Does the eigenratio λ₂/λ_N represent the synchronizability of a complex network?

In the study of complex networks,it is commonly believed that the eigenratio λ2/λ N of the Laplacian matrix of a network represents the network synchronizability,especially for symmetric networks.This paper gives two counterexamples to show that this is not true for the case where the network has a disconnected synchronized region.Consequently,a simple answer is presented to the question of when the eigenratio λ2/λ N does represent the network synchronizability.     

Does the eigenratio synchronizability of λ2/λN represent the a complex network？

In the study of complex networks, it is commonly believed that the eigenratio λ2/λN of the Laplacian matrix of a network represents the network synchronizability, especially for symmetric networks. This paper gives two counterexamples to show that this is not true for the case where the network has a disconnected synchronized region. Consequently, a simple answer is presented to the question of when the eigenratio λ2/λN does represent the network synchronizability.     

Disturbance rejection and H∞ pinning control of linear complex dynamical networks

This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances.A dynamical network is said to be robust to disturbance,if the H ∞ norm of its transfer function matrix from the disturbance to the performance variable is satisfactorily small.It is shown that the disturbance rejection problem of a dynamical network can be solved by analysing the H ∞ control problem of a set of independent systems whose dimensions are equal to that of a single node.A counter-intuitive result is that the disturbance rejection level of the whole network with a diffusive coupling will never be better than that of an isolated node.To improve this,local feedback injections are applied to a small fraction of the nodes in the network.Some criteria for possible performance improvement are derived in terms of linear matrix inequalities.It is further demonstrated via a simulation example that one can indeed improve the disturbance rejection level of the network by pinning the nodes with higher degrees than pinning those with lower degrees.     

Bifurcations of the normal modes of the Ne?Br2 complex

We study the classical dynamics of the rare gas-dihalogen Ne?Br₂ complex in its ground electronic state. By considering the dihalogen bond frozen at its equilibrium distance, the system has two degrees of freedom and its potential energy surface presents linear and T-shape isomers. We find the nonlinear normal modes of both isomers that determine the phase space structure of the system. By means of surfaces of section and applying the numerical continuation of families of periodic orbits, we detect and identify the different bifurcations suffered by the normal modes as a function of the system energy. Finally, using the Orthogonal Fast Lyapunov Indicator (OFLI), we study the evolution of the fraction of the phase space volume occupied by regular motions.     

High-Resolution FTIR Spectra of CD2Cl2: Analysis of the ν3/ν7/ν9 Triad

The infrared spectra of isotopically pure CD₂³⁵Cl₂ have been recorded at a resolution of 0.0026 cm⁻¹ (FWHM) in the range 600-1160 cm⁻¹ with a Bruker IFS 120 HR Fourier transform interferometer. The absorption between 670 and 750 cm⁻¹ is due to three fundamentals, ν₃ (weak), ν₇ (very weak), and ν₉ (strong). A satisfactory analysis of the observed spectra has been obtained by including a c-Coriolis coupling between ν₃ and ν₉ and a b-Coriolis term between ν₇ and ν₉. Although no transitions could be observed for the very weak ν₇ band, its band origin could be estimated from the Coriolis interaction with ν₉. From the analysis of about 4200 assigned transitions of the ν₃ and ν₉ bands, excited state constants have been determined up to sextic terms. The Coriolis parameters obtained are compared to those calculated from a harmonic force field.     

Analysis of ν2, ν4 Infrared Hot Bands of SO3: Resolution of the Puzzle of the ν1 CARS Spectrum

Further analysis of the high-resolution (0.0015 cm⁻¹) infrared spectrum of ³²S¹⁶O₃ has led to the assignment of more than 3100 hot band transitions from the ν₂ and ν₄ levels to the states 2ν₂ (l=0), ν₂+ν₄ (l=±1), and 2ν₄ (l=0,±2). These levels are strongly coupled via Fermi resonance and indirect Coriolis interactions to the ν₁ levels, which are IR-inaccessible from the ground state. The unraveling of these interactions has allowed the solution of the unusual and complicated structure of the ν₁ CARS spectrum. This has been accomplished by locating over 400 hot-band transitions to levels that contain at least 10% ν₁ character. The complex CARS spectrum results from a large number of avoided energy-level crossings between these states. Accurate rovibrational constants are deduced for all the mixed states for the first time, leading to deperturbed values of 1064.924(11), 0.000 840 93(64), and 0.000 418 19(58) cm⁻¹ for ν₁, α₁^B, and α₁^C, respectively. The uncertainties in the last digits are shown in parentheses and represent two standard deviations. In addition, new values for some of the anharmonicity constants have been obtained. Highly accurate values for the equilibrium rotational constants B_e and C_e are deduced, yielding independent, nearly identical values for the SO r_e bond length of 141.734 03(13) and 141.732 54(18) pm, respectively.     

