Normal Modes

GaAs, GaAs:Si and GaAs:C films were deposited on GaAs substrates by Metal Organic Chemical Vapor Deposition( MOCVD) technique. The vibrational study of the heterostructures was performed by mu-Raman technique, and measurements were made at different temperatures using a sample holder with a micro-heater included within it. The spectral information was used to determine the strain caused in GaAs heterostructure because

Temperature dependent normal modes and lattice thermal expansion of the Sr 2 B'UO 6 (B' = Ni, Co) double perovskites were investigated by Raman/infrared spectroscopies and synchrotron Xray diffraction, respectively. Monoclinic crystal structures with space group P2 1 /n were confirmed for both compounds, with no clear structural phase transition between 10 and 400 K. As predicted for this structure, the first-order Raman and infrared spectra show a plethora of active modes. In addition, the Raman spectra reveal an enhancement of the integrated area of an oxygen stretching mode, which is also observed in higher-order Raman modes, and an anomalous softening of ~1 cm -1 upon cooling below T* ~ 300 K. In contrast, the infrared spectra show conventional temperature dependence. The band profile phonon anomalies are possibly related to an unspecified electronic property of Sr 2 B'UO 6 (B' = Ni, Co).

We put forward schemes to prepare photons in multi-dimensional vector states of orbital angular momentum. We show realizable light distributions that yield prescribed states with finite or infinite normal modes. In particular, we show that suitable light vortex-pancakes allow the add-drop of specific vector projections. We suggest that such photons might allow the generation of engineered quNits in multi-dimensional quantum information systems.

A linear stability analysis was carried out for a dilute suspension of rigid spherical particles in cylindrical Couette flow. The perturbation equations for both the continuous fluid phase and the discontinuous particle phase were decomposed into normal modes resulting in an eigenvalue problem that was solved numerically. At a given radius ratio, the theoretical critical Taylor number at which Taylor vortices first appear decreases as the particle concentration increases. Increasing the ratio of particle density to fluid density above one decreases the stability. However, using an effective Taylor number based on the suspension density and viscosity largely accounts for this effect. The axial wave number is the same for a suspension as it is for a pure fluid. Experiments using neutrally buoyant particles in a Taylor-Couette apparatus show that the flow is more stable as the particle concentration increases. The reason that the theory does not fully capture the physics of the flow should be addressed in future research.

A set of vibrational circular dichroism (VCD) spectra in the CH-stretching fundamental region for about twenty compounds belonging to the class of essential oils was empirically analyzed by the use of a sort of vibrational exciton mechanism, involving three centers. Through a general formula applicable to many coupled dipole oscillators, the rotational strengths of the previously identified vibrational excitons are evaluated. The results are then critically reviewed by the use of recent ab initio methodology, as applied to selected molecules of the original set. Further insight is gained by model calculations adding up the contribution of the coupling between electric dipole moments associated with normal mode behavior and that of the polarizability from polarizable groups. The former part is responsible for the excitonic behavior of the VCD spectra. For the same selected molecules we have also investigated whether some excitonic behavior is taking place in the second overtone region, and have concluded that this is not the case.

Determination of the lattice dynamics of Sn at high pressure has represented a major experimental challenge and eluded previous attempts. Here we report the first successful measurement of the phonon density of states of Sn at high pressure to 64 GPa using nuclear resonant inelastic x-ray scattering. We also present density functional theory calculations that are in excellent agreement with the measured data. The results of this combined experimental and theoretical study establish reliable phonon density of states of Sn at high pressure. It makes possible an accurate description of its thermodynamic properties that are of great importance and interest in high pressure research.

