Heat transport by laminar boundary layer flow with polymers

Motivated by recent experimental observations, we consider a steady-state Prandtl-Blasius boundary layer flow with polymers above a slightly heated horizontal plate and study how the heat transport might be affected by the polymers. We discuss how a set of equations can be derived for the problem and how these equations can be solved numerically by an iterative scheme. By carrying out such a scheme, we find that the effect of the polymers is equivalent to producing a space-dependent effective viscosity that first increases from the zero-shear value at the plate then decreases rapidly back to the zero-shear value far from the plate. We further show that such an effective viscosity leads to an enhancement in the drag, which in turn leads to a reduction in heat transport.Comment: 7 pages, 8 figures, 1 tabl

Exploration of Effective Spatial Performance of Accessible Neighbourhood Green (Ang), Including its Proportion and Standard Distance from User in Dhanmondi Residential Area, Dhaka

Urban physical context can be analyzed across three key matrixes (3-P) among others i.e. place, path, and people. So, pragmatic analysis of spatial effective performances connecting 3-P, require provoking frequency of people’s experience. Acknowledging this issue, the demand for accessible neighbourhood green (ANG) at an appropriate distance becomes the primary concern to enhance the quality of life and liveability in a city. However, with the continued urban growth and densification, the discrepancy between the demand and supply of open space continues to vary requiring adjustments to remain responsive. The real-life circumstance results in a shortage of parks and open areas in terms of demand and supply within accessible distance in Dhaka city. This paper intends to examine this issue through the case of the planned Dhanmondi Residential Area (DRA) in Dhaka. Despite having provision of multiple open spaces in DRA, visitor’s frequency varies due to age and gender group accessibility conditions and varying distances. Considering existing spatial norms set by Detail Area Plan (DAP), Dhaka structure plan (DSP), and numerous research works on Dhaka open spaces, the major inquiry posed here is whether these open spaces are appropriate for DRA or not. Therefore, the objective of this paper focuses on examining the quality of the physical environment of Neighbourhood public open spaces termed here as accessible neighbourhood green (ANG) in DRA to examine their adequacy concerning proportion and distance synchronized with the frequency of visits. The initial part of the paper focuses on conceptualizing the problem vis-à-vis the existing scenario.  Surveys and interviews have been conducted to assess people’s perceptions in terms of comfort, accessibility, sociability, and user frequency aligned with proximity. The result indicates that the provision of one appropriate ANG within two or three standard blocks apart contribute to enhancing the quality of life for the city dwellers and their liveability

Unconventional Gravitational Excitation of a Schwarzschild Black Hole

Besides the well-known quasinormal modes, the gravitational spectrum of a Schwarzschild black hole also has a continuum part on the negative imaginary frequency axis. The latter is studied numerically for quadrupole waves. The results show unexpected striking behavior near the algebraically special frequency $\Omega=-4i$. This reveals a pair of unconventional damped modes very near $\Omega$, confirmed analytically.Comment: REVTeX4, 4pp, 6 EPS figure files. N.B.: "Alec" is my first, and "Maassen van den Brink" my family name. v2: better pole placement in Fig. 1. v3: fixed Refs. [9,20]. v4: added context on "area quantum" research; trimmed one Fig.; textual clarification

High-Order Contamination in the Tail of Gravitational Collapse

It is well known that the late-time behaviour of gravitational collapse is {\it dominated} by an inverse power-law decaying tail. We calculate {\it higher-order corrections} to this power-law behaviour in a spherically symmetric gravitational collapse. The dominant ``contamination'' is shown to die off at late times as $M^2t^{-4}\ln(t/M)$. This decay rate is much {\it slower} than has been considered so far. It implies, for instance, that an `exact' (numerical) determination of the power index to within $\sim 1$ requires extremely long integration times of order $10^4 M$. We show that the leading order fingerprint of the black-hole electric {\it charge} is of order $Q^2t^{-4}$.Comment: 12 pages, 2 figure

Mode-coupling in rotating gravitational collapse: Gravitational and electromagnetic perturbations

We consider the late-time evolution of {\it gravitational} and electromagnetic perturbations in realistic {\it rotating} Kerr spacetimes. We give a detailed analysis of the mode-coupling phenomena in rotating gravitational collapse. A consequence of this phenomena is that the late-time tail is dominated by modes which, in general, may have an angular distribution different from the original one. In addition, we show that different types of fields have {\it different} decaying rates. This result turns over the traditional belief (which has been widely accepted during the last three decades) that the late-time tail of gravitational collapse is universal.Comment: 16 page

Wave Propagation in Gravitational Systems: Late Time Behavior

It is well-known that the dominant late time behavior of waves propagating on a Schwarzschild spacetime is a power-law tail; tails for other spacetimes have also been studied. This paper presents a systematic treatment of the tail phenomenon for a broad class of models via a Green's function formalism and establishes the following. (i) The tail is governed by a cut of the frequency Green's function $\tilde G(\omega)$ along the $-$~Im~$\omega$ axis, generalizing the Schwarzschild result. (ii) The $\omega$ dependence of the cut is determined by the asymptotic but not the local structure of space. In particular it is independent of the presence of a horizon, and has the same form for the case of a star as well. (iii) Depending on the spatial asymptotics, the late time decay is not necessarily a power law in time. The Schwarzschild case with a power-law tail is exceptional among the class of the potentials having a logarithmic spatial dependence. (iv) Both the amplitude and the time dependence of the tail for a broad class of models are obtained analytically. (v) The analytical results are in perfect agreement with numerical calculations