Observation of simultaneous ν1(SF6) + ν3(NF3) and ν2(SF6) + ν3(NF3) transitions enhanced by the resonance dipole-dipole interaction with the ν1 + ν3 and ν2 + ν3 states of the SF6 molecule

IR spectra of the solution of SF₆ molecules in liquid NF₃ at 84 K have been recorded. In a solvent transmission window of 1500–1750 cm⁻¹, two wide absorption bands with pronounced peaks in the high-frequency part are observed. The profile of these bands is explained by the influence of the resonance dipole-dipole (RDD) interaction of the states of the simultaneous transition ν₁(SF₆) + ν₃(NF₃) and ν₂(SF₆) + ν₃(NF₃) with the states (ν₁ + ν₃) and (ν₂ + ν₃) of the SF₆ molecules, respectively. The use of three isotopic modifications ³²SF₆, ³³SF₆, and ³⁴SF₆ has allowed us to vary the resonance detuning and thus to change the strength of the RDD interaction. With the liquid near the melting point being represented as a close-packed cubic crystal, the profile was calculated and its spectral characteristics were determined. The frequencies of the main peaks coincide with the experimental values accurate to the error.     

Robust H_∞ observer-based control for synchronization of a class of complex dynamical networks

This paper is concerned with the robust H∞ synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each node and to improve the H∞ performance related to the synchronization error and observation error despite the external disturbance. Based on the Lyapunov stability theory, a synchronization criterion is obtained under which the controlled network can be robustly stabilized onto a desired state with a guaranteed H∞ performance. The controller and the observer gains can be given by the feasible solutions of a set of linear matrix inequalities (LMIs). The effectiveness of the proposed control scheme is demonstrated by a numerical example through simulation.     

On the Study of Resonance Interactions and Splittings in the PH3 Molecule: ν1, ν3, ν2+ν4, and 2ν4 Bands

The high-resolution (0.005 cm⁻¹) Fourier transform infrared spectrum of PH₃ is recorded and analyzed in the region of the fundamental stretching bands, ν₁ and ν₃. The ν₂+ν₄ and 2ν₄ bands are taken into account also. Experimental transitions are assigned to the ν₁, ν₃, ν₂+ν₄, and 2ν₄ bands with the maximum value of quantum number J equal to 15, 15, 13, and 15, respectively. a₁-a₂ splittings are observed and described up to the value of quantum number K equal to 10. The analysis of a₁/a₂ splittings is fulfilled with a Hamiltonian model which takes into account numerous resonance interactions among all the upper vibrational states.     

Short pulse Z -scan investigations of optical nonlinearities of a novel organometallic complex: [(C2H5)4N]2[Cu(dmit)2] at 532 and 1064?nm

A novel dmit organometallic complex: [(C₂H₅)₄N]₂[Cu(dmit)₂] (dmit^2-=1,3-dithiole-2-thione-4,5-dithiolate), abbreviated as EtCu, was synthesized. Afterwards its optical nonlinearities in acetone solution at 532 nm and 1064 nm were studied by the Z-scan technique with laser pulses of picosecond duration. The two-photon absorption at 1064 nm and the saturable absorption at 532 nm were observed. The Z-scan curves also revealed that EtCu sample solutions exhibited self-defocusing effects at both wavelengths. The origins were analyzed for the differences between the results. All the outcomes suggest that this material is potential for nonlinear optical device applications. PACS 42.65.An; 42.65.Hw; 42.65.Jx; 81.20.Ka; 78.30.Jw     

Temperature Variations of the Interaction Induced Absorption of CO2 in the ν1, 2ν2 Region: FTIR Measurements and Dimer Contribution

The temperature variations in collision-induced absorption (CIA) spectra of carbon dioxide in the region of the Fermi doublet are examined. New FTIR CIA spectra are recorded in the temperature range T=206-296 K. The spectra were subject to decomposition in order to separate true dimer contributions to the CIA profile from the base absorption caused by unbound pairs. The use of statistical physics theory allowed for quite nice reproduction of the observed temperature variations of the normalized dimer intensity.     