Raman spectra of neat thiophene (THP) and its highly diluted (<20% THP) solution with two polar solvents, dimethyl sulfoxide (DMSO) and methanol were recorded in order to explore the influence of molecular interaction on spectral features corresponding to some selected vibrational bands of THP in the range, 400-1600 cm À1 . Only few vibrational bands of THP show a slight change in their peak position in going from neat THP to (THP + DMSO/methanol) solution. Ab initio and density functional calculations were performed employing HF, MP2 and B3LYP methods and high level basis set, 6-311++G(d,p) to obtain the ground state geometry of neat THP and its hydrogen bonded complexes with DMSO and methanol in gas phase. In order to account for the solvent effect on vibrational features and changes in optimized structural parameters of THP, polarizable continuum model (PCM) calculations at HF, MP2 and B3LYP level were performed to simulate the vibrational spectra of THP in both the solvents, DMSO and methanol. The calculated wavenumbers of neat thiophene were compared with the reported experimental data on wavenumbers of 21 normal modes of thiophene and for a detailed vibrational assignment of the various normal modes, potential energy distribution (PED) calculation was also performed. No significant variation was found in the Raman spectra as a function of medium polarity. However, the ground state energy of THP decreases in going from gas phase to solution in both the cases. The dipole-dipole interaction between THP and the solvent molecules, DMSO and methanol was also calculated at different levels of theory.

Low-frequency acoustic data acquired in the central East China Sea basin at two locations are analyzed for the purpose of making inferences on seabed acoustics. Previous geophysical studies indicate that the first sediment layer is composed of a fine to medium sand. The current analysis employs octave-averaged transmission loss (TL) versus range data and pressure time series generated from explosive sources. The TL and time series data were collected in locations separated by about 65 km during the same month of the year. Both locations are near the same longitude, with water depths of 100-120 m. A linear frequency dependence of the attenuation in the 25-800 Hz band, with or without sound speed dispersion, leads to a geoacoustic solution using the TL data consistent with a soft clay, and thus inconsistent with the existing geophysical data. However, seabed representations that allow for a nonlinear frequency dependence of the attenuation, such as a Kramers-Kronig dispersion relationship, a simplified six-parameter Biot description, and an empirical frequency power law of the attenuation, all give similar values of the attenuation as a function of frequency and sediment sound speeds that are consistent with the previous geophysical studies in the area. Geoacoustic solutions obtained with the TL inversions produce reasonably good fits to the measured time series data. Inversions of the time series indicate that the sound speed at the top of the sediment is lower as compared to the values estimated from the location where the TL data were acquired. While the data have significant limitations as to the information they contain on the properties of the seabed, the analysis aids in quantifying the sensitivity of geoacoustic inversion of acoustic data in shallow water littoral regions to assumptions about the frequency dependence of attenuation and sound speed.

The well-known Regge-Wheeler equation describes the axial perturbations of Schwarzschild metric in the linear approximation. From a mathematical point of view it presents a particular case of the confluent Heun equation and can be solved exactly, due to recent mathematical developments. We present the basic properties of its general solution. A novel analytical approach and numerical techniques for study the boundary problems which correspond to quasi-normal modes of black holes and other simple models of compact objects are developed.

Conformational stability Xenon and krypton solutions Infrared and Raman spectra r 0 Structural parameters Ab initio calculations Ethylisocyanate a b s t r a c t Variable temperature (À55 to À155°C) studies of the infrared spectra (400-3500 cm À1 ) of ethylisocyanate, CH 3 CH 2 NCO, dissolved in liquid xenon and krypton have been recorded. Additionally the infrared spectra of the gas and solid have been re-investigated. These spectroscopic data indicate two conformers in the fluid states which are the cis and trans forms with a large proportion of molecules in the gas phase at ambient temperature in the excited states of the NCO torsional mode which has a very low barrier to conformational interchange. Variable temperature (À110 to À155°C) studies of krypton solutions were carried out and by using two conformer pairs, an enthalpy difference of 100 ± 4 cm À1 (1.20 ± 0.05 kJ/mol) was obtained with the cis conformer the more stable form. To aid in the analyses of the vibrational and rotational spectra, ab initio calculations have been carried out by the perturbation method to the second order (MP2) with full electron correlation using a variety of basis sets up to 6-311+G(2df,2pd) and cc-PVQZ. With the basis sets 6-311+G(2d,2p) and larger, the barrier at the cis position ranged from a low value of 11 cm À1 to a high value of 31 cm À1 with a value of 19 cm À1 from the largest basis set of cc-PVQZ. Thus, the gauche well is probably so shallow that it does not contain a bound vibrational state. This results in the cis conformer as the most stable form which is consistent with the experimental rotational and vibrational data. The predicted energy difference from these calculations between the cis conformer and the transitional-state skew form is $100 cm À1 which is consistent with the assigned microwave lines for four excited states of the NCO torsion. Density functional theory calculation by the B3LYP method with many of the same basis sets provided little information. By utilizing the previously reported microwave rotational constants with the structural parameters predicted by the ab initio MP2(full)/6-311+G(d,p) calculations, adjusted r 0 structural parameters have been obtained for the cis form. The determined heavy atom parameters are: r(C@N) = 1.211(5), r(C@O) = 1.167(5), r(CAN) = 1.448(5), r(CAC) = 1.516(5) Å for the distances and angles of \CCN = 112.6(5), \CNC = 137.5(5), \NCO = 172.9(5)°. The centrifugal distortion constants, dipole moments, conformational stability, vibrational frequencies, infrared intensities and Raman activities have been predicted from ab initio calculations and compared to experimental quantities when available. These results are compared to the corresponding quantities of some similar molecules.

