Non-linear resonance in strings under narrow band random excitation, part I: Planar response and stability

Non-linear planar response of a string to planar narrow band random excitation is investigated in this paper. A response equation for the mean square deflection σ2 is obtained under a single mode approximation by using the equivalent linearization technique. It is shown that the response is triple valued, as in the case of harmonic excitation, if the centre frequency of excitation Ω lies in a certain specified range. The triple valued response occurs only if the excitation bandwidth β is smaller than a critical value βcrit which is a monotonically increasing function of the intensity of excitation. An approximate method of investigating the almost sure asymptotic stability of the solution is presented and regions of instability in the Ω-σ2 plane have been charted. It is shown that planar response can become unstable either due to an unbounded growth of the in-plane component of motion or due to a spontaneous appearance of an out-of-plane component.

Incompressible boundary layer for longitudinal flow over a cylinder with an applied magnetic field

The flow, heat and mass transfer problem for a steady laminar incompressible boundary layer flow in an electrically conducting fluid over a longitudinal cylinder with an applied magnetic field has been studied. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The results are found to be strongly dependent on the magnetic field and dissipation parameter. The effect of the mass transfer is more pronounced on the skin friction than on the heat transfer. The results have been compared with those of the series solution, the asymptotic solution, the Glauert and Lighthill's solution, local similarity, local nonsimilarity and difference-differential methods. Good agreement is found with all of them, except with the results of the local similarity and series solution methods.

A Magnetic Susceptibility Study of Spin-state Transitions in Rare-earth TrioxocobaItates( III)

Rare-earth trioxocobaltates(lll), Ln[CoO,], with Ln = Pr, Nd, Tb, Dy. and Yb exhibit low-spin to high-spin transitions of cobalt characterised by a maximum in the Ax-l against temperature plots where Ax is the cobalt contribution to the magnetic susceptibility. The susceptibility behaviour is distinct from that of La[CoO,] which shows a plateau in the x-I-T curve accompanied by a structural transition. The temperature at which the AX- I-T curve shows a maximum increases with the decrease in the size of the rare-earth ion. The susceptibility behavior of solid solutions of La,,Nd,CoO, has been investigated to see how the behaviour characteristic of Nd[CoO,] changes to that of La[CoO,].

Magnetic Field Induced Instabilities In Localized Two-Dimensional Electron Systems

The results of extensive transport studies in localized regime of mesoscopic two-dimensional electron systems (2DES) with varying disorder are presented. A quick overview of previously achieved result is given. The main focus is on the observation of density dependent instabilities manifested by strong resistance oscillations induced by high perpendicular magnetic fields B-perpendicular to. While the amplitude of the oscillations is strongly enhanced with increasing B-perpendicular to, their position in electron density remains unaffected. The temperature dependence of resistivity shows a transition from an activated behaviour at high temperature to a saturated behaviour at low T. In the positions of resistance minima, the T dependence can even become metal-like (d rho/dT > 0). The activation energies obtained from the high T behaviour exhibit a formation of plateaux in connection with the resistance oscillations when analyzed as a function of electron density. We suggest the interplay between a strongly interacting electron phase and the background disorder as a possible explanation for our observation.

Molecular Dynamics in [(CH8)aN]z Cd14 A Proton Magnetic Relaxation Study

second moment measurements are carried out on [(CH,),N], CdI, in the temperature range 77 to 400 K. The results are interpreted based on a molecular dynamical model of randomly reorienting methyl groups and isotropically tumbling tetramethyl ammonium group. The relaxation data show contributions from spin-rotation interaction at high temperatures and presence of inequivalent methyl groups. The correlation times and associated activation energies, connected with this model, are calculated from the data. The structure in the absorption line and in the free-induction decay signal at 77 K indicates the possibility of tunnelling motion of the methyl groups. Im Temperaturbereich 77 bis 400 K werden an [(CH,),N],CdI, Protonen-Spin-Gitter-Relaxationsexperimente (bei Larmorfrequenzen von 10,20 und 30 MHz) und Messungen des zweiten Moments durchgefiihrt. Die Ergebnisse werden an Hand eines molekularen dynamischen Modells sich statistisch umorientierender Methylgruppen und isotrop taumelnder Tetramethyl-Ammoniumgruppen interpretiert. Die Relaxationswerte zeigen Beitriige von Spin-Rotations-Wechselwirkung bei hohen Temperaturen und die Anwesenheit von inaquivalenten Methylgruppen. Die Korrelationszeiten und verknupften Aktivierungsenergien, die mit diesem Model1 verbunden sind, werden am den Werten berechnet. Die Struktur in der Absorptionslinie und im Abklingsignal der freien Induktion bei 77 K zeigt die Moglichkeit einer Tunnelbewegung der Methylgruppen.

Steady-State Response of Thick Rectangular Plates

The classical theory of plates neglects the effects of rotatory inertia and shear deformation, and due to this assumption it is applicable only for thin plates. Mindlin presented an improved plate theory which is fairly accurate.