The approximation method for calculation of the exponents of the gluon distribution, λ g , and the structure function, λ S ,at low x

We present a set of formulas using the solution of the QCD Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation to extract of the exponents of the gluon distribution, λ _g , and structure function, λ _S , from the Regge-like behavior at low x. The exponents are found to be independent of x and to increase linearly with lnQ ² and are compared with the most data from the H1 Collaboration. We also calculated the structure function F ₂(x,Q ²) and the gluon distribution G(x,Q ²) at low x assuming the Regge-like behavior of the gluon distribution function at this limit and compared them with an NLO-QCD fit to theH1 data, two-Pomeron fit, multipole Pomeron exchange fit, and MRST (A.D. Martin, R.G. Roberts, W.J. Stirling, and R.S. Thorne), DL (A. Donnachie and P.V. Landshoff), and NLO GRV (M. Glük, E. Reya, and A. Vogt) fit results. The text was submitted by the authors in English.     

N2 and O2 pressure broadening and pressure shift in the 4ν2 band of OCS

To measure accurately OCS concentrations in planetary atmospheres, it is important to know precisely nitrogen and oxygen pressure broadening and pressure-induced shift coefficients for the lines used in the retrievals. We present in this study the corresponding coefficients for lines of the P and R branches of the 4ν₂ band of the primary isotopologue of carbonyl sulfide (¹⁶O¹²C³²S).For this purpose, infrared absorption spectra of a natural carbonyl sulfide (OCS) gas sample were recorded at an unapodized resolution of 0.004 cm⁻¹, at room temperature for different pressures of N₂ and O₂, using a Bruker IFS125HR spectrometer at the LISA Laboratory in France. The line parameters were derived using the multispectrum fitting method applied to the measured shapes of the lines, including the interference effects caused by the line overlaps.The results are compared with earlier measurements and with values calculated using a semi-classical model based upon the Robert and Bonamy formalism that reproduces rather well the experimental m (m=−J for P(J) lines and m=J+1 for R(J) lines) quantum number dependence of the N₂ and O₂ broadening coefficients. On the other hand most of the lines studied here have positive shift coefficients, which do not show any systematic dependence on m. However, in previous studies of the ν₃, 2ν₃ and ν₂ bands, these coefficients were negative for all lines.     

Profile of the refractive index distribution over the depth of (HfO2)x(Al2O3)1 ? x films

Capabilities of the method of laser null ellipsometry for the study of optical parameters of thin films of multicomponent alloys are demonstrated. Films of alloys (HfO₂) _x (Al₂O₃)_{1 − x} on single-crystal silicon are obtained by the chemical vapor deposition with the use of the following volatile compounds: hafnium dipivaloylmethanate (IV) and aluminum acetylacetonate (III). The selection of initial sets for their optical parameters is justified. The selected model is shown to correspond to experimental data. In films deposited from the mixture of precursors, the refractive index increases from a substrate to a film surface. Due to the separation of sources, films described by a single-layer model were deposited. This fact is indicative of the homogeneous distribution of components over the film thickness.     

High-Resolution Fourier-Transform Intracavity Laser Absorption Spectroscopy of D2O in the Region of the 4ν1+ν3 Band

The high-resolution absorption spectrum of the D₂O molecule was recorded with the Fourier-transform intracavity laser absorption spectrometer in the region 12 570-12 820 cm⁻¹ where the band 4ν₁+ν₃ is located. Transitions belonging to the 4ν₁+ν₃ band, and the bands 3ν₁+2ν₃ and 3ν₁+2ν₂+ν₃, of which the up states are strongly interacted with that of the 4ν₁+ν₃, were assigned in the recorded spectrum. Up state energy levels were fitted to derive effective spectroscopic parameters, which reproduce majority of the assigned transitions within the experimental accuracy.     