We present the polarized Raman spectra of LaCrO 3 measured between 5 and 863 K in several exact scattering configurations. All Raman lines below 600 cm −1 are assigned to definite phonon modes of Pnma ͑T Ͻ 528 K͒ or R3c ͑T Ͼ 528 K͒ structures on the basis of their polarization properties, comparison to spectra of isostructural compounds, and comparison to mode frequencies predicted by calculations of lattice dynamics. The broad overlapping high-frequency bands between 600 and 750 cm −1 of A g character, which are sample dependent and vary significantly upon annealing in vacuum or change of excitation photon energy, are assigned to local vibrations of Cr 4+ -related defect species. These results can serve as a ground for further study of microstructure-property relationships in practically important doped rare earth chromates.

An approach combining the method of fundamental solutions (MFS) in conjunction with the normal modes technique (NMT) is proposed to simulate the acoustic wave propagation over the shallow water region. It is assumed that the sound-speed is the isovelocity profile, the free surface is quiescent and the topography of seabed is rugged. The considered model, ranging from smooth to abrupt variation, is descritized into simple rectangular geometry and cosine bell deformation at the bottom in terms of the irregular topography. Mathematical formulations of the eigenfunction expansion, in point of NMT, are implemented clearly to describe the radiation conditions on the open boundaries. Effects of node resolution and small aspect ratios over the computational domain are discussed. Accuracy of the results by the proposed approach is assessed and verified by comparison with analytic solution and the boundary element method (BEM).

Since 1969, seismology has been extendedbeyond the Earth, and seismic sensors have been placed on the surface of other bodies of the solar system. A Lunar seismic network thus operated for the 8 years after 1969, with up to 4 stations, and detected some 1000 Moonquakes per year. A single seismic station was also operated on the Martian surface for 19 months since 1977. Unfortunately, it did not detect any Marsquakes, but produced useful information for future experiments. Remotesensing seismic experiments using Doppler shift observation have also been applied to Jupiter in the last two years and are beginning to return information on the normal modes. Planetary seismology is thus now well developed, and will provide increasing information on the structure and dynamics of the planets and bodies of the solar system. In this paper we review the state of the art in planetary seismology. For the terrestrial planets, we compare the seismic sources, structure and experiments on Earth, Moon and Mars. Such a comparison is useful in evaluating the design of past or future experiments. Results in the seismology of giant planets are also reviewed, stressing the connection between methods and theory.

