Infinite dimensional slow modulations in a well known delayed model for cutting tool vibrations

We apply the method of multiple scales (MMS) to a well-known model of regenerative cutting vibrations in the large delay regime. By ``large'' we mean the delay is much larger than the timescale of typical cutting tool oscillations. The MMS up to second order, recently developed for such systems, is applied here to study tool dynamics in the large delay regime. The second order analysis is found to be much more accurate than the first order analysis. Numerical integration of the MMS slow flow is much faster than for the original equation, yet shows excellent accuracy in that plotted solutions of moderate amplitudes are visually near-indistinguishable. The advantages of the present analysis are that infinite dimensional dynamics is retained in the slow flow, while the more usual center manifold reduction gives a planar phase space; lower-dimensional dynamical features, such as Hopf bifurcations and families of periodic solutions, are also captured by the MMS; the strong sensitivity of the slow modulation dynamics to small changes in parameter values, peculiar to such systems with large delays, is seen clearly; and though certain parameters are treated as small (or, reciprocally, large), the analysis is not restricted to infinitesimal distances from the Hopf bifurcation.

Raman induced phase conjugation spectroscopy

Raman induced phase conjugation (RIPC) spectroscopy is a relatively new coherent Raman spectroscopic (CRS) technique using optical phase conjugation (OPC), with which complete Raman spectra of transparent media can be obtained. It is a non-degenerate four-wave mixing technique in which two pulsed laser beams at Ω1 and Ω1 ± Δ where A corresponds to a vibrational frequency of a nonlinear medium mix with a third laser beam at Ω1 to generate a fourth beam Ω1 ± Δ, which is nearly phase conjugate to one of the beams at Ω1. With this technique one can measure the ratio of the resonant and nonresonant components of the third-order nonlinear susceptibilities of the nonlinear media. We have used this technique to get Raman spectra of well-known organic solvents like benzene etc., using pulsed Nd: YAG -dye laser systems. We have also studied the effect of delaying one of the interacting beams with respect to the others and the phase conjugate property of RIPC signals.

Temperature-dependent chirped coherent phonon dynamics in Bi2Te3 using high-intensity femtosecond laser pulses

Degenerate pump-probe reflectivity experiments have been performed on a single crystal of bismuth telluride (Bi2Te3) as a function of sample temperature (3 K to 296 K) and pump intensity using similar to 50 femtosecond laser pulses with central photon energy of 1.57 eV. The time-resolved reflectivity data show two coherently generated totally symmetric A(1g) modes at 1.85 THz and 3.6 THz at 296 K which blue-shift to 1.9 THz and 4.02 THz, respectively, at 3 K. At high photoexcited carrier density of similar to 1.7 x 10(21) cm(-3), the phonon mode at 4.02 THz is two orders of magnitude higher positively chirped (i.e the phonon time period decreases with increasing delay time between the pump and the probe pulses) than the lower-frequency mode at 1.9 THz. The chirp parameter, beta is shown to be inversely varying with temperature. The time evolution of these modes is studied using continuous-wavelet transform of the time-resolved reflectivity data. Copyright (C) EPLA, 2010

Direct versus kinetic exchange in multiband models for organic ferromagnetism

Multiband Hubbard and Pariser-Parr-Pople calculations have been carried out on mixed donor-acceptor (DA) stacks with doubly degenerate acceptor orbitals and nondegenerate donor orbitals at two-thirds filling. Model exact results for 2, 3, and 4 DA units show that McConnell's prediction of high-spin ground states in these systems is, in general, incorrect. The larger phase space available for the low-spin states leads to their kinetic stabilization in preference to high-spin states. However, for large electron-correlation strengths, the direct exchange dominates over the kinetic exchange resulting in a high-spin ground state

Excitation and relaxation energies of trans-stilbene: Confined singlet, triplet, and charged bipolarons

The π-electronic excitations and excited-state geometries of trans-stilbene (tS) are found by combining exact solutions of the Pariser-Parr-Pople (PPP) model and semiempirical Parametric Method 3 (PM3) calculations. Comprehensive comparisons with tS spectra are obtained and related to the fluorescence and topological alternation of poly(paraphenylenevinylene) (PPV). The one-photon absorption and triplet of tS correspond, respectively, to singlet and triplet bipolarons confined to two phenyls, while the tS2- ground state is a confined charged bipolaron. Independent estimates of the relaxation energy between vertical and adiabatic excitation show the bipolaron binding energy to depend on both charge and spin, as expected for interacting π electrons in correlated or molecular states. Complete configuration interaction within the PPP model of tS accounts for the singlet-triplet gap, for the fine-structure constants and triplet-triplet spectra, for two-photon transitions and intensities, and for one-photon spectra and the radiative lifetime, although the relative position of nearly degenerate covalent and ionic singlets is not resolved. The planar PM3 geometry and low rotational barrier of tS agree with resolved rotational and vibrational spectra in molecular beams. PM3 excitation and relaxation energies for tS bipolarons are consistent with experiment and with PPP results. Instead of the exciton model, we interpret tS excitations in terms of states that are localized on each ring or extended over an alternating chain, as found exactly in Hückel theory, and find nearly degenerate transitions between extended and localized states in the singlet, triplet, and dianion manifolds. The large topological alternation of the extended system increases the ionicity and interchanges the order of the lowest one- and two-photon absorption of PPV relative to polyenes.

