A method for nonlinear modal analysis and synthesis: Application to harmonically forced and self-excited mechanical systems

The recently developed generalized Fourier–Galerkin method is complemented by a numerical continuation with respect to the kinetic energy, which extends the framework to the investigation of modal interactions resulting in folds of the nonlinear modes. In order to enhance the practicability regarding the investigation of complex large-scale systems, it is proposed to provide analytical gradients and exploit sparsity of the nonlinear part of the governing algebraic equations.     

Advanced computational method for studying molecular vibrations and spectra for symmetrical systems with many degrees of freedom,and its application to fullerene

A computational method for studying molecular vibrations and spectra for symmetrical systems with many degrees of freedom was developed. The algorithm allows overcoming difficulties on the automation of calculus related to the symmetry determination of such oscillations in complex systems with many degrees of freedom. One can find symmetrized displacements and, consequently, obtain and classify normal oscillations and their frequencies. The problem is therefore reduced to the determination of eigenvectors by common numerical methods, and the algorithm simplifies the procedure of symmetry determination for normal oscillations. The proposed method was applied to studying molecular vibrations and spectra of the fullerene molecule C₆₀, and the comparison of theoretical results with experimental data is drawn. The computational method can be further extended to other problems of group theory in physics with applications in clusters and nanostructured materials.     

A new mechanism for the anomalous hall coefficient with application to liquid metals

The effect of spin-orbit coupling of conduction electrons on the Hall coefficient of liquid metals is studied and a new mechanism for the anomalous Hall coefficient is suggested. S.O. coupling causes asymmetric scattering and a current, perpendicular to the magnetic field and to the electric field, is set up. This leads to an additional Hall coefficient , as was first calculated by Luttinger. But S.O. coupling also causes a dipole to appear near each ion, leading to an electrical polarization and an additional Hall coefficient,R _so.R _so is calculated for liquid normal metals and transition metals to first order in S.O. coupling. In normal metals,R _so and are proportional to the Pauli susceptibility. Both are positive for electron-like charge carriers. S.O. coupling leads to a maximum deviation from nearly free electron value in the Hall coefficient of a heavy, four or five-valent liquid metal with short mean free path. In transition metals, different expressions are obtained forR _so depending whether localized moments are present (magnetic model) or not (non-magnetic model). The sign ofR _so is determined by the value of thed-phase shift alone.R _so is proportional to the susceptibility ofd-electrons and can be large, leading to a positive Hall coefficient in the liquid transition metal.     

Asymptotic degeneracy of the transfer matrix spectrum for systems with interfaces: Relation to surface stiffness and step free energy

Two- and three-dimensional Ising-type systems are considered in the finite-cross-section cylindrical geometry. An interface is forced along the cylinder (strip in 2d) by the antiperiodic or +– boundary conditions. Detailed predictions are presented for the largest asymptotically degenerate set of the transfer matrix eigenvalues. For rough interfaces, i.e., for 0<T<T _c in 2d,T _R<T<T _c in 3d, the eigenvalues are split algebraically, and the spectral gaps are governed by thesurface stiffness coefficient. For rigid interfaces, i.e., 0<T<T _R in 3d, the eigenvalues are split exponentially, with the gaps determined by thestep free energy.     

一维变系数耗散系统Lagrange函数和Hamilton函数的新构造方法

提出构造二阶微分方程的Lagrange函数和Hamilton函数的新路径. 将二阶方程写成一阶方程组并构造出对应的一阶Lagrange函数后,直接从一阶Lagrange函数导出二阶Lagrange函数和Hamilton函数. 利用上述方法得到若干耗散和类耗散系统的一阶和二阶Lagrange函数以及Hamilton函数;讨论了这种方法的优点. 举例说明所得结果的应用. 关键词： 逆问题 耗散系统 Lagrange函数 Hamilton函数     

A finite element method for damped acoustic systems: An application to evaluate the performance of reactive mufflers

The approximate equations governing the forced harmonic motion of a damped acoustic system are set up by using a variational principle. Acoustic finite elements are then used in a computer program to study the transmission loss and insertion loss performance of some expansion chamber mufflers. The manner in which the equations are set up allows a number of input and output nodes, and two-dimensional effects involving the influence of transverse acoustic modes to be taken into account. Although only the simplest of elements and coarse mesh sizes are used the resulting accuracy of the solutions is extremely good; thus the method should be a viable one for studying the performance of more complicated mufflers, having variable cross-sections and internal energy dissipation.     