Three different sites of the Cr 3ϩ ions in the fluoride perovskite KMgF 3 have been identified by absorption, selective optical excitation, and time-resolved emission spectroscopy of the 4 T 2 ↔ 4 A 2 transition. Highpressure measurements showing the crossover from low-crystal field to high-crystal field, allows us to situate the Dq/B values of the different chromium sites clearly below 2.3. The different spin-orbit components associated with the zero-phonon lines of the 4 T 2 ↔ 4 A 2 transition of each type of site are clearly shown on the optical spectra and identified by group-theory analysis. The decay profiles of the 4 T 2 level are exponential and the lifetimes at 15 K are 903, 919, and 473 s for the cubic, quadratic, and trigonal sites, respectively. The trigonal center which presents the lowest energy levels was peculiarly studied. Emission and excitation spectra are compared; their evolution versus temperature is followed and explained by the thermal population of the different spin-orbit sublevels. The phonon sideband of the trigonal site is compared with our previous lattice dynamic studies of the pure compound. The different peaks of the emission broadband are described in terms of phonons of the matrix and normal modes of the ͓CrF 6 ͔ 3Ϫ complex. ͓S0163-1829͑97͒03430-9͔

FT-IR (4000-100 cm −1 ) and FT-Raman (4000-100 cm −1 ) spectra of solid sample of 4-chloro-2-fluoro toluene (4Cl2FT) have been recorded using Bruker IFS 66 V spectrometer. Ab initio-HF (HF/6-311++G (d, p)) and DFT (B3LYP/6-311++G and B3PW91/6-311++G (d, p)) calculations have been performed giving energies, optimized structures, harmonic vibrational frequencies, depolarization ratios, IR intensities, Raman activities. The vibrational frequencies are calculated and scaled values are compared with FT-IR and FT-Raman experimental values. The isotropic HF and DFT analyses showed good agreement with experimental observations. The differences between the observed and scaled wave number values of most of the fundamentals are very small in B3LYP than HF. Comparison of the simulated spectra provides important information about the ability of the computational method (B3LYP) to describe the vibrational modes. The influences of substitutions on the geometry of molecule and its normal modes of vibrations have also been discussed. The changes made by substitutions on the benzene are much responsible for the non-linearity of the molecule. This is an attractive entity for the future studies of non-linear optics.

An improved analytical procedure has been developed that allows for an efficient solution of the finite plate noise transmission problem. Both isotropic and symmetrically laminated composite plates are considered. The plate is modeled with classic thin-plate theory and is assumed to be simply supported on all four sides. The incident acoustic pressure is modeled as a plane wave impinging on the plate at an arbitrary angle. The reradiated pressure is assumed t o be negligible compared with the blocked pressure, and the plate vibrations are calculated by a normal-mode approach. A Green's function integral equation is used to link the plate vibrations to the transmitted far-field sound waves, and transmission loss is calculated from the ratio of incident to transmitted acoustic powers. The result is a versatile research and engineering analysis tool that not only enables the determination of which modes are dominating the noise transmission but also allows for the problem to be broken down into its component parts. This includes determining what the modal behavior is, such as coupling between the incident noise and the plate vibrations, the plate resonance behavior, and the coupling between the plate vibrations and the transmitted noise. The effect of varying the angle of incidence and the far-field directivity can also be determined from the analytical model. The analysis approach was specifically developed to study noise transmission into aircraft, although it should be equally applicable to sound transmission through building walls, floors, and windows.

Zirconia, ZrO 2 , is one of the most important ceramic materials in modern technology. Its versatility is closely related to phase transformations. Although the transformations have been repeatedly investigated by experiments, fundamental aspects of the transformations are still under debate. In the present paper, we have made first principles calculations to study the lattice dynamics of ZrO 2 polymorphs and phase transformation at finite temperatures. Cubic phase shows a soft mode at the X point in the Brillouin zone, which should spontaneously induce cubic-to-tetragonal transformation. In tetragonal and monoclinic ZrO 2 , all vibrational modes have real frequency. Calculations of Helmholtz free energies show that the tetragonal phase becomes more stable than the monoclinic phase above 1350 K, which is in quantitative agreement with experimental results. This confirms that vibrational entropy contributes to destabilize monoclinic ZrO 2 at elevated temperatures.

Assuming the compactification of 4 + K-dimensional space-time implied in Kaluza-Kleintype theories, we consider the case in which the internal manifold is a quotient space, G/H. We develop normal mode expansions on the internal manifold and show that the conventional ...