A High-Resolution FT-IR Study of the Fundamental Bands ν6, ν10, and ν11 of trans-Glyoxal

The high-resolution Fourier transform infrared spectrum of trans-glyoxal in the gas phase has been recorded in the spectral regions 700-900 cm⁻¹, 1200-1400 cm⁻¹, and 1600-1800 cm⁻¹ with a resolution ranging from 0.0020 to 0.0025 cm⁻¹. The spectrum displays extensive rotational structures which are assigned to the three fundamental bands ν₆ (A_u, 801.5 cm⁻¹), ν₁₀ (B_u, 1732.1 cm⁻¹), and ν₁₁ (B_u, 1312.5 cm⁻¹). A total of ca. 5000 absorption lines have been assigned to these three bands. A simultaneous ground state combination difference analysis of all three bands yields improved ground state spectroscopic constants for trans-glyoxal. Furthermore, a number of spectroscopic constants for the ν₆ and ν₁₁ levels have been determined for the first time.     

Modification of the optical spectra of mixed K2CoxNi1–x(SO4)2?6H2O crystals

We propose a new method for obtaining K₂Co _x Ni_1–x (SO₄)₂⋅6H₂O (x = 0, 0.4, 0.8, 1) crystals, involving the use of the chlorides (CoCl₂⋅6H₂O and NiCl₂⋅6H₂O) in an aqueous solution instead of the widely used sulfates. We have studied the transmission spectra of the grown single crystals in the range λ = 200–900 nm and the IR reflectance spectra in the 2.5–20 μm region. We have observed a change in the position and intensity of the absorption bands as a function of the composition of the crystals. Based on the Tanabe–Sugano diagrams, we determined the crystal field splitting (D_q) and its dependence on the nickel concentration. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 1, pp. 126–130, January–February, 2009.     

The role of vacancy,impurity,impurity-vacancy complex in the kinetics of LiNH2 complex hydrides:a first-principles study

This paper studies first-principles plane-wave pseudopotential based on density functional theory of hydrogen vacancy,metal impurity,impurity-vacancy complex in LiNH 2,a promising material for hydrogen storage.It finds easy formation of H vacancy in the form of impurity-vacancy complex,and the rate-limiting step to the H diffusion.Based on the analysis of the density of states,it finds that the improvement of the dehydrogenating kinetics of LiNH 2 by Ti catalysts and Mg substitution is due to the weak bonding of N-H and the new system metal-like,which makes H atom diffuse easily.The mulliken overlap population analysis shows that H vacancy leads to the H local diffusion,whereas impurity-vacancy complexes result from H nonlocal diffusion,which plays a dominant role in the process of dehydrogenation reaction of LiNH 2.     

First Gas Phase Infrared Spectroscopy of F2BOH: High-Resolution Study of the ν8 and ν9 Bands

For the first time the infrared spectrum of F₂BOH in the gas phase has been observed. After optimizing the conditions for the synthesis we have been able to obtain high-resolution (2.4-3.3×10⁻³ cm⁻¹) infrared spectra in the ν₈, ν₉, and ν₄ regions with both natural and ¹¹B monoisotopic material. Analyses of the ν₈ (BF₂ out-of-plane bending) and ν₉ (OH torsion) fundamental bands located at 684.160 and 522.870 cm⁻¹, respectively, for F₂¹¹BOH are presented here. Existing J≤10 microwave transitions were combined with novel ground state combination differences with J≤55 formed from A-type (ν₄) and C-type (ν₈, ν₉) bands to yield substantially improved and extended ground state parameters. Using a standard Watson-type Hamiltonian, 8¹ and 9¹ upper state parameters were obtained by fitting about 2000 lines each with σ(fit) ca. 3.5×10⁻⁴ cm⁻¹. The 8¹ and 9¹ states both appear to be unperturbed, as indicated by the agreement of the ground and excited state centrifugal distortion constants.     

Assignment of the 15NH3 ν2(2a->2s) Rotational MIR Laser Transitions Pumped by a Tunable CO2 Laser

The assignment of the ¹⁵NH₃ MIR rotational laser lines previously observed (T. Tillert, et at. Int. J. of IR&MMW 17,1011-21(1996)) inside the 2₂ vibrational level is reported. The most part of the reported emissions of this isotopic species is due to the off resonance two photon pumping (Oa->1s->2a) with intermediate detunings as large as 800GHz