The influence of the extent of excluded volume interactions on the linear viscoelastic properties of dilute polymer solutions

The Rouse model has recently been modified to take into account the excluded volume interactions that exist between various parts of a polymer chain by incorporating a narrow Gaussian repulsive potential between pairs of beads on the Rouse chain (cond-mat/0002448). The narrow Gaussian potential is characterized by two parameters: z* - which accounts for the strength of the interaction, and d* - which accounts for the extent of the interaction. In the limit of d* going to zero, the narrow Gaussian potential tends to the more commonly used delta-function repulsive potential. The influence of the parameter d*, in the limit of infinite chain length, on equilibrium and linear viscoelastic properties, and on universal ratios involving these properties, is examined here. A renormalization group calculation of the end-to-end vector suggests that the value chosen for the variable d* will not affect critical exponents, or universal ratios. A similar trend is also observed for results obtained with an approximate solution, which is based on the assumption that the non-equilibrium configurational distribution function is Gaussian.Comment: 23 pages, 6 figures, LaTe

The Kinetic Theory of Dilute Solutions of Flexible Polymers: Hydrodynamic Interaction

The development of a coherent conceptual basis for the treatment of non-linear microscopic phenomena, such as, hydrodynamic interaction, finite extensibility, excluded volume and internal viscosity, in molecular theories of dilute polymer solutions, is discussed. In particular, recent advances in the treatment of hydrodynamic interaction are reviewed, and the successive refinements which have ultimately led to the prediction of universal viscometric functions in theta solvents are highlighted.Comment: 31 pages, 1 figure, latex, To appear in: Advances in the Flow and Rheology of Non-Newtonian Fluids, D. A. Siginer, D. D. Kee, R. P Chabra, eds., Elsevier Science, 199

Controlled Quantum Teleportation of Superposed Coherent State using GHZ Entangled Coherent State

Controlled quantum teleportation of superposed coherent states using GHZ entangled 3-mode coherent states is studied. Proposed scheme can be implemented experimentally using linear optical components such as a symmetric lossless beam splitter, two phase-shifters and two photon counters. Fidelity is found close to unity for appreciable mean number of photons in coherent states and is 0.99 for mean photon number equal to two.Comment: A preliminary version was presented at National Laser Symposium-26 held at BARC, Mumbai, in December 201

Saturation of number variance in embedded random matrix ensembles

We study fluctuation properties of embedded random matrix ensembles of non-interacting particles. For ensemble of two non-interacting particle systems, we find that unlike the spectra of classical random matrices, correlation functions are non-stationary. In the locally stationary region of spectra, we study the number variance and the spacing distributions. The spacing distributions follow the Poisson statistics which is a key behavior of uncorrelated spectra. The number variance varies linearly as in the Poisson case for short correlation lengths but a kind of regularization occurs for large correlation lengths, and the number variance approaches saturation values. These results are known in the study of integrable systems but are being demonstrated for the first time in random matrix theory. We conjecture that the interacting particle cases, which exhibit the characteristics of classical random matrices for short correlation lengths, will also show saturation effects for large correlation lengths.Comment: 14 pages, 13 figure

On the Polarization of non-Guassian optical quantum field: higher-order optical-polarization

Polarization of light signifies transversal, anisotropic and asymmetrical statistical property of electromagnetic radiation about direction of propagation. Traditionally, optical-polarization is characterized by Stokes theory susceptible to be insufficient in assessing polarization structure of optical quantum fields and, also, does not decipher twin characteristic polarization parameters (ratio of real amplitudes and difference in phases). An alternative way, in spirit of classical description of optical-polarization, is introduced which can be generalized to deal higher-order polarization of quantum light, particularly, prepared in non-Guassian Schrodinger Cat or Cat-like states and entangled bi-modal coherent states. On account of pseudo mono-modal or multi-modal nature of such optical quantum field, higher-order polarization is seen to be highly sensitive to the basis of description.Comment: 15 pages, To appear in Annals of Physic

Viscoelastic fluid flow in a 2D channel bounded above by a deformable finite thickness elastic wall

The steady flow of three viscoelastic fluids (Oldroyd-B, FENE-P, and Owens model for blood) in a two-dimensional channel, partly bound by a deformable, finite thickness neo-Hookean solid, is computed. The limiting Weissenberg number beyond which computations fail to converge is found to increase with increasing dimensionless solid elasticity parameter {\Gamma}, following the trend Owens > FENE- P > Oldroyd-B. The highly shear thinning nature of Owens model leads to the elastic solid always collapsing into the channel, for the wide range of values of {\Gamma} considered here. In the case of the FENE-P and Oldroyd-B models, however, the fluid-solid interface can be either within the channel, or bulge outwards, depending on the value of {\Gamma}. This behaviour differs considerably from predictions of earlier models that treat the deformable solid as a zero-thickness membrane, in which case the membrane always lies within the channel. The capacity of the solid wall to support both pressure and shear stress, in contrast to the zero-thickness membrane that only responds to pressure, is responsible for the observed difference. Compar- ison of the stress and velocity fields in the channel for the three viscoelastic fluids, with the predictions for a Newtonian fluid, reveals that shear thinning rather than elasticity is the key source of the observed differences in behaviour.Comment: 32 pages, 17 figures, accepted for publication in J. Non-Newton. Fluid Mec