Coherent phonons in pyrochlore titanates A(2)Ti(2)O(7) (A = Dy, Gd, Tb): A phase transition in Dy2Ti2O7 at 110 K

We study the generation of coherent optical phonons in spin-frustrated pyrochlore single crystals Dy2Ti2O7, Gd2Ti2O7, and Tb2Ti2O7 using femtosecond laser pulses (65 fs, 1.57 eV) in degenerate time-resolved transmission experiments as a function of temperature from 4 to 296 K. At 4 K, two coherent phonons are observed at similar to 5.3 THz (5.0 THz) and similar to 9.3 THz (9.4 THz) for Dy2Ti2O7 (Gd2Ti2O7), whereas three coherent phonons are generated at similar to 5.0, 8.6, and 9.7 THz for Tb2Ti2O7. In the case of spin-ice Dy2Ti2O7, a clear discontinuity is observed in the linewidths of both the coherent phonons as well as in the phase of lower-energy coherent phonon mode, indicating a subtle structural change at 110 K. Another important observation is a phase difference of pi between the modes in all the samples, thus suggesting that the driving forces behind the generation of these modes could be different in nature, unlike a purely impulsive or displacive mechanism.

Collective Effects on Single Particle Orientational Relaxation in Slow Dipolar Liquids

Theoretical and computer simulation studies of orientational relaxation in dense molecular liquids are presented. The emphasis of the study is to understand the effects of collective orientational relaxation on the single-particle orientational dynamics. The theoretical analysis is based on a recently developed molecular hydrodynamic theory which allows a self-consistent description of both the collective and the single-particle orientational relaxation. The molecular hydrodynamic theory can be used to derive a relation between the memory function for the collective orientational correlation function and the frequency-dependent dielectric function. A novel feature of the present work is the demonstration that this collective memory function is significantly different from the single-particle rotational friction. However, a microscopic expression for the single-particle rotational friction can be derived from the molecular hydrodynamic theory where the collective memory function can be used to obtain the single-particle orientational friction. This procedure allows, us to calculate the single-particle orientational correlation function near the alpha-beta transition in the supercooled liquid. The calculated correlation function shows an interesting bimodal decay below the bifurcation temperature as the glass transition is approached from above. Brownian dynamics simulations have been carried out to check the validity of the above procedure of translating the memory function from the dielectric relaxation data. We have also investigated the following two issues important in understanding the orientational relaxation in slow liquids. First, we present an analysis of the ''orientational caging'' of translational motion. The value of the translational friction is found to be altered significantly by the orientational caging. Second, we address the question of the rank dependence of the dielectric friction using both simulation and the molecular hydrodynamic theory.

Seebeck Coefficient in Bulk and Quantum Wells of Non-Parabolic Kane-Type Materials

We present a simplified and quantitative analysis of the Seebeck coefficient in degenerate bulk and quantum well materials whose conduction band electrons obey Kane's non-parabolic energy dispersion relation. We use k.p formalism to include the effect of the overlap function due to the band non-parabolicity in the Seebeck coefficient. We also address the key issues and the conditions in which the Seebeck coefficient in quantum wells should exhibit oscillatory dependency with the film thickness under the acoustic phonon and ionized impurity scattering. The effect of screening length in degenerate bulk and quantum wells has also been generalized for the determination of ionization scattering. The well-known expressions of the Seebeck coefficient in non-degenerate wide band gap materials for both bulk and quantum wells has been obtained as a special case and this provides an indirect proof of our generalized theoretical analysis.

Singularity structure and chaotic behavior of the homopolar disk dynamo

We study in great detail a system of three first-order ordinary differential equations describing a homopolar disk dynamo (HDD). This system displays a large variety of behaviors, both regular and chaotic. Existence of periodic solutions is proved for certain ranges of parameters. Stability criteria for periodic solutions are given. The nonintegrability aspects of the HDD system are studied by investigating analytically the singularity structure of the system in the complex domain. Coexisting attractors (including period-doubling sequence) and coexisting strange attractors appear in some parametric regimes. The gluing of strange attractors and the ungluing of a strange attractor are also shown to occur. A period of bifurcation leading to chaos, not observed for other chaotic systems, is shown to characterize the chaotic behavior in some parametric ranges. The limiting case of the Lorenz system is also studied and is related to HDD.

Isolation of transforming growth factor-beta 2 cDNA from a fish, Cyprinus carpio by RT-PCR

Transforming Growth Factors-beta (TGF-beta s) have been described in many vertebrate species of amphibians, aves and mammals. In this report we demonstrate the presence of TGF-beta 2 in pisces. TGF-beta 2 has been cloned from a fish, Cyrinus carpio, by RT-PCR using degenerate oligonucleotide primers. Sequence analysis of the amplified product and alignment of the deduced amino acid sequence with the human TGF-beta 2 amino acid sequence revealed 81% and 93% identity in the precursor and the mature regions, respectively. The northern blot analysis of fish heart RNA shows a major messenger RNA species of about 8.0 kb and two messages of very low abundance of about 5.0 kb and 4.0 kb. The identification of TGF-beta 2 isoform in Pisces and it's high degree of homology with the mammalian isoform suggests that among all TGF-beta isoforms, TGF-beta 2 is the most conserved during evolution. (C) 1997 Elsevier Science B.V.