The use of normal-modes procedures for the study of boundary layers is examined, taking into account aspects of formulation, the parallel-flow assumption, the form of disturbance, and the properties of the disturbance equations. A description is presented of the results of normal-modes calculations. Nonparallel-flow effects are considered along with flat-plate boundary layers in air and water and the effect of surface curvature. An investigation of receptivity is conducted. Receptivity denotes the means by which a particular forced disturbance enters the boundary layer. Attention is given to the prediction of transition and the directions of current and future investigations.

This paper describes several optimization models for the design of a typical wind turbine tower structure. The main tower body is considered to be built from uniform segments where the eective design variables are chosen to be the cross-sectional area, radius of gyration and height of each segment. The nacelle/rotor combination is regarded as a rigid non-rotating mass attached at the top of the tower. Five optimization strategies are developed and tested. The last one concerning reduction of vibration level by direct maximization of the system natural frequencies works very well and has shown excellent results for both tower alone and the combined tower/rotor model. Extensive computer experimentation has shown that global optimality is attainable from the proposed discretized model and a new mathematical concept is given for the exact placement of the system frequencies. The normal mode method is applied to obtain forced response for dierent types of excitations. The optimization problem is formulated as a nonlinear mathematical programming problem solved by the interior penalty function technique. Finally, the model is applied to the design of a 100-kW horizontal axis wind turbine (ERDA-NASA MOD-0). It has succeeded in arriving at the optimum solutions showing signi®cant improvements in the overall system performance as compared with a reference or baseline design. #

The objective of this work has been the study of the laser cleaning technique when applied to wall paintings. In particular, this study has been devoted to understanding how the characteristics of the laser apparatus and its specific use are linked with the nature of the substances to be removed from the painting. A number of paintings were selected with paint layers that were composed of different pigments such as lapis lazuli, lamp black and ochres. They had been applied using the fresco technique or a secco natural resins, on surfaces that had been treated with organic (natural resins, drying oils, caseinate glues, etc.) and inorganic substances (calcium carbonate or oxalate) applied during previous restorations. The analyses carried out were the following: FTIR spectroscopy with and without microscope and the study of thin sections of the surface of the paintings. The apparatus we used was a Nd:YAG laser operating in Q-switch or in normal mode; in Q-switch operation the laser could emit at two different wavelengths: in the infra-red and in the visible (1 064 and 532 nm). The main objective of the work was to determine the optimum working conditions for the substances to be removed, through the establishment of laser parameters such as the pulse modality (Q-switch or N-mode), the wavelength, the repetition rate and the energy density. The effects of the laser radiation on the surfaces of the paintings were checked by measuring temperature, pH, conductivity and spectro-colorimetric tests. © 2000 É ditions scientifiques et médicales Elsevier SAS

John Milton sought in the narrative of Paradise Lost a solution to a theological problem that defied the normal modes of theological analysis: the difficulty of conceiving how an infinite, timeless God could interact with his finite and time-bound creation. In examining the poem’s attempt to bring God into narrative--a form that, because it simulates existence in time, offers itself as a particularly useful way to approach this problem--this essay proposes a new approach to the complaints readers since William Empson have lodged against the poem’s God and reconsiders the relationship between philosophical thought and poetic expression in Milton’s work.

We describe the development, current features, and some directions for future development of the AMBER package of computer programs. This package has evolved from a program that was constructed to do Assisted Model Building and Energy Refinement to a group of programs embodying a number of the powerful tools of modem computational chemistry-molecular dynamics and free energy calculations. consult the Web site: http://www, amber, ucsf. edu/ amber/amber, html.

We present a computer program for calculating rate constants of gas.phase chemical reactions involving one or two reactants with a total of three to ten atoms. The program accepts information about the potential energy surface in the form of either an analytic potential energy function or a sequence of geometries, energies, gradients and second (or higher) derivative matrices at points along the reaction path. In the former case the program itself calculates the reaction path and the sequence of derivative matrices. From this information the program calculates the rate constant for quantized internal degrees of freedom and classical reaction-path motion by variational transition state theory (VTST). The probabilities for tunneling and nonclassical reflection are estimated by semiclassical methods and incorporated by a transmission coefficient, which for thermal reactions is based on the ground state. There are several options for including the effects of anharmonicity in the independent-normal-mode approximation, and the reaction-path curvature may be included in the tunneling calculation by the small-curvature approximation. The article also presents test calculations illustrating the use of new reaction-path interpolation and extrapolation procedures which should be useful in conjunction with VTST calculations based on ab initio gradients and Hessian calculations.

