the value of the phase transition point T(K) and the specific heat in the low temperature phase.  相似文献   
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The synthesis and characterization of three dinuclear copper(II) complexes and one mixed-valence tetranuclear cluster with the asymmetric imidazole-containing ligand bis(1,1'-imidazole-2-yl)(4-imidazole-4(5)-yl)-2-azabutane (biib) are described. X-ray crystallographic parameters for the copper complexes are as follows. [Cu(2)(biib)(2)(BF(4))(2)](BF(4))(2)(H(2)O)(4): triclinic, space group P&onemacr;, a = 10.178(1) ?, b = 9.4881(9) ?, c = 11.037(1) ?, alpha = 95.130(10) degrees, beta = 112.20(1) degrees, gamma = 92.142(9) degrees, and Z = 1. [Cu(2)(biib)(2)(NO(3))(2)](NO(3))(2)(H(2)O)(4): monoclinic, space group &Pmacr;2(1)/n, a = 9.207(6) ?, b = 17.0516(6) ?, c = 12.6107(7) ?, beta = 109.82(1) degrees, and Z = 2. [Cu(2)(biib)(2)(CuBr(3))(2)]: monoclinic, space group P2(1)/c, a = 11.583(2) ?, b = 11.864(2) ?, c = 16.070(2) ?, beta = 112.459(12) degrees, and Z = 2. The two Cu(II) ions in all four complexes are coordinated in a square-pyramidal geometry by three imidazole nitrogens and one amine nitrogen donor in the equatorial plane, and each copper ion is weakly coordinated at the axial position by respectively a tetrafluoroborate, a perchlorate, a nitrate, or a tribromocuprate(I) anion. By comparison of the structural data of the four complexes a relationship has been established between the donor strength of the anion and some structural features, like the Cu(II)-Cu(II) distance, of the dinuclear Cu(II)-Cu(II) unit in the four complexes. Single-crystal EPR spectra of [Cu(2)(biib)(2)(BF(4))(2)](BF(4))(2)(H(2)O)(4) were recorded at room temperature at X-band frequencies. The triplet spectra have been fit with nonparallel g and D tensors, whose principle values are as follows: g(xx)() = 2.022(8), g(yy)() = 2.060(7), g(zz)() = 2.211(8), D(x)()(')(x)()(') = -0.0182(9) cm(-)(1), D(y)()(')(y)()(') = -0.081(6) cm(-)(1), D(z)()(')(z)()(') = 0.0264(7) cm(-)(1). The compounds were further characterized and studied by ligand field and by frozen-solution and polycrystalline powder EPR spectroscopy. EPR spectra recorded at 77 K of frozen solutions of the perchlorate complex show that upon dilution in methanol the dinuclear complex reacts to form a mononuclear species.  相似文献   
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