Self-interrupted regenerative metal cutting in turning

A new approach is used to study the global dynamics of regenerative metal cutting in turning. The cut surface is modeled using a partial differential equation (PDE) coupled, via boundary conditions, to an ordinary differential equation (ODE) modeling the dynamics of the cutting tool. This approach automatically incorporates the multiple-regenerative effects accompanying self-interrupted cutting. Taylor's 3/4 power law model for the cutting force is adopted. Lower dimensional ODE approximations are obtained for the combined tool–workpiece model using Galerkin projections, and a bifurcation diagram computed. The unstable solution branch off the subcritical Hopf bifurcation meets the stable branch involving self-interrupted dynamics in a turning point bifurcation. The tool displacement at that turning point is estimated, which helps identify cutting parameter ranges where loss of stability leads to much larger self-interrupted motions than in some other ranges. Numerical bounds are also obtained on the parameter values which guarantee global stability of steady-state cutting, i.e., parameter values for which there exist neither unstable periodic motions nor self-interrupted motions about the stable equilibrium.

Drop formation in non-newtonian liquids under pulsed conditions

Drop formation from single nozzles under pulsed flow conditions in non-Newtonian fluids following the power law model has been studied. An existing model has been modified to explain the experimental data. The flow conditions employed correspond to the mixer—settler type of operation in pulsed sieve-plate extraction columns. The modified model predicts the drop sizes satisfactorily. It has been found that consideration of non-Newtonian behaviour is important at low pulse intensities and its significance decreases with increasing intensity of pulsation. Further, the proposed model for single orifices has been tested to predict the sizes of drops formed from a sieve-plate distributor having four holes, and has been found to predict the sizes fairly well in the absence of coalescence.

Methanation of CO2 over Ru?SiO2 catalyst

Using Ru - SiO2 catalyst, the kinetics of methanation of carbon dioxide has been studied. In the temperature range of 320-460-degrees-C a simple power law model is found to predict experimental results with a good agreement over the range of variables studied.

Timing and broad-band spectroscopy of 1A 1118-61 with Suzaku

We present a timing and broad-band pulse-phase-resolved spectral analysis of the transient Be X-ray binary pulsar 1A 1118-61 observed during its outburst in 2009 January using Suzaku observations. The Suzaku observations were made twice, once at the peak of the outburst, and the other 13 d later at its declining phase. Pulse profiles from both observations exhibit strong energy dependence with several peaks at low energies and a single peak above similar to 10 keV. A weak, narrow peak is detected at the main dip of the pulse profiles from both observations in the energy bands below 3 keV, indicating the presence of a phase-dependent soft excess in the source continuum. The broad-band energy spectrum of the pulsar could be fitted well with a partial covering cut-off power-law model and a narrow iron fluorescence line. We also detect a broad cyclotron feature at similar to 50 keV from both observations which is a feature common for accretion-powered pulsars with high magnetic field strength. The pulse-phase-resolved spectral analysis shows an increase in the absorption column density of the partial covering component, as well as variation in the covering fraction at the dips of the pulse profiles, which naturally explains energy dependence of the same. The cyclotron line parameters also show significant variation with pulse phase with an similar to 10 keV variation in the cyclotron line energy and a variation in depth by a factor of 3. This can be explained either as the effect of different viewing angles of the dipole field at different pulse phases, or due to a more complex underlying magnetic field geometry.

Statistical Methods for Accelerated Life Testing with Particular Reference to Resin Impregnated Paper Bushings

Electrical failure of insulation is known to be an extremal random process wherein nominally identical pro-rated specimens of equipment insulation, at constant stress fail at inordinately different times even under laboratory test conditions. In order to be able to estimate the life of power equipment, it is necessary to run long duration ageing experiments under accelerated stresses, to acquire and analyze insulation specific failure data. In the present work, Resin Impregnated Paper (RIP) a relatively new insulation system of choice used in transformer bushings, is taken as an example. The failure data has been processed using proven statistical methods, both graphical and analytical. The physical model governing insulation failure at constant accelerated stress has been assumed to be based on temperature dependent inverse power law model.