A model for the enzyme activity in systems with large composition fluctuations. An application to the unusual kinetics of phospholipase A2

A non-equilibrium thermodynamics based model is proposed in order to describe the role of large concentration fluctuations of enzymes, reactants and products in modulating the macroscopic time evolution of chemical kinetics. The encounter probabilities between reactants and enzyme depend on their local concentration. Fluctuations modify the bimolecular encounter probability. Since, in turn, the amplitude of fluctuations depends itself on the instantaneous composition of the reacting mixture, the time-varying chemical composition acts as a positive feedback mechanism for the reactive fluid mixture near the critical temperature for phase separation. The model is applied to rationalize the unusual features of phospholipase kinetics, an enzyme which catalyzes the hydrolisis of membrane forming phospholipids, yielding products which are still soluble in the lipid matrix. A typical feature of the enzyme reaction is the long induction time prior to a ”burst” of activity. This effect is well reproduced by the theory, together with the dependence of the induction time on the exogeneous addition of products or other liposoluble substances, the effects of enzyme and substrate concentration, and the temperature dependence of the enzyme activation. All these properties emerge as a consequence of the coupling between enconter probability and time-varying bilayer heterogeneity. A good qualitative agreement between theoretical results and the available experimental results has been generally found. Received: 25 June 1996 / Revised: 17 April 1997 / Accepted: 26 November 1997     

A uniqueness condition for Gibbs measures,with application to the 2-dimensional Ising antiferromagnet

A uniqueness condition for Gibbs measures is given. This condition is stated in terms of (absence of) a certain type of percolation involving two independent realisations. This result can be applied in certain concrete situations by comparison with ordinary percolation. In this way we prove that the Ising antiferromagnet on a square lattice has a unique Gibbs measure if (4–|h)<1/2ln(P _c /(1–P _c )), whereh denotes the external magnetic field, the inverse temperature, andP _c the critical probability for site percolation on that lattice. SinceP _c is larger than 1/2, this extends a result by Dobrushin, Kolafa and Shlosman (whose proof was computer-assisted).The research which led to this paper started while the author was at Cornell University, partly supported by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University     

A model for the Auger electron spectroscopy of systems exhibiting layer growth,and its application to the deposition of silver on nickel

The dependence of Auger intensities on deposition time for deposits which grow in layer-by-layer fashion is analysed in terms of a simple model. It is shown that it is possible in principle to calibrate the Auger signals as a function of thickness absolutely with no prior assumption of values for sticking coefficients. The extent to which theory and experimental data for the deposition of silver on nickel are in agreement is examined, and values deduced for sticking coefficients and escape depths of Auger electrons in silver. It is also found that silver grows epitaxially on nickel at room temperature, and that silver/nickel bicrystals do not alloy after heat treatment.     

A new boson expansion for the solution of the n-fermion problem with an application to 4He

A new approximation method for the n-fermion problem is developed and tested within the exactly solvable model of Lipkin, Meshkov and Glick. Results are compared with the exact solutions and RPA. Applying the method to the ⁴He nucleus, excitation energies, total binding energy and the ground-state energies of ³He and ⁵He are calculated.     

A new application for an old concept: Constant time (CT)-REDOR for an accurate determination of second moments in multiple spin systems with strong heteronuclear dipolar couplings

In this contribution we present a constant time version of the well known REDOR pulse sequence which enables us to determine the second moments in multiple spin systems with strong dipolar couplings. From the resulting dipolar evolution curves, accurate values for the second moments can be obtained without the need to incorporate the full information about the detailed spin geometry of the multiple spin systems into the simulation protocol.     

