Dynamo onset as a first-order transition: Lessons from a shell model for magnetohydrodynamics

We carry out systematic and high-resolution studies of dynamo action in a shell model for magnetohydro-dynamic (MHD) turbulence over wide ranges of the magnetic Prandtl number Pr-M and the magnetic Reynolds number Re-M. Our study suggests that it is natural to think of dynamo onset as a nonequilibrium first-order phase transition between two different turbulent, but statistically steady, states. The ratio of the magnetic and kinetic energies is a convenient order parameter for this transition. By using this order parameter, we obtain the stability diagram (or nonequilibrium phase diagram) for dynamo formation in our MHD shell model in the (Pr-M(-1), Re-M) plane. The dynamo boundary, which separates dynamo and no-dynamo regions, appears to have a fractal character. We obtain a hysteretic behavior of the order parameter across this boundary and suggestions of nucleation-type phenomena.

Shell-model calculation of defect energies in alkali halides employing crystal-independent interionic potential parameters

Shell model calculation of defect energies in alkali halides have been carried out using the ion-dependent, crystal-independent potential parameters of Sangster and Atwood (1978). Results indicate that appreciable differences exist between barrier heights for migration of cations and anions. While barrier heights for cations are generally lower than for anions in alkali halides of NaCl structure, the opposite is true in alkali halides of CsCl structure.

A Revisit to Capture the Entire Behavior of Ultrasonic Wave Dispersion Characteristics of Single Walled Carbon Nanotubes Based on Nonlocal Elasticity Theory and Flugge Shell Model

In this paper, an ultrasonic wave propagation analysis in single-walled carbon nanotube (SWCNT) is re-studied using nonlocal elasticity theory, to capture the whole behaviour. The SWCNT is modeled using Flugge's shell theory, with the wall having axial, circumferential and radial degrees of freedom and also including small scale effects. Nonlocal governing equations for this system are derived and wave propagation analysis is also carried out. The revisited nonlocal elasticity calculation shows that the wavenumber tends to infinite at certain frequencies and the corresponding wave velocity tends to zero at those frequencies indicating localization and stationary behavior. This frequency is termed as escape frequency. This behavior is observed only for axial and radial waves in SWCNT. It has been shown that the circumferential waves will propagate dispersively at higher frequencies in nonlocality. The magnitudes of wave velocities of circumferential waves are smaller in nonlocal elasticity as compared to local elasticity. We also show that the explicit expressions of cut-off frequency depend on the nonlocal scaling parameter and the axial wavenumber. The effect of axial wavenumber on the ultrasonic wave behavior in SWCNTs is also discussed. The present results are compared with the corresponding results (for first mode) obtained from ab initio and 3-D elastodynamic continuum models. The acoustic phonon dispersion relation predicted by the present model is in good agreement with that obtained from literature. The results are new and can provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave propagation properties of single-walled carbon nanotubes.

Ultrasonic Wave Dispersion Characteristics of Fluid-Filled Single-Walled Carbon Nanotubes Based on Nonclassical Shell Model

In this paper, ultrasonic wave propagation analysis in fluid filled single-walled carbon nanotube (SWCNT) is studied using nonlocal elasticity theory. The SWCNT is modeled using Flugge's shell theory, with the wall having axial, circumferential and radial degrees of freedom and also including small scale effects. The fluid inside the SWCNT is assumed as water. Nonlocal governing equations for this system are derived and wave propagation analysis is also carried out. The presence of fluid in SWCNT alters the ultrasonic wave dispersion behavior. The wavenumber and wave velocity are smaller in presence of fluid as compared to the empty SWCNT. The nonlocal elasticity calculation shows that the wavenumber tends to reach the continuum limit at certain frequencies and the corresponding wave velocity tends to zero at those frequencies indicating localization and stationary behavior. It has been shown that the circumferential. waves will propagate non-dispersively at higher frequencies in nonlocality. The magnitudes of wave velocities of circumferential waves are smaller in nonlocal elasticity as compared to local elasticity. We also show that the cut-off frequency depend on the nonlocal scaling parameter and also on the density of the fluid inside the SWCNT, and the axial wavenumber, as the fluid becomes denser the cut-off frequency decreases. The effect of axial wavenumber on the ultrasonic wave behavior in SWCNTS filled with water is also discussed.