Non-linear regression model for spatial variation in precipitation chemistry for South India

Chemical composition of rainwater changes from sea to inland under the influence of several major factors - topographic location of area, its distance from sea, annual rainfall. A model is developed here to quantify the variation in precipitation chemistry under the influence of inland distance and rainfall amount. Various sites in India categorized as 'urban', 'suburban' and 'rural' have been considered for model development. pH, HCO3, NO3 and Mg do not change much from coast to inland while, SO4 and Ca change is subjected to local emissions. Cl and Na originate solely from sea salinity and are the chemistry parameters in the model. Non-linear multiple regressions performed for the various categories revealed that both rainfall amount and precipitation chemistry obeyed a power law reduction with distance from sea. Cl and Na decrease rapidly for the first 100 km distance from sea, then decrease marginally for the next 100 km, and later stabilize. Regression parameters estimated for different cases were found to be consistent (R-2 similar to 0.8). Variation in one of the parameters accounted for urbanization. Model was validated using data points from the southern peninsular region of the country. Estimates are found to be within 99.9% confidence interval. Finally, this relationship between the three parameters - rainfall amount, coastline distance, and concentration (in terms of Cl and Na) was validated with experiments conducted in a small experimental watershed in the south-west India. Chemistry estimated using the model was in good correlation with observed values with a relative error of similar to 5%. Monthly variation in the chemistry is predicted from a downscaling model and then compared with the observed data. Hence, the model developed for rain chemistry is useful in estimating the concentrations at different spatio-temporal scales and is especially applicable for south-west region of India. (C) 2008 Elsevier Ltd. All rights reserved.

Nonequilibrium phase transition in the kinetic Ising model: Critical slowing down and the specific-heat singularity

The nonequilibrium dynamic phase transition, in the kinetic Ising model in the presence of an oscillating magnetic field has been studied both by Monte Carlo simulation and by solving numerically the mean-field dynamic equation of motion for the average magnetization. In both cases, the Debye ''relaxation'' behavior of the dynamic order parameter has been observed and the ''relaxation time'' is found to diverge near the dynamic transition point. The Debye relaxation of the dynamic order parameter and the power law divergence of the relaxation time have been obtained from a very approximate solution of the mean-field dynamic equation. The temperature variation of appropriately defined ''specific heat'' is studied by the Monte Carlo simulation near the transition point. The specific heat has been observed to diverge near the dynamic transition point.

Nonequilibrium phase transition in the kinetic Ising model: Divergences of fluctuations and responses near the transition point

The nonequilibrium dynamic phase transition in the kinetic Ising model in the presence of an oscillating magnetic field is studied by Monte Carlo simulation. The fluctuation of the dynamic older parameter is studied as a function of temperature near the dynamic transition point. The temperature variation of appropriately defined ''susceptibility'' is also studied near the dynamic transition point. Similarly, the fluctuation of energy and appropriately defined ''specific heat'' is studied as a function of temperature near the dynamic transition point. In both cases, the fluctuations (of dynamic order parameter and energy) and the corresponding responses diverge (in power law fashion) near the dynamic transition point with similar critical behavior (with identical exponent values).

Phase diagram of a two-species lattice model with a linear instability

We discuss the properties of a one-dimensional lattice model of a driven system with two species of particles in which the mobility of one species depends on the density of the other. This model was introduced by Lahiri and Ramaswamy (Phys. Rev. Lett., 79, 1150 (1997)) in the context of sedimenting colloidal crystals, and its continuum version was shown to exhibit an instability arising from linear gradient couplings. In this paper we review recent progress in understanding the full phase diagram of the model. There are three phases. In the first, the steady state can be determined exactly along a representative locus using the condition of detailed balance. The system shows phase separation of an exceptionally robust sort, termed strong phase separation, which survives at all temperatures. The second phase arises in the threshold case where the first species evolves independently of the second, but the fluctuations of the first influence the evolution of the second, as in the passive scalar problem. The second species then shows phase separation of a delicate sort, in which long-range order coexists with fluctuations which do not damp down in the large-size limit. This fluctuation-dominated phase ordering is associated with power law decays in cluster size distributions and a breakdown of the Porod law. The third phase is one with a uniform overall density, and along a representative locus the steady state is shown to have product measure form. Density fluctuations are transported by two kinematic waves, each involving both species and coupled at the nonlinear level. Their dissipation properties are governed by the symmetries of these couplings, which depend on the overall densities. In the most interesting case,, the dissipation of the two modes is characterized by different critical exponents, despite the nonlinear coupling.