On the integrability and chaotic behavior of an ecological model

A three-species food chain model is studied analytically as well as numerically. Integrability of the model is studied using Painleve analysis while chaotic behavior is studied using numerical techniques, such as calculation of Lyapunov exponents, plotting the bifurcation diagram and phase plots. We correct and critically comment on the wrong results reported recently on this ecological model, in a paper by Rai [1995].

Ising pyrochlore magnets: Low-temperature properties, "ice rules," and beyond

Pyrochlore magnets are candidates for what Harris et al. [Phys. Rev. Lett. 79, 2554 (1997)] call "spin-ice" behavior. We present theoretical simulations of relevance for the pyrochlore family R2Ti2O7 (R = rare earth) supported by magnetothermal measurements on selected systems. Ey considering long-ranged dipole-dipole as well as short-ranged superexchange interactions, we get three distinct behaviors: (i) an ordered doubly degenerate state, (ii) a highly disordered state with a broad transition to paramagnetism, and (iii) a partially ordered state with a sharp transition to paramagnetism. Closely corresponding behavior is seen in the real compounds.

Classification of microwatersheds based on morphological characteristics

Three classification techniques, namely, K-means Cluster Analysis (KCA), Fuzzy Cluster Analysis (FCA), and Kohonen Neural Networks (KNN) were employed to group 25 microwatersheds of Kherthal watershed, Rajasthan into homogeneous groups for formulating the basis for suitable conservation and management practices. Ten parameters, mainly, morphological, namely, drainage density (D-d), bifurcation ratio (R-b), stream frequency (F-u), length of overland flow (L-o), form factor (R-f), shape factor (B-s), elongation ratio (R-e), circulatory ratio (R-c), compactness coefficient (C-c) and texture ratio (T) are used for the classification. Optimal number of groups is chosen, based on two cluster validation indices Davies-Bouldin and Dunn's. Comparative analysis of various clustering techniques revealed that 13 microwatersheds out of 25 are commonly suggested by KCA, FCA and KNN i.e., 52%; 17 microwatersheds out of 25 i.e., 68% are commonly suggested by KCA and FCA whereas these are 16 out of 25 in FCA and KNN (64%) and 15 out of 25 in KNN and CA (60%). It is observed from KNN sensitivity analysis that effect of various number of epochs (1000, 3000, 5000) and learning rates (0.01, 0.1-0.9) on total squared error values is significant even though no fixed trend is observed. Sensitivity analysis studies revealed that microwatershecls have occupied all the groups even though their number in each group is different in case of further increase in the number of groups from 5 to 6, 7 and 8. (C) 2010 International Association of Hydro-environment Engineering and Research, Asia Pacific Division. Published by Elsevier B.V. All rights reserved.

Nonlinear dynamics and chaotic motions in feedback-controlled two- and three-degree-of-freedom robots

The dynamics of a feedback-controlled rigid robot is most commonly described by a set of nonlinear ordinary differential equations. In this paper we analyze these equations, representing the feedback-controlled motion of two- and three-degrees-of-freedom rigid robots with revolute (R) and prismatic (P) joints in the absence of compliance, friction, and potential energy, for the possibility of chaotic motions. We first study the unforced or inertial motions of the robots, and show that when the Gaussian or Riemannian curvature of the configuration space of a robot is negative, the robot equations can exhibit chaos. If the curvature is zero or positive, then the robot equations cannot exhibit chaos. We show that among the two-degrees-of-freedom robots, the PP and the PR robot have zero Gaussian curvature while the RP and RR robots have negative Gaussian curvatures. For the three-degrees-of-freedom robots, we analyze the two well-known RRP and RRR configurations of the Stanford arm and the PUMA manipulator respectively, and derive the conditions for negative curvature and possible chaotic motions. The criteria of negative curvature cannot be used for the forced or feedback-controlled motions. For the forced motion, we resort to the well-known numerical techniques and compute chaos maps, Poincare maps, and bifurcation diagrams. Numerical results are presented for the two-degrees-of-freedom RP and RR robots, and we show that these robot equations can exhibit chaos for low controller gains and for large underestimated models. From the bifurcation diagrams, the route to chaos appears to be through period doubling.

Multiple scales without center manifold reductions for delay differential equations near Hopf bifurcations

We study small perturbations of three linear Delay Differential Equations (DDEs) close to Hopf bifurcation points. In analytical treatments of such equations, many authors recommend a center manifold reduction as a first step. We demonstrate that the method of multiple scales, on simply discarding the infinitely many exponentially decaying components of the complementary solutions obtained at each stage of the approximation, can bypass the explicit center manifold calculation. Analytical approximations obtained for the DDEs studied closely match numerical solutions.