A nuclear magnetic resonance study of tetramethylammonium tribromocadmate

Proton spin lattice relaxation (T1) in (CH3)4NCdBr3 at different Larmor frequencies (10, 20 and 30 MHz) has been studied in the temperature range 77 to 400 K. The variations in T1 at high temperature are independent of frequency and show a maximum due to spin rotation- interaction. The other features are interpreted as being due to isotropic tumbling of the tetramethylammonium ion and random reorientation of the CH3 group. The CW spectrum remained narrow up to 77 K and develops a wing structure at low temperatures. This observation is attributed to a possible tunnelling motion of the CH3 group, which has rather low activation energy as demonstrated by the study of T1.

Spatial correlations around a Kondo impurity

We present a method for calculating zero-frequency, spatially varying response and correlation functions around a magnetic impurity in metals. We illustrate the procedure which involves a combination of perturbative scaling and nonperturbative renormalization-group methods for the spin-(1/2) Kondo impurity. We explain the factorization of the temperature and spatial dependence of the Knight shift observed in NMR experiments.

Note On The Stability Of Parallel Magnetic-Fields - Comment

It is shown that the conclusions arrived at regarding the instability of an incompressible fluid cylinder in the presence of the magnetic field and the streaming velocity in a recent communication easily follow from the study of propagation characteristics of Alfvén surface waves along cylindrical plasma columns made earlier.

On the Landau damping of sound waves in a plasma with magnetic flux tubes

The Landau damping of sound wave in a plasma consisting of an ensemble of magnetic flux tubes with reference to the work by Ryutov and Ryutova (1976) is discussed. Sound waves cannot be Landau damped in general but under certain restriction conditions on plasma parameters the possibility of absorption of these waves can exist.

Circular dichroism and nuclear magnetic resonance studies on the complexation of valinomycin with calcium

Complexation of valinomycin (VM) with the divalent cation Ca2+ in a lipophilic solvent, acetonitrile (CH3-CN), has been studied by using circular dichroism and proton and carbon- 13 nuclear magnetic resonance (‘H NMR and I3C NMR). From analyses of the spectral data, it is concluded that VM forms a 2:l (peptideion-peptide) sandwich complex with Ca2+, at low concentration of VM. At moderate conocentrations of the salt, in addition to the sandwich complex, an equimolar (1:l) complex different from those observed for potassium and sodium is also observed. At very large concentrations of the calcium salt, the data suggested a complex with a conformation similar to that of the free VM in polar solvents. Possible conformations for the sandwich and the equimolar VM-calcium complexes are proposed.

Hydrogen- 1 and Carbon- 13 Magnetic Resonance Studies of Nonactin-Calcium Complex

For an understanding of the cation selectivity and general binding characteristics of macrotetralide antibiotic nonactin (NA) with ions of different sizes and charges, the nature of binding of divalent cation, Ca2+, to NA and conformation of the NA-Ca2+ complex have been studied by use of 270-MHz proton nuclear magnetic resonance ('H NMR) and carbon-13 nuclear magnetic resonance (13C NMR). The calcium ion induced significantly large changes in chemical shifts for H7, H2, H3, and H5 protons of NA and relatively small changes for H18 and H2' protons. Changes in I3C chemical shift were quite large for carbonyl carbon, C,; it is noteworthy that in the NA-K+ complex, H2 and H2' protons practically do not show any change during complexation and carbonyl carbon shows a much smaller chemical shift change.

Magnetohydrodynamic unsteady flow in a tube of variable cross section in an axial magnetic field

Oscillatory flow in a tube of slowly varying cross section is investigated in the presence of a uniform magnetic field in the axial direction. A perturbation solution including steady streaming is presented. The pressure and shear stress on the wall for various parameters governing the flow are discussed. Physics of Fluids is copyrighted by The American Institute of Physics.

Nuclear magnetic resonance spectra of oriented bicyclic systems containing heteroatom(s):the spectrum of 2-thiocoumarin

From the proton nmr studies of 2-thiocoumarin and coumarin, it is concluded that the relative interproton distances in the two oxygen heteroatom bicyclic systems are similar. The values for the phenyl ring protons do not deviate significantly from the regular hexagonal geometry, unlike bicyclic systems with nitrogens as the heteroatoms, such as diazanaphthalenes. Larger values of the indirect spin-spin couplings within the protons of the ring containing the oxygen heteroatom, compared to the values between the ortho protons in the phenyl rings in coumarin and 2-thiocoumarin, correspond to the olefinic nature of these protons. This is in contrast to results for the nitrogen heterocycles where both the rings are aromatic.

Side-band intensities in the deuterium magnetic resonance spectra of oriented molecules spinning near the magic angle

The appearance of spinning side bands in the 2H NMR spectra of oriented molecules is investigated. A theoretical interpretation of the side-band intensities is carried out. Information derived on the director orientation and distribution as a function of spinning speedis reported.