Multiscaling in Hall-Magnetohydrodynamic Turbulence: Insights from a Shell Model

We show that a shell-model version of the three-dimensional Hall-magnetohydrodynamic (3D Hall-MHD) equations provides a natural theoretical model for investigating the multiscaling behaviors of velocity and magnetic structure functions. We carry out extensive numerical studies of this shell model, obtain the scaling exponents for its structure functions, in both the low-k and high-k power-law ranges of three-dimensional Hall-magnetohydrodynamic, and find that the extended-self-similarity procedure is helpful in extracting the multiscaling nature of structure functions in the high-k regime, which otherwise appears to display simple scaling. Our results shed light on intriguing solar-wind measurements.

Threshold photoproduction of charged pions on14N

Pion photoproduction processes14Ngs(gamma, pgr +)14C and14Ngs(gamma, pgr –)14O have been studied in the threshold region. These processes provide an excellent tool to study the corrections to soft pion theorems and Kroll-Ruderman limit as applied to nuclear processes. The agreement with the available experimental data for these processes is better with the empirical wave functions while the shell-model wave functions predict a much higher value. Detailed experimental studies of these reactions at threshold, it is shown, are expected to lead to a better understanding of the shell-model inputs and radial distributions in the 1p state. We thank Dr. S.C.K. Nair for a helpful discussion during the initial stages of this work. One of us (MVN) thanks Dr. J.M. Laget for sending some unpublished data on pion photoproduction. He is also thankful to Dr. J. Pasupathy and Dr. R. Rajaraman for their interest and encouragement.

Raman spectrum of rubidium iodide

Raman spectrum of rubidium iodide has been recorded for the first time using the resonance radiation of mercury (λ 2537 ) as the exciter. The frequencies of the 24p limiting modes (p = 2, the number of non-equivalent atoms in the unit cell), postulated by Raman in 1943, which correspond to the frequencies from the critical points Γ, L and X, have been worked out using the shell model of Cochran, taking into account the nearest and the next-nearest neighbour short-range interactions and the polarization of both the ions. The observed Raman lines have been assigned to the overtones and the combinations of the phonon branches from Γ, L and X.

A model for the interaction of trifluoroethanol with peptides and proteins

The structural stabilizing property of 2,2,2-trifluoroethanol (TFE) in peptides has been widely demonstrated, More recently, TFE has been shown to enhance secondary structure content in globular proteins, and to influence quaternary interactions in protein multimers. The molecular mechanisms by which TFE exerts its Influence on peptide and protein structures remain poorly understood. The present analysis integrates the known physical properties of TFE with a variety of experimental observations on the interaction of TFE with peptides and proteins and on the properties of fluorocarbons. Two features of TFE, namely the hydrophobicity of the trifluoromethyl group and the hydrogen bonding character (strong donor and poor acceptor), emerge as the most important factors for rationalising the observed effects of TFE. A model is proposed for TFE interaction with peptides which involves an initial replacement of the hydration shell by fluoroalcohol molecules, a process driven by apolar interactions and favourable entropy of dehydration. Subsequent bifurcated hydrogen-bond formation with peptide carbonyl groups, which leave intramolecular interactions unaffected, promotes secondary structure formation.

Simplified dispersion curves for circular cylindrical shells using shallow shell theory.

An alternative derivation of the dispersion relation for the transverse vibration of a circular cylindrical shell is presented. The use of the shallow shell theory model leads to a simpler derivation of the same result. Further, the applicability of the dispersion relation is extended to the axisymmetric mode and the high frequency beam mode.

Estimation Of Properties Of Rare-Gas Solids From Compression Characteristics Of Closed-Shell Ions

We present a unified approach to repulsion in ionic and van der Waals solids based on a compressible-ion/atom model. Earlier studies have shown that repulsion in ionic crystals can be viewed as arising from the compression energy of ions, described by two parameters per ion. Here we obtain the compression parameters of the rare-gas atoms Ne. Ar. Kr and Xe by interpolation using the known parameters of related equi-electronic ions (e.g. Ar from S2-. Cl-, K- and Ca2-). These parameters fit the experimental zero-temperature interatomic distances and compressibilities of the rare-gas crystals satisfactorily. A hightemperature equation of state based on an Einstein model of thermal motions is used to calculate the thermal expansivities, compressibilities and their temperature derivatives for Ar. Kr and Xe. It is argued that an instability at higher temperatures represents the limit to which the solid can be superheated. beyond which sublimation must occur.