A simple and informative method of solving for the normal modes and the normal mode frequencies of coupled oscillating systems is presented. A dimensionless parameter uniquely determines the normal modes and normal mode frequencies of the oscillating system.

The Raman spectra of epitaxial thin films of La 2 CoMnO 6 on ͑001͒-oriented SrTiO 3 substrates have been measured in several exact scattering configuration between 12 and 890 K. The polarization dependence of the spectra provide clear evidence for ordered P12 1 / n1 structure, differing from its parent Fm3m structure by the presence of rotational distortions. The correlation between the phonon modes in Fm3m, R3, and P12 1 / n1 phases is analyzed and the corresponding types of atomic motions as well as their expected frequency range are determined by comparison to the predictions of lattice dynamical calculations. The ferromagnetic ordering and spin-phonon coupling below T C result in softening of some of the phonon modes. The evolution of the Raman spectra at high temperatures shows no indication for P12 1 / n1-R3 transition up to 800 K.

The normal modes of vibration and their frequencies are calculated for beryl, a mineral whose crystal structure (space group D6h) consists of six-membered silicate rings (Si 6 018) linked by Be 2 " and Al 3 " ions. A valence force potential is used, consisting of central interactions between nearest neighbors and bond-bending interactions centered at the Si 4 " Be 2 , and Al 3 " ions. The force constants are determined by fitting the calculated frequencies to the results of a complete study of the Raman spectra of a large single crystal. The calculated frequencies are in reasonable agreement with experiment, permitting unambiguous assignment of normal modes to the observed spectral lines. In several cases, the resulting interpretation of spectral features differs significantly from those published previously. Considerable mixing of Al and Be motions with those of the ring is found for the Raman-active modes near 750 cm-and above 850 cm' , respectively. The normal modes and frequencies of the hypothetical isolated ring with C 6 h symmetry are determined by neglecting all interactions between the rings and the surrounding Be and Al atoms. This identification of normal modes characteristic of six-membered silicate rings and the effect of the environment on these modes may prove useful in the interpretation of infrared and Raman spectra of amorphous silicates.

The polarized Raman spectra from ab and ac surfaces of single crystal Na x CoO 2 (x≈0.7), parent compound of recently discovered superconductor Na x CoO 2 • yH 2 O, are reported and discussed. The crystals were hexagon platelets of typical size 3×3×0.1 mm. Three of the five (A 1g +E 1g +3E 2g) Raman active phonons were unambiguously identified at 458 (E 1g), 494(E 2g) and 574 (A 1g) cm-1. The spectra from ab and ac surfaces differ significantly and provide evidence that within hours after preparation the ac surface, unlike the ab one, is strongly disordered. Within several days the disorder extends over the ab surface too.

Graphene is the two-dimensional building block for carbon allotropes of every other dimensionality. We show that its electronic structure is captured in its Raman spectrum that clearly evolves with the number of layers. The D peak second order changes in shape, width, and position for an increasing number of layers, reflecting the change in the electron bands via a double resonant Raman process. The G peak slightly down-shifts. This allows unambiguous, high-throughput, nondestructive identification of graphene layers, which is critically lacking in this emerging research area.

We describe a new method and a software, called GANM (Genetic Algorithm with Normal Modes), that combines genetic algorithm and normal mode analysis in order to achieve protein-ligand docking simulations that take into account global and local conformational adjustments. The energetical and structural optimization during the ligand binding process is achieved with GA that uses a rotamer library for changing the side chain conformations within and around the binding site. The methodology uses normal modes to account for the global conformational changes of the protein. This software is implemented in distinct versions using different levels of approximations. In this article, we describe the methodology and discuss the results and the performance obtained with the first two versions of GANM. The protein-ligand complexes considered for the test calculations are: (1) Dihydrofolate Reductase (DHFR) and MTX as ligands, (2) HIV-1 Aspartyl Protease with ritonavir, nelfinavir and DMP323 as ligands, and (3) CDK-2 and DT-5 as ligands.

