Effect of density discontinuity on Alfvén internal gravity waves

The stability characteristics of Alfvén Internal gravity waves for an inviscid, nondissipative, Boussinesq fluid undergoing shear in the presence of a density discontinuity with and without a rigid boundary is studied.

Structural dependence of density in high molecular weight esters

The effect of molecular structure on density has been examined in high molecular weight esters (molecular weight 300-900), having varying degrees of branching. Densities were calculated from an empirical equation, which agrees well with the experimental values (error +/-1.5%), irrespective of branching. Since density is related to molecular packing and hence to the molecular rotation, in n-alkanes, the glass transition temperature (T(g)) and density both increase with molecular weight, and hence T(g) is directly related to the density. The esters exhibit a complex behavior. In linear esters the T(g) decreases with molecular weight which is explained from group contribution and molecular interactions. In the +-branched esters, however, T(g) decreases with molecular weight until the molecular weight reaches 600 and increases sharply thereafter. The Y-branched esters show an intermediate behavior. The dependence of T(g) on molecular weight has been explained from the segmental motion.

Effect of density variation and non-covalent functionalization on the compressive behavior of carbon nanotube arrays

Arrays of aligned carbon nanotubes (CNTs) have been proposed for different applications, including electrochemical energy storage and shock-absorbing materials. Understanding their mechanical response, in relation to their structural characteristics, is important for tailoring the synthesis method to the different operational conditions of the material. In this paper, we grow vertically aligned CNT arrays using a thermal chemical vapor deposition system, and we study the effects of precursor flow on the structural and mechanical properties of the CNT arrays. We show that the CNT growth process is inhomogeneous along the direction of the precursor flow, resulting in varying bulk density at different points on the growth substrate. We also study the effects of non-covalent functionalization of the CNTs after growth, using surfactant and nanoparticles, to vary the effective bulk density and structural arrangement of the arrays. We find that the stiffness and peak stress of the materials increase approximately linearly with increasing bulk density.

Absolute/Convective Instability Transition in a Backward Facing Step Combustor: Fundamental Mechanism and Influence of Density Gradient

Hydrodynamic instabilities of the flow field in lean premixed gas turbine combustors can generate velocity perturbations that wrinkle and distort the flame sheet over length scales that are smaller than the flame length. The resultant heat release oscillations can then potentially result in combustion instability. Thus, it is essential to understand the hydrodynamic instability characteristics of the combustor flow field in order to understand its overall influence on combustion instability characteristics. To this end, this paper elucidates the role of fluctuating vorticity production from a linear hydrodynamic stability analysis as the key mechanism promoting absolute/convective instability transitions in shear layers occurring in the flow behind a backward facing step. These results are obtained within the framework of an inviscid, incompressible, local temporal and spatio-temporal stability analysis. Vorticity fluctuations in this limit result from interaction between two competing mechanisms-(1) production from interaction between velocity perturbations and the base flow vorticity gradient and (2) baroclinic torque in the presence of base flow density gradients. This interaction has a significant effect on hydrodynamic instability characteristics when the base flow density and velocity gradients are colocated. Regions in the space of parameters characterizing the base flow velocity profile, i.e., shear layer thickness and ratio of forward to reverse flow velocity, corresponding to convective and absolute instability are identified. The implications of the present results on understanding prior experimental studies of combustion instability in backward facing step combustors and hydrodynamic instability in other flows such as heated jets and bluff body stabilized flames is discussed.

Quantitative estimation of density variation in high-speed flows through inversion of the measured wavefront distortion

A simple method employing an optical probe is presented to measure density variations in a hypersonic flow obstructed by a test model in a typical shock tunnel. The probe has a plane light wave trans-illuminating the flow and casting a shadow of a random dot pattern. Local slopes of the distorted wavefront are obtained from shifts of the dots in the pattern. Local shifts in the dots are accurately measured by cross-correlating local shifted shadows with the corresponding unshifted originals. The measured slopes are suitably unwrapped by using a discrete cosine transform based phase unwrapping procedure and also through iterative procedures. The unwrapped phase information is used in an iterative scheme for a full quantitative recovery of density distribution in the shock around the model through refraction tomographic inversion. Hypersonic flow field parameters around a missile shaped body at a free-stream Mach number of 5.8 measured using this technique are compared with the numerically estimated values. (C) 2014 Society of Photo-Optical Instrumentation Engineers (SPIE)