On a finite element model for the analysis of through cracks in laminated anisotropic cylindrical shells

A finite element model for the analysis of laminated composite cylindrical shells with through cracks is presented. The analysis takes into account anisotropic elastic behaviour, bending-extensional coupling and transverse shear deformation effects. The proposed finite element model is based on the approach of dividing a cracked configuration into triangular shaped singular elements around the crack tip with adjoining quadrilateral shaped regular elements. The parabolic isoparametric cylindrical shell elements (both singular and regular) used in this model employ independent displacement and rotation interpolation in the shell middle surface. The numerical comparisons show the evidence to the conclusion that the proposed model will yield accurate stress intensity factors from a relatively coarse mesh. Through the analysis of a pressurised fibre composite cylindrical shell with an axial crack, the effect of material orthotropy on the crack tip stress intensity factors is shown to be quite significant.

Path-integral derivation of the superconformal anomaly for the Wess-Zumino model

Fujikawa's method of evaluating the anomalies is extended to the on-shell supersymmetric (SUSY) theories. The supercurrent and the superconformal current anomalies are evaluated for the Wess-Zumino model using the background-field formulation and heat-kernel regularization. We find that the regularized Jacobians for SUSY and superconformal transformations are finite. The results can be expressed in a form such that there is no supercurrent anomaly but a finite nonzero superconformal anomaly, in agreement with similar results obtained using other methods.

Asymptotic expansions for the coupled wavenumbers in an infinite orthotropic flexible fluid-filled cylindrical shell

Analytical expressions are found for the coupled wavenumbers in flexible, fluid-filled, circular cylindrical orthotropic shells using the asymptotic methods. These expressions are valid for arbitrary circumferential orders. The Donnell-Mushtari shell theory is used to model the shell and the effect of the fluid is introduced through the fluid-loading parameter mu. The orthotropic problem is posed as a perturbation on the corresponding isotropic problem by defining a suitable orthotropy parameter epsilon, which is a measure of the degree of orthotropy. For the first study, an isotropic shell is considered (by setting epsilon = 0) and expansions are found for the coupled wavenumbers using a regular perturbation approach. In the second study, asymptotic expansions are found for the coupled wavenumbers in the limit of small orthotropy (epsilon << 1). For each study, isotropy and orthotropy, expansions are found for small and large values of the fluid-loading parameter mu. All the asymptotic solutions are compared with numerical solutions to the coupled dispersion relation and the match is seen to be good. The differences between the isotropic and orthotropic solutions are discussed. The main contribution of this work lies in extending the existing literature beyond in vacuo studies to the case of fluid-filled shells (isotropic and orthotropic).

EFFECT OF CORE-SHELL STRUCTURE OF HYDROGEL BEADS ON THE THRESHOLD CONCENTRATION OF WATER FOR SWELLING AND ITS PH SENSITIVITY

In this paper we investigate the effect of core-shell structure of Sodium Alginate based hydrogel beads and their size on certain activation threshold concentration of water for applications in swelling and pH sensing. This type of hydrogel experiences diffusive pressure due to transport of certain free charges across its interface with a solvent or electrolyte. This process is essentially a dynamic equilibrium of the electric force field, stress in the polymeric network with cage like structure and molecular diffusion including phase transformation due to pressure imbalance between the hydrogel and its surroundings. The effect of pH of the solvant on the swelling rate of these beads has been studied experimentally. A mathematical model of the swelling process has been developed by considering Nernst-Planck equation representing the migration of mobile ions and Er ions, Poisson equation representing the equilibrium of the electric field and mechanical field equation representing swelling of the gel. An attempt has been made to predict the experimentally observed phenomena using these numerical simulations. It is observed experimentally that certain minimum concentration called activation threshold concentration of the water molecules must be present in the hydrogel in order to activate the swelling process. For the required activation threshold concentration of water in the beads, the pH induced change in the rate of swelling is also investigated. This effect is analyzed for various different core-shell structures of the beads.