Micro-electromechanical systems (MEMS) capacitive pressure sensors operating at harsh environments (e.g. high temperature) are proposed because of SiC owing excellent electrical stability, mechanical robustness, and chemical inertness properties. The principle of this paper is, design, simulation. The application of SiC pressure sensors are in a harsh environments such as automotive industries, aerospace, oil/logging equipments, nuclear station, power station. The sensor demonstrated a high temperature sensing capability up to 400 °C, the device achieves a linear characteristic response and consists of a circular clamped-edges poly-sic diaphragm suspended over sealed cavity on a silicon carbide substrate. The sensor is operating in touch mode capacitive pressure sensor, The advantages of a touch mode are the robust structure that make the sensor to withstand harsh environment, near linear output, and large over-range protection, operating in wide range of pressure, higher sensitivity than the near linear operation in normal mode, so in this case some of stray capacitance effects can be neglected.

The effect of local thermal non-equilibrium on linear and non-linear thermal instability in a horizontal porous medium saturated by a nanofluid has been investigated analytically. The Brinkman Model has been used for porous medium, while nanofluid incorporates the effect of Brownian motion along with thermophoresis. A three-temperature model has been used for the effect of local thermal non-equilibrium among the particle, fluid, and solid-matrix phases. The linear stability is based on normal mode technique, while for nonlinear analysis, a minimal representation of the truncated Fourier series analysis involving only two terms has been used. The critical conditions for the onset of convection and the heat and mass transfer across the porous layer have been obtained numerically.

Innovative algorithms have been developed during the past decade for simulating Newtonian physics for macromolecules. A major goal is alleviation of the severe requirement that the integration timestep be small enough to resolve the fastest components of the motion and thus guarantee numerical stability. This timestep problem is challenging if strictly faster methods with the same all-atom resolution at small timesteps are sought. Mathematical techniques that have worked well in other multiple-timescale contexts-where the fast motions are rapidly decaying or largely decoupled from others-have not been as successful for biomolecules, where vibrational coupling is strong.

Perturbations of stars and black holes have been one of the main topics of relativistic astrophysics for the last few decades. They are of particular importance today, because of their relevance to gravitational wave astronomy. In this review we present the theory of quasi-normal modes of compact objects from both the mathematical and astrophysical points of view. The discussion includes perturbations of black holes (Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman) and relativistic stars (nonrotating and slowly-rotating). The properties of the various families of quasi-normal modes are described, and numerical techniques for calculating quasi-normal modes reviewed. The successes, as well as the limits, of perturbation theory are presented, and its role in the emerging era of numerical relativity and supercomputers is discussed.

ALTHOUGH much has been done in an attempt to understand the kinetics of biological processes in terms of their molecular motions1-4, it appears that until now no one has attempted to calculate or measure the proper (normal) modes of motion of helical biological polymers. We think it might help understanding of the mechanism of biological processes (such as the enzyme action of certain proteins or the replication of nucleic acids) if it were possible both to measure and to calculate the proper modes of motion of the polymers themselves since these motions may play an important part in biological processes. This communication presents a very simple calculation of the phonon dispersion of the acoustical modes of the Pauling alpha-helix in the harmonic approximation. The excitation of the higher (anharmonic) levels of this mode almost certainly leads to the well known helix &rlhar2; coil transition5.

Until recently superconducting gravimeters (SGs) have been used principally in tidal studies (periods 6^24 hr) due to their high sensitivity and low drift rates. This paper considers the performance of these instruments as long-period seismometers, particularly in the normal mode band (periods 1^54 min). To judge their suitability in providing useful information to seismology, it is important to determine their noise characteristics compared to other established instruments such as spring gravimeters.