A General Method of Solution for the Cluster Variation Method in Ionic Solids,with Application to Diffusionless Transitions in Yttria-Stabilized Zirconia

A new, general method of solution for the cluster variation method using a reduced conjugate gradient approach with a truncated line-search algorithm is presented. The method is generally convergent. Additionally, the truncation of the line-search algorithm may increase the speed of convergence considerably, as the size of the problem is progressively reduced (especially for strongly ordered phases), opening up the possibility of a considerable increase in the size of maximal clusters. The method is successfully demonstrated for a single, eight-atom maximal cluster in the fluorite lattice. Using pairwise defect interaction energies calculated for cubic, yttria-doped zirconia and fixed defect concentrations, a pair of metastable states are found in a composition and temperature range which is experimentally characterized by metastable, diffusionless phase transitions.     

A new torsion-rotation fitting program for molecules with a sixfold barrier: Application to the microwave spectrum of toluene

A new program is described for fitting rotation-torsion energy levels in molecules like toluene, in which the frame (C₆H₅) has C_2v symmetry and the methyl top has C_3v symmetry, i.e., for molecules where the internal rotation barrier is expanded in cos6nα, where α is the internal rotation angle and n = 1,2,…. The program is based on the theoretical framework developed by Sørensen and Pedersen in their application of the Longuet-Higgins permutation-inversion group G₁₂ to the microwave spectrum of CH₃NO₂. It is specifically designed for sixfold barrier molecules, and allows the user to select almost any symmetry-allowed torsion-rotation term for inclusion in the fitting Hamiltonian. This program leads to a very successful fit of transitions in the microwave spectrum of toluene characterized by J ? 30, K_a ? 12, and by the free-rotor quantum number ∣m∣ ? 3. In these fits we included both published and rather extensive unpublished new measurements, for which fits using other torsion-rotation programs have not been very successful. The fit presented here uses 28 parameters to give an overall standard deviation of 7.4 kHz for 372 line frequencies, and results in a much improved value for the sixfold barrier for toluene, V₆ = 13.832068(3) cal mol⁻¹.     

A new graphical representation for a systematic study of the defect structure in ternary oxides,with a specific application to forsterite Mg2SiO4

The defect structure of a ternary oxide such as forsterite that is responsible for departures from the ideal composition Mg₂SiO₄ depends on three thermodynamic parameters under a constant total pressure according to the Gibbs phase rule. These are the temperature T and two activities that may be chosen as the oxygen partial pressure P_o2 and the silica activity a_SiO2 Therefore the precise state of the compound can be described by a point in a 3 dimensional space, the coordinates of which are related to T,p_o2, a_SiO2. In a given region characterized by a majority defect pair, the overall electroneutrality equation simplifies and, provided that interaction between defects remains negligible, the use of mass action laws leads to a simple functional dependence of the defect concentrations on the three thermodynamic parameters. These analytical expressions define a range of existence for every selected majority defect pair, that can be easily depicted in isothermal sections of the 3 dimensional space. It is shown that the boundaries between these domains in Ln p_o2- Ln a_SiO2 plots are straight lines intersecting at points where several majority defects coexist. Such representations permit a logical deduction of the different possible configurations and may be quite useful when analyzing experimental data. Their evolution with temperature is considered and finally the case of quaternary solid solutions is briefly discussed.     

A theory of vibrational frequency shifts revisited: application to dimers of LiH with the inert gases He,Ne, Ar and Kr

The objective of this paper is to contribute towards an understanding of the anomalous blue vibrational shifts that have been observed on forming some hydrogen bonds. It is shown that linear complexes of the LiH molecule with an inert gas atom Rg exhibit red or blue shifts of the LiH vibrational frequency depending upon whether Rg is attached to the Li or the H atom.

The shifts in the frequency of the Li–H vibration on forming the weakly bound linear complexes Li–H…Rg and H–Li…Rg (Rg?=?He, Ne, Ar, Kr) were determined by ab initio computations at the MP2/6-311++G(2d,?2p) level of theory. These frequency shifts were found to be in good agreement with predictions from a model based on perturbation theory and involving first and second derivatives U′ and U′′ of the interaction energy with respect to displacement of the Li–H bond length from its equilibrium value in the isolated molecule. Concentration of the Li–H vibrational motion in the light H atom causes U′ and U′′ to be dominated by repulsion in Li–H…Rg and by attraction in H–Li…Rg, producing blue and red shifts, respectively. The bond length changes on complexation are well predicted by U′.     

A new method for the study of chemical diffusion in oxides with application to cerium oxide CeO2−x

We describe a new experimental technique for the determination of chemical-diffusion coefficients in oxides. This method does not involve any transfer of matter through an interface.Results obtained at 971°C for various deviations for stoichiometry x of CeO_2?x are reported and compared with calculated chemical-diffusion coefficient D? values from other independent transport quantities obtained on the same sample. The reasonable correlation between experimental and calculated D? indicates that the precision of the experimental D? is better than 5%.     

The initial oxidation of molybdenum: V. A model for the nucleation of epitaxial oxide and its application to molybdenum

A new model for the phenomenon of epitaxial oxidation nucleation is presented growth characteristics of the oxide suggest that the prenucleation growth is governed by the oxygen adsorption rate of the oxide/gas boundary. As the oxide grows the calculated rate of dissolution of cations at the oxide/metal interface falls until this becomes rate determining. At this point low work function facet sided pits are etched in the substrate with corresponding bulges in the outer oxide film. These bulges are identified as epitaxial nuclei. Based on this model several parameters relating to oxide growth may be calculated. The agreement between theory and experiment is very good. In particular a lower and upper temperature limit for nucleation are found and the pressure dependence is shown to be quite complicated. The basis of the model can be extended to the chemisorption regime. It is shown that above a surface potential of about 1 V cations migrate rapidly through the oxygen layer. The onset of this rapid migration is identified with molecular oxide production and the start of faceting.     

Processing high-energy proton events: A new approach to searching for primary cosmic ray particles in emulsion chambers,using data from the RUNJOB experiment

Primary single-charged particles were identified in ～50% of the proton events in the Russian-Japanese RUNJOB balloon experiment. In reprocessing the experimental data obtained via long-term exposure of the RUNJOB-3B, 6A, 11A, and 11B emulsion chambers (ECs) using a new approach to searching for primary cosmic-ray particles in groups of proton events with primary particle energy E ₀ > 20 TeV and zenith angle tan(θ) ≤ 5, ～50% of the primary single-charged particles went unidentified, as was the case earlier. In this work, we describe the new approach to searching for and tracking particles in ECs and present the parameters of the processed events (energy, zenith angle, depth of particle penetration into an EC up to interaction).     

Belt-like VO2(M) with a rectangular cross section: A new route to prepare, the phase transition and the optical switching properties

Belt-like VO₂(M) with a rectangular cross section was first synthesized by the irreversible transformation of VO₂(A) at the elevated temperatures under the inert atmosphere to the best of our knowledge. The as-obtained samples were characterized by a combination of techniques including XRD, SEM and TEM. The processes of converting VO₂(A) to VO₂(M) were briefly discussed. The as-obtained VO₂(M) has belt-like morphology with a rectangular cross section with typical lengths up to several tens of micrometers, widths ranging from tens of nanometers to several micrometers, and thicknesses about 60-150 nm. The morphology and size of the VO₂(M) were dependent on that of the precursor VO₂(A). The phase transition properties of VO₂(M) were investigated by DSC, indicating that it exhibited a strong phase transition at 67.9 °C in the heating cycle and 61.1 °C in the cooling cycle. Furthermore, the optical switching property of VO₂(M) was studied by the variable-temperature infrared spectra, and it was found that the as-obtained VO₂(M) could be used as the optical switch.