Confinement-deconfinement transition and spin correlations in a generalized Kitaev model

We present a spin model, namely, the Kitaev model augmented by a loop term and perturbed by an Ising Hamiltonian, and show that it exhibits both confinement-deconfinement transitions from spin liquid to antiferromagnetic/spin-chain/ferromagnetic phases and topological quantum phase transitions between gapped and gapless spin-liquid phases. We develop a fermionic resonating-valence-bonds (RVB) mean-field theory to chart out the phase diagram of the model and estimate the stability of its spin-liquid phases, which might be relevant for attempts to realize the model in optical lattices and other spin systems. We present an analytical mean-field theory to study the confinement-deconfinement transition for large coefficient of the loop term and show that this transition is first order within such mean-field analysis in this limit. We also conjecture that in some other regimes, the confinement-deconfinement transitions in the model, predicted to be first order within the mean-field theory, may become second order via a defect condensation mechanism. Finally, we present a general classification of the perturbations to the Kitaev model on the basis of their effect on it's spin correlation functions and derive a necessary and sufficient condition, within the regime of validity of perturbation theory, for the spin correlators to exhibit a long-ranged power-law behavior in the presence of such perturbations. Our results reproduce those of Tikhonov et al. [Phys. Rev. Lett. 106, 067203 (2011)] as a special case.

Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

We study the scaling behavior of the fidelity (F) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice. We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of F for an anisotropic quantum critical point for both the thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of F inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate F through the overlap between the ground states for the angle of rotation eta and eta + d eta, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary.

Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

We study the scaling behavior of the fidelity (F) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice.We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of F for an anisotropic quantum critical point for both the thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of F inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate F through the overlap between the ground states for the angle of rotation η and η + dη, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary

A general geomorphological recession flow model for river basins

Recession flows in a basin are controlled by the temporal evolution of its active drainage network (ADN). The geomorphological recession flow model (GRFM) assumes that both the rate of flow generation per unit ADN length (q) and the speed at which ADN heads move downstream (c) remain constant during a recession event. Thereby, it connects the power law exponent of -dQ/dt versus Q (discharge at the outlet at time t) curve, , with the structure of the drainage network, a fixed entity. In this study, we first reformulate the GRFM for Horton-Strahler networks and show that the geomorphic ((g)) is equal to D/(D-1), where D is the fractal dimension of the drainage network. We then propose a more general recession flow model by expressing both q and c as functions of Horton-Strahler stream order. We show that it is possible to have = (g) for a recession event even when q and c do not remain constant. The modified GRFM suggests that is controlled by the spatial distribution of subsurface storage within the basin. By analyzing streamflow data from 39 U.S. Geological Survey basins, we show that is having a power law relationship with recession curve peak, which indicates that the spatial distribution of subsurface storage varies across recession events. Key Points The GRFM is reformulated for Horton-Strahler networks. The GRFM is modified by allowing its parameters to vary along streams. Sub-surface storage distribution controls recession flow characteristics.

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.

A model for probing large distance behaviour in high energy collisions

We apply to total cross-sections our model for soft gluon resummation in the infrared region. The model aims to probe large distance interactions in QCD. Our ansatz for an effective coupling for gluons and quarks in the infrared region follows an inverse power law which is singular but integrable. In the context of an eikonal formalism with QCD mini-jets, we study total hadronic cross-sections for protons, pions, photons. We estimate the total inelastic cross-section at LHC comparing with recent measurements and update previous results for survival probability.