6 research outputs found
Spherically Symmetric Static Solutions in General Relativity
No full textThis thesis studies spherically symmetric static solutions in general relativity.
The most general form of matter in general relativity compatible with staticity and spherical
symmetry is anisotropic fluid. We study all possible algorithms that can generate all solutions
of the anisotropic fluid system via quadrature using all possible pairs of the four basic
functions of the system as input functions. We also study sub-algorithms that generate all
solutions that are regular at the center and, for this, we revisit the conditions for central
regularity for both isotropic and anisotropic systems and obtain all possible sets of equivalent
initial conditions for regularity by combining the Einstein equations with the previouslyknown geometric conditions of regularity. Our study provides a reformulation of an existing
algorithm for the system and provides its first regularity analysis. A surprisingly simple
new algorithm for the anisotropic system follows from our study that aligns itself with the
regularity conditions. This concordance enables us to find solutions that satisfy all the
other hard-to-achieve conditions of physical acceptability. Anisotropy has increasingly been
shown to be physically relevant in recent times. We keep the well-studied isotropic system
as a special case and use it as a frame of reference for measuring the success of our study of
the anisotropic system.
We then study the hydrostatic equilibrium of static (an)isotropic fluid spheres. From the
condition of hydrostatic equilibrium, we explore maps between (an)isotropic solutions with
the same density profiles and develop solution-generating techniques to find new solutions
from existing ones. We compare and give physical interpretations of several equilibrium
configurations in terms of fluid variables and provide several examples where the solutiongenerating theorems can be utilized to find physically acceptable anisotropic solutions. This
include a new exact solution that satisfies all physically desirable conditions.
Finally, we study light propagation in Kottler, i.e., Schwarzschild-(anti-)de Sitter, spacetime.
The metric of this spacetime is known in canonical coordinates and, unlike its Λ = 0 version
(i.e, Schwarzschild metric), this metric was not known in isotropic coordinates (in which the
constant-time hypersurfaces are flat). We obtain the Kottler metric in isotropic coordinates.
This further enables us to plot the refractive indices of Kottler spacetime and show that the
invariance of Snell’s law in ordinary geometric optics is analogous to projective equivalence
in isotropic static coordinates.
We conclude with a summary and some future directions
VHF-UHF Measurements of Lightning
No full textUniversal software radio peripheral (USRP) was utilized to receive the radiation produced by lightning flashes in VHF and UHF bands, with the bandwidth ranging from 2MHz to 8MHz. The software radio was programmed to record this radiation by integrating GPS clock and absolute timing. Moreover, two USRP N210 were employed to simultaneously record data at VHF and UHF bands with different programmable gain settings. This data was compared with the data from National Lightning Detection Network (available as location, type and peak current of lightning) and the magnetic sensor operating at LF (30 to 300 kHz). The output of USRP is the antenna displacement current ∂E/∂t (uncalibrated) and of LF magnetic sensor is the induced voltage ∂B/∂t. From comparison, the following results were obtained. K processes or regular pulse bursts in both cloud and cloud to ground discharges were clearly visible at UHF-VHF-LF. These processes were even visible at VHF with 0 dB gain, if superimposed on high magnitude slow (electric field change) processes such as J process probably. Distant Narrow bipolar pulses were observed with significant magnitude at VHF. Initial breakdown in cloud discharge was strong at LF and VHF but not significant at UHF. Instead the short pulses, probably stepped leaders, with 1 to 2.5 µs of time duration produced high magnitudes at UHF (while LF pulses remained small yet visible). Moreover, in few cloud discharges some processes occurring during final stage produced strong VHF-UHF radiation.</p
Advances in metal forming: expert system for metal forming
No full textThis comprehensive book offers a clear account of the theory and applications of advanced metal forming. It provides a detailed discussion of specific forming processes, such as deep drawing, