Spin squeezing and quantum correlations

We discuss the notion of spin squeezing considering two mutually exclusive classes of spin-s states, namely, oriented and non-oriented states. Our analysis shows that the oriented states are not squeezed while non-oriented states exhibit squeezing. We also present a new scheme for construction of spin-s states using 2s spinors oriented along different axes. Taking the case of s=1, we show that the ‘non-oriented’ nature and hence squeezing arise from the intrinsic quantum correlations that exist among the spinors in the coupled state.     

A class of solvable coupled nonlinear oscillators with amplitude independent frequencies

Existence of amplitude independent frequencies of oscillation is an unusual property for a nonlinear oscillator. We find that a class of N coupled nonlinear Liénard type oscillators exhibit this interesting property. We show that a specific subset can be explicitly solved from which we demonstrate the existence of periodic and quasiperiodic solutions. Another set of N coupled nonlinear oscillators, possessing the amplitude independent nature of frequencies, is almost integrable in the sense that the system can be reduced to a single nonautonomous first order scalar differential equation which can be easily integrated numerically.     

Pancyclicity and extendability in strong products

In this paper, we first prove that for any connected graph G with at least two vertices, there is an integer m for which the strong product X⌅G^m has pancyclic ordering from each vertex. After characterizing the graphs G for which GX⌅K₂ is Hamiltonian, we determine a criterion for extendability of cycles. We also prove that if G is a connected, K_1.3-free graph with δ ≥ 2, then GX⌅XK₂ is fully cycle extendable as well as 1-edge Hamiltonian. © 1996 John Wiley & Sons, Inc.     

An Experimental Approach to Correcting Counting Errors in the Aerodynamic Particle Sizer (APS Model 3310)

This paper describes the different ways of analyzing the output of a real-time device for measuring and counting airborne particles, the aerodynamic particle sizer (APS). This instrument is very widely used in aerosol research throughout the world. It is a time-of-flight instrument in which a particle's measured transit time in the changing flow in a jet passing between two laser beams is converted to its aerodynamic diameter. As the particle passes between the two laser beams, two signal processors, the small particle processor (SPP) and the large particle processor (LPP), independently provide measures of the particle's transit time from the light pulses that are produced. This information is related to the aerodynamic particle diameter of the particle (d_ae) by means of calibration against ‘unit’ density (1000 kg/m³) spheres. If more than one particle is involved in the analysis of particle transit time, then it gives rise to coincidence effects, resulting in ‘phantom’ particle generation. The SPP is known to generate phantom counts, while the LPP is known to reduce phantom counts. A new method is described in this paper that gives guidance on how to deal with such coincidence problems. The principle is that it relies on additional information to obtain ‘correction factors’. In this case, well-established theory for the aspiration efficiencies of thin-walled aerosol sampling probes has been used along with corresponding experimental data obtained in a wind tunnel using the APS. Results using this method are compared with various other methods that have been tried in the past. The paper provides insights on to how the user can operate the APS to avoid counting errors like those described, and the advantages and limitations of different correction methods are discussed.     

Imaging in turbid media using quasi-ballistic photons

We study by means of experiments and Monte Carlo simulations, the scattering of light in random media, to determine the distance up to which photons travel along almost undeviated paths within a scattering medium, and are therefore capable of casting a shadow of an opaque inclusion embedded within the medium. Such photons are isolated by polarisation discrimination wherein the plane of linear polarisation of the input light is continuously rotated and the polarisation preserving component of the emerging light is extracted by means of a Fourier transform. This technique is a software implementation of lock-in detection. We find that images may be recovered to a depth far in excess of that predicted by the diffusion theory of photon propagation. To understand our experimental results, we perform Monte Carlo simulations to model the random walk behaviour of the multiply scattered photons. We present a new definition of a diffusing photon in terms of the memory of its initial direction of propagation, which we then quantify in terms of an angular correlation function. This redefinition yields the penetration depth of the polarisation preserving photons. Based on these results, we have formulated a model to understand shadow formation in a turbid medium, the predictions of which are in good agreement with our experimental results.     

On πd elastic scattering using aligned deuteron targets

A theoretical study is made of the advantages to be gained in polarizing a deuteron target by applying an external electric quadrupole field with non-zero asymmetry parameter for carrying outd(π, π)d experiments, in order to determine empirically the helicity amplitudes A, B, C, D characterizing the scattering, without any phase ambiguities.     

Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves

Flows in which shock waves and turbulence are present and interact dynamically occur in a wide range of applications, including inertial confinement fusion, supernovae explosion, and scramjet propulsion. Accurate simulations of such problems are challenging because of the contradictory requirements of numerical methods used to simulate turbulence, which must minimize any numerical dissipation that would otherwise overwhelm the small scales, and shock-capturing schemes, which introduce numerical dissipation to stabilize the solution. The objective of the present work is to evaluate the performance of several numerical methods capable of simultaneously handling turbulence and shock waves. A comprehensive range of high-resolution methods (WENO, hybrid WENO/central difference, artificial diffusivity, adaptive characteristic-based filter, and shock fitting) and suite of test cases (Taylor–Green vortex, Shu–Osher problem, shock-vorticity/entropy wave interaction, Noh problem, compressible isotropic turbulence) relevant to problems with shocks and turbulence are considered. The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation. The hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor. Artificial diffusivity methods in which the artificial bulk viscosity is based on the magnitude of the strain-rate tensor resolve vortical structures well but damp dilatational modes in compressible turbulence; dilatation-based artificial bulk viscosity methods significantly improve this behavior. For well-defined shocks, the shock fitting approach yields good results.     

Cellular Automata Models of Traffic Behavior in Presence of SpeedBreaking Structures

In this article, we study traffic flow in the presence ofspeed breaking structures. The speed breakers are typically used toreduce the local speed of vehicles near certain institutions such asschools and hospitals. Through a cellular automata model we study the impact of such structures on global traffic characteristics. The simulation results indicate that the presence of speed breakers could reduce the global flow under moderate global densities. However, under low and high global density traffic regime the presence of speed breakers does not have an impact on the global flow. Further the speed limit enforced by the speed breaker createsa phase distinction. For a given global density and slowdown probability, as the speed limit enforced by the speed breaker increases, the traffic moves from the reduced flow phase to maximum flow phase. This underlines the importance of proper design of these structures to avoid undesired flow restrictions.     

Polarization of line radiation in the presence of external electric quadrupole and uniform magnetic fields: II. Arbitrary orientation of magnetic field

In continuation of our earlier investigation (referred to hereafter as part I) where we considered the mathematically simple case of magnetic field orientation along the Z-axis of the principal axes frame (PAF) of the electric quadrupole field, we take up here the general problem of arbitrary orientation of the magnetic field with respect to the PAF, and investigate the nature of polarized line spectra of an atom making a transition from an upper level with spin J_u to a lower level with spin J_l. Explicit formulae for the emitted Stokes parameters are obtained and we discuss their physical significance by computing numerically the cases of transitions J_u=1→J_l=0 and . Specific features or signatures of the polarized line spectra are discussed as functions of the relevant physical parameters. The Stokes parameters are also analyzed in terms of the Zeeman term contributions and the cross-term contributions (which arise due to quantum interference).     

A micro-convection model for thermal conductivity of nanofluids

Increase in the specific surface area as well as Brownian motion are supposed to be the most significant reasons for the anomalous enhancement in thermal conductivity of nanofluids. This work presents a semi-empirical approach for the same by emphasizing the above two effects through micro-convection. A new way of modeling thermal conductivity of nanofluids has been explored which is found to agree excellently with a wide range of experimental data obtained by the present authors as well as the data published in literature