A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Testing approximate theories of first-order phase transitions on the two-dimensional Potts model

The two-dimensional,q-state (q>4) Potts model is used as a testing ground for approximate theories of first-order phase transitions. In particular, the predictions of a theory analogous to the Ramakrishnan-Yussouff theory of freezing are compared with those of ordinary mean-field (Curie-Wiess) theory. It is found that the Curie-Weiss theory is a better approximation than the Ramakrishnan-Yussouff theory, even though the former neglects all fluctuations. It is shown that the Ramakrishnan-Yussouff theory overestimates the effects of fluctuations in this system. The reasons behind the failure of the Ramakrishnan-Yussouff approximation and the suitability of using the two-dimensional Potts model as a testing ground for these theories are discussed.

On the alleged equivalence of certain field theories

Abstract. We critically examine some recent claims that certain field theories with and without boson kinetic energy terms are equivalent. We point out that the crucial element in these claims is the finiteness or otherwise of the boson wavefunction renormalisation constant. We show that when this constant is finite, the equivalence proof offered in the literature fails in a direct way. When the constant is divergent, the claimed equivalence is only a consequence of improper use of divergent quantities.

On the relationship between finger width, velocity, and fluxes in thermohaline convection

Double-diffusive finger convection occurs in many natural processes.The theories for double-diffusive phenomena that exist at present consider systems with linear stratification in temperature and salinity. The double-diffusive systems with step change in salinity and temperature are, however, not amenable to simple stability analysis. Hence factors that control the width of the finger, velocity, and fluxes in systems that have step change in temperature and salinity have not been understood so far. In this paper we provide new physical insight regarding factors that influence finger convection in two-layer double-diffusive system through two-dimensional numerical simulations. Simulations have been carried out for density stability ratios (R-rho) from 1.5 to 10. For each density stability ratio, the thermal Rayleigh number (Ra-T) has been systematically varied from 7x10(3) to 7x10(8). Results from these simulations show how finger width, velocity, and flux ratios in finger convection are interrelated and the influence of governing parameters such as density stability ratio and the thermal Rayleigh number. The width of the incipient fingers at the time of onset of instability has been shown to vary as Ra-T-1/3. Velocity in the finger varies as Ra(T)1/3/R-rho. Results from simulation agree with the scale analysis presented in the paper. Our results demonstrate that wide fingers have lower velocities and flux ratios compared to those in narrow fingers. This result contradicts present notions about the relation between finger width and flux ratio. A counterflow heat-exchanger analogy is used in understanding the dependence of flux ratio on finger width and velocity.

Studies on the Tracking and Erosion Resistance of RTV Silicone Rubber Nanocomposite

One of the problems associated with outdoor polymeric insulators is tracking and erosion of the weathershed which can directly influence the reliability of the power system. Flame retardants are added to the base material to enhance its tracking and erosion resistance. Hydroxide fillers are regarded as the best flame retardants. This paper deals with studies related to nano - sized magnesium dihydroxide (MDH) and micron-sized Alumina Trihydrate (ATH) fillers as flame retardants in RTV silicone rubber. Tracking and erosion resistance studies were carried out on MDH and ATH silicone rubber composites using an inclined plane tracking and erosion (IPT) resistance tester. The MDH filled (5% by wt) composites performed much better than ATH composites in terms of eroded mass, depth of erosion, width and length of erosion. The eroded mass of MDH composite is 49.8 % that of ATH composite which can be attributed to high surface area and higher thermal stability of MDH nanofillers.

Effect of Polymer Grafting on the Bilayer Gel to Liquid-Crystalline Transition

Grafted polymers oil the surface of lipid membranes have potential applications in liposome-based drug delivery and Supported membrane systems. The effect of polymer grafting on the phase behavior of bilayers made up of single-tail lipids is investigated using dissipative particle dynamics. The bilayer is maintained in a tensionless state using a barostat. Simulations are carried Out by varying the grafting fraction, G(f), defined as the ratio of the number of polymer molecules to the number of lipid molecules, and the length of the lipid tails. At low G(f), the bilayer shows I sharp transition from the gel (L-beta) to the liquid-crystalline (L-alpha) phase. This main melting transition temperature is lowered as G(f) is increased, and above a critical value of G(f), the interdigitated L-beta I phase is observed prior to the main transition. The temperature range over which the intermediate phases are observed is a function of the lipid tail length and G(f). At higher grafting fractions, the presence of the L-beta I, phase is attributed to the increase in the area per head group due to the lateral pressure exerted by the polymer brush. The areal expansion and decrease in the melting temperatures as a function of G(f) were found to follow the scalings predicted by the self-consistent mean field theories for grafted polymer membranes. Our study shows that the grafted polymer density can be used to effectively control the temperature range and occurrence of a given bilayer phase.

On the DC Conductivity of HV DC Cable Insulation - Cautions in using the Empirical Models

The electrical conduction in insulating materials is a complex process and several theories have been suggested in the literature. Many phenomenological empirical models are in use in the DC cable literature. However, the impact of using different models for cable insulation has not been investigated until now, but for the claims of relative accuracy. The steady state electric field in the DC cable insulation is known to be a strong function of DC conductivity. The DC conductivity, in turn, is a complex function of electric field and temperature. As a result, under certain conditions, the stress at cable screen is higher than that at the conductor boundary. The paper presents detailed investigations on using different empirical conductivity models suggested in the literature for HV DC cable applications. It has been expressly shown that certain models give rise to erroneous results in electric field and temperature computations. It is pointed out that the use of these models in the design or evaluation of cables will lead to errors.