The cold mode: a phenomenological model for the evolution of density perturbations in the intracluster medium

Cool cluster cores are in global thermal equilibrium but are locally thermally unstable. We study a non-linear phenomenological model for the evolution of density perturbations in the intracluster medium (ICM) due to local thermal instability and gravity. We have analysed and extended a model for the evolution of an overdense blob in the ICM. We find two regimes in which the overdense blobs can cool to thermally stable low temperatures. One for large t(cool)/t(ff) (t(cool) is the cooling time and t(ff) is the free-fall time), where a large initial overdensity is required for thermal runaway to occur; this is the regime which was previously analysed in detail. We discover a second regime for t(cool)/t(ff) less than or similar to 1 (in agreement with Cartesian simulations of local thermal instability in an external gravitational field), where runaway cooling happens for arbitrarily small amplitudes. Numerical simulations have shown that cold gas condenses out more easily in a spherical geometry. We extend the analysis to include geometrical compression in weakly stratified atmospheres such as the ICM. With a single parameter, analogous to the mixing length, we are able to reproduce the results from numerical simulations; namely, small density perturbations lead to the condensation of extended cold filaments only if t(cool)/t(ff) less than or similar to 10.

ABSOLUTE/CONVECTIVE INSTABILITY TRANSITION IN A BACKWARD FACING STEP COMBUSTOR: FUNDAMENTAL MECHANISM AND INFLUENCE OF DENSITY GRADIENT

Hydrodynamic instabilities of the flow field in lean premixed gas turbine combustors can generate velocity perturbations that wrinkle and distort the flame sheet over length scales that are smaller than the flame length. The resultant heat release oscillations can then potentially result in combustion instability. Thus, it is essential to understand the hydrodynamic instability characteristics of the combustor flow field in order to understand its overall influence on combustion instability characteristics. To this end, this paper elucidates the role of fluctuating vorticity production from a linear hydrodynamic stability analysis as the key mechanism promoting absolute/convective instability transitions in shear layers occurring in the flow behind a backward facing step. These results are obtained within the framework of an inviscid, incompressible, local temporal and spatio-temporal stability analysis. Vorticity fluctuations in this limit result from interaction between two competing mechanisms - (1) production from interaction between velocity perturbations and the base flow vorticity gradient and (2) baroclinic torque in the presence of base flow density gradients. This interaction has a significant effect on hydrodynamic instability characteristics when the base flow density and velocity gradients are co-located. Regions in the space of parameters characterizing the base flow velocity profile, i.e. shear layer thickness and ratio of forward to reverse flow velocity, corresponding to convective and absolute instability are identified. The implications of the present results on prior observations of flow instability in other flows such as heated jets and bluff-body stabilized flames is discussed.

Maximum-entropy calculation of the electron density at 4 A resolution of Pf1 filamentous bacteriophage

A 4 A electron-density map of Pf1 filamentous bacterial virus has been calculated from x-ray fiber diffraction data by using the maximum-entropy method. This method produces a map that is free of features due to noise in the data and enables incomplete isomorphous-derivative phase information to be supplemented by information about the nature of the solution. The map shows gently curved (banana-shaped) rods of density about 70 A long, oriented roughly parallel to the virion axis but slewing by about 1/6th turn while running from a radius of 28 A to one of 13 A. Within these rods, there is a helical periodicity with a pitch of 5 to 6 A. We interpret these rods to be the helical subunits of the virion. The position of strongly diffracted intensity on the x-ray fiber pattern shows that the basic helix of the virion is right handed and that neighboring nearly parallel protein helices cross one another in an unusual negative sense.