A Critical Survey Of Privacy Infrastructures

Over the last two decades, the scale and complexity of the Internet and its associated technologies built on the World Wide Web has grown exponentially with access to Internet as a facility occupying a prime place with other amenities of modern lives. In years to come, usage of Internet may unravel more pleasant surprises for us as far as novelty in its usage is concerned. As a democratic function of Internet, and relying on the open model on which it has been built, there has been concerted efforts in the direction of privacy protection and use of privacy enhancing tools which have gained tangible traction. Innovation in use of VPN, TLS/SSL and cryptographic tools are a testimony to it. Another popular tool is Tor, which has gained widespread popularity as it is being increasingly used by anonymity seeking users to effectively maintain their discretion while surfing the web. However, there is a darker side to increased proliferation of Internet in our everyday routine. We are certainly not living in a utopian age and there are potentials of misuse of Internet as well. Across every nook and cranny of Internet's sprawling virtual world, there are cyber criminals lurking n dangerous alleys to use the very same Internet as malevolent tool to abuse it and cause financial, physical and social harm to ordinary people. Failing to manage the widespread spawning of World Wide Web has rendered it weak against misuse. In last few decades especially, Internet has been inundated with malware, ransomware, viruses, Trojans, illegal spy tools and what not created with malignant sentiments. In this paper, we will analyze few of the subverting privacy infrastructures

Degree of Polarization in Quantum Optics through second generalization of Intensity

Classical definition of degree of polarization is expressed in quantum domain by replacing intensities through quantum mechanical average values of relevant number operators and is viewed as first generalization of Intensity. This definition assigns inaccurately the unpolarized status to some typical optical fields such as amplitude coherent phase randomized and hidden polarized, which are not truly unpolarized light. The apparent paradoxical trait is circumvented by proposing a new definition of degree of polarization in Quantum Optics through second generalization of Intensity. The correspondence of new degree of polarization to usual degree of polarization in Quantum Optics is established. It is seen that the two definitions disagree significantly for intense optical fields but coincides for weak light (thermal light) or for optical fields in which occupancy of photons in orthogonal mode is very feeble. Our proposed definition of degree of polarization, similar to other proposals in literature, reveals an interesting feature that states of polarization of optical quantum fields depend upon the average photons (intensity) present therein.Comment: 17 pages, Accepted in PR

Universal consequences of the presence of excluded volume interactions in dilute polymer solutions undergoing shear flow

The role of solvent quality in determining the universal material properties of dilute polymer solutions undergoing steady simple shear flow is examined. A bead-spring chain representation of the polymer molecule is used, and the influence of solvent molecules on polymer conformations is modelled by a narrow Gaussian excluded volume potential that acts pair-wise between the beads of the chain. Brownian dynamics simulations data, acquired for chains of finite length, and extrapolated to the limit of infinite chain length, are shown to be model independent. This feature of the narrow Gaussian potential, which leads to results identical to a $\delta$-function repulsive potential, enables the prediction of both universal crossover scaling functions and asymptotic behavior in the excluded volume limit. Universal viscometric functions, obtained by this procedure, are found to exhibit increased shear thinning with increasing solvent quality. In the excluded volume limit, they are found to obey power law scaling with the characteristic shear rate $\beta$, in close agreement with previously obtained renormalization group results. The presence of excluded volume interactions is also shown to lead to a weakening of the alignment of the polymer chain with the flow direction.Comment: 14 pages, 14 figures. Minor revision: After Eq. (14): angle pi/4 at equilibrium -> close to equilibrium. To appear in J. Chem. Phy

Coil-Stretch Transition and the Break Down of Continuum Models

The breakdown of finite element (FEM) computations for the flow of an Oldroyd-B fluid around a cylinder confined between parallel plates, at Weissenberg numbers Wi = O(1), is shown to arise due to a coil-stretch transition experienced by polymer molecules traveling along the centerline in the wake of the cylinder. With increasing Wi, the coil-stretch transition leads to an unbounded growth in the stress maximum in the cylinder wake. Finite element computations for a FENE-P fluid reveal that, although polymer molecules undergo a coil-stretch transition in the cylinder wake, the mean extension of the molecules saturates to a value close to the fully extended length, leading to bounded stresses with increasing Wi. The existence of a coil-stretch transition has been deduced by examining the behavior of ultra-dilute Oldroyd-B and FENE-P fluids. In this case, the solution along the centerline in the cylinder wake can be obtained exactly since the velocity field is uncoupled from the stress and conformation tensor fields. Estimation of the number of finite elements required to achieve convergence reveals the in-feasibility of obtaining solutions for the Oldroyd-B model for Wi > 1.Comment: 36 pages, 15 figures, Submitted to Journal of Rheolog