Polymer composite/nanocomposite processing and its effect on the electrical properties

One of the biggest challenges when considering polymer nanocomposites for electrical insulation applications lies in determining their electrical properties accurately, which in turn depend on several factors, primary being dispersion of particles in the polymer matrix. With this background, this paper reports an experimental study to understand the effects of different processing techniques on the dispersion of filler particles in the polymer matrix and their related effect on the dielectric properties of the composites. Polymer composite and nanocomposite samples for the study were prepared by mixing 10% by weight of commercially available TiO2 particles of two different sizes in epoxy using different processing methods. A considerable effect of the composite processing method could be seen in the dielectric properties of nanocomposites.

Immediate hypersensitivity to Parthenium hysterophorus. II. Clinical studies on the prevalence of parthenium rhinitis

The airborne pollen of the South American weed, Parthenium hysterophorus (American feverfew), accidentally introduced into India was found to be responsible for severe allergic rhinitis. A random clinical survey conducted on 2035 residents of Bangalore city with the aid of questionnaires and skin tests revealed that 7.1% of the study population was suffering from allergic rhinitis due to exposure to Parthenium pollen. Skin-prick tests performed on 1294 clinic patients suffering from nasobronchial allergy during the past 4 years have also shown that 42.5% were sensitive to Parthenium pollen. IgE and IgG antibodies specific for Parthenium pollen allergens were demonstrable in the sera of Parthenium-sensitive rhinitis patients. The specificity of these antibodies to Parthenium allergens was established by ELISA. A 7- to 11-fold higher stimulation was observed when lymphocytes from two Parthenium-sensitive rhinitis patients were treated in vitro with Parthenium pollen extract. To our knowledge, nowhere in the world has such a high incidence of allergic rhinitis due to a single pollen ever been reported.

On the evidence for the effect of bubble interference on cavitation noise

Cavitation-noise measurements from an axisymmetric body with ‘controlled’ generation of cavitation are reported. The control was achieved by seeding artificial nuclei in the boundary layer by electrolysis. It was possible to alter the number density of nuclei by varying the electrolysis voltage, polarity and the geometry of the electrode. From the observed trend of cavitation-noise data it is postulated that there exists an ‘interference effect’ which influences cavitation noise. When the nucleus-number density is high and cavitation numbers are low this effect is strong. Under these conditions the properties of cavitation noise are found to differ considerably from those expected based on theories concerning noise from single-spherical-bubble cavitation.

Influence of planning and governance on the level of urban services

A theoretical framework to analyse the interaction of planning and governance on the extent of outgrowth and level of services is proposed. An indicator framework for quantifying sprawl is also proposed and the same is operationalised for Bangalore. The indicators comprise spatial metrics (derived from temporal satellite remote sensing data) and other metrics obtained from a house-hold survey. The interaction of different indicators with respect to the core city and the outgrowth is determined by multi-dimensional scaling. The analysis reveals the underlying similarities (and dissimilarities) that relate with the different governance structures that prevail here. The paper concludes outlining the challenges in addressing urban sprawl while ensuring adequate level of services that planning and governance have to ensure towards achieving sustainable urbanisation.

Effect of AC&DC field on the dielectric response of (Pb,La)TiO3 thin films

Lanthanum doped lead titanate thin films are the potential candidates for the capacitors, actuators and pyroelectric sensor applications due to their excellent dielectric, and ferroelectric properties. Lanthanum doped lead titanate thin films are grown on platinum coated Si substrates by excimer laser ablation technique. A broad diffused phase transition with the maximum dielectric permittivity (ϵmax) shifting to higher temperatures with the increase of frequency, along with frequency dispersion below Tc, which are the signatures of the relaxor like characteristics were observed. The dielectric properties are investigated from −60°C to 200°C with an application of different dc fields. With increasing dc field, the dielectric constant is observed to reduce and phase transition temperature shifted to higher temperature. With the increased ac signal amplitude of the applied frequency, the magnitude of the dielectric constant is increasing and the frequency dispersion is observed in ferroelectric phase, whereas in paraelectric phase, there is no dispersion has been observed. The results are correlated with the existing theories.

Heterotic string on the CHL orbifold of K3

We study N = 2 compactifications of heterotic string theory on the CHL orbifold (K3 x T-2)/Z(N) with N = 2, 3, 5, 7. Z(N) acts as an automorphism on K3 together with a shift of 1/N along one of the circles of T-2. These compactifications generalize the example of the heterotic string on K3 x T-2 studied in the context of dualities in string theories. We evaluate the new supersymmetric index for these theories and show that their expansion can be written in terms of the McKay-Thompson series associated with the Z(N) automorphism embedded in the Mathieu group M-24. We then evaluate the difference in one-loop threshold corrections to the non-Abelian gauge couplings with Wilson lines and show that their moduli dependence is captured by Siegel modular forms related to dyon partition functions of N = 4 string theories.

Heterotic string on the CHL orbifold of K3

We study N = 2 compactifications of heterotic string theory on the CHL orbifold (K3 x T-2)/Z(N) with N = 2, 3, 5, 7. Z(N) acts as an automorphism on K3 together with a shift of 1/N along one of the circles of T-2. These compactifications generalize the example of the heterotic string on K3 x T-2 studied in the context of dualities in string theories. We evaluate the new supersymmetric index for these theories and show that their expansion can be written in terms of the McKay-Thompson series associated with the Z(N) automorphism embedded in the Mathieu group M-24. We then evaluate the difference in one-loop threshold corrections to the non-Abelian gauge couplings with Wilson lines and show that their moduli dependence is captured by Siegel modular forms related to dyon partition functions of N = 4 string theories.