On optimum stratification with proportional allocation for a class of pareto distributions

Cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0001.gif rule [Singh (1975)] has been suggested in the literature for finding approximately optimum strata boundaries for proportional allocation, when the stratification is done on the study variable. This paper shows that for the class of density functions arising from the Wang and Aggarwal (1984) representation of the Lorenz Curve (or DBV curves in case of inventory theory), the cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0002.gif rule in place of giving approximately optimum strata boundaries, yields exactly optimum boundaries. It is also shown that the conjecture of Mahalanobis (1952) “. . .an optimum or nearly optimum solutions will be obtained when the expected contribution of each stratum to the total aggregate value of Y is made equal for all strata” yields exactly optimum strata boundaries for the case considered in the paper.

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.

Laboratory Test Methods For The Evaluation Of Flammability Of Polymers

Combustion is a complex phenomena involving a multiplicity of variables. Some important variables measured in flame tests follow [1]. In order to characterize ignition, such related parameters as ignition time, ease of ignition, flash ignition temperature, and self-ignition temperature are measured. For studying the propagation of the flame, parameters such as distance burned or charred, area of flame spread, time of flame spread, burning rate, charred or melted area, and fire endurance are measured. Smoke characteristics are studied by determining such parameters as specific optical density, maximum specific optical density, time of occurrence of the densities, maximum rate of density increase, visual obscuration time, and smoke obscuration index. In addition to the above variables, there are a number of specific properties of the combustible system which could be measured. These are soot formation, toxicity of combustion gases, heat of combustion, dripping phenomena during the burning of thermoplastics, afterglow, flame intensity, fuel contribution, visual characteristics, limiting oxygen concentration (OI), products of pyrolysis and combustion, and so forth. A multitude of flammability tests measuring one or more of these properties have been developed [2]. Admittedly, no one small scale test is adequate to mimic or assess the performance of a plastic in a real fire situation. The conditions are much too complicated [3, 4]. Some conceptual problems associated with flammability testing of polymers have been reviewed [5, 6].

AC conductivity of a quantum Hall line junction

We present a microscopic model for calculating the AC conductivity of a finite length line junction made up of two counter-or co-propagating single mode quantum Hall edges with possibly different filling fractions. The effect of density-density interactions and a local tunneling conductance (sigma) between the two edges is considered. Assuming that sigma is independent of the frequency omega, we derive expressions for the AC conductivity as a function of omega, the length of the line junction and other parameters of the system. We reproduce the results of Sen and Agarwal (2008 Phys. Rev. B 78 085430) in the DC limit (omega -> 0), and generalize those results for an interacting system. As a function of omega, the AC conductivity shows significant oscillations if sigma is small; the oscillations become less prominent as sigma increases. A renormalization group analysis shows that the system may be in a metallic or an insulating phase depending on the strength of the interactions. We discuss the experimental implications of this for the behavior of the AC conductivity at low temperatures.

Dispersion of the stress-optic coefficient in glasses

The stress-optic coefficient (n3/2)(q11-q12) has been determined for a series of 18 optical glasses of different compositions in the wavelength range 5700-3200 Å. The coefficients are negative for all the glasses except for a high-lead-content glass of density 6·7 and refractive index 1·89. The numerical value of the coefficient decreases as one proceeds to the ultraviolet. This behaviour is just the opposite of what is observed in fused silica. By applying Mueller's theory, the strain polarizability constant and its dispersion have been evaluated.

Vertex-Fused Metallaborane Clusters: Synthesis, Characterization and Electronic Structure of [(eta(5)-C5Me5Mo)(3)MoB9H18]

The reaction of the [(eta(5)-C5Me5)MoCl4] complex with [LiBH4 - TH F] in toluene at - 70 degrees C, followed by pyrolysis at 110 degrees C, afforded dark brown [(eta(5)-C5Me5Mo)(3)MoB9H18], 2, in parallel with the known [(eta(5)-C5Me5Mo)(2)B5H9], 1. Compound 2 has been characterized in solution by H-1, B-11, and C-13 NMR spectroscopy and elemental analysis, and the structural types were unequivocally established by crystallographic studies. The title compound represents a novel class of vertex-fused clusters in which a Mo atom has been fused in a perpendicular fashion between two molybdaborane clusters. Electronic structure calculations employing density functional theory yield geometries in agreement with the structure determinations, and on grounds of density functional theory calculations, we have analyzed the bonding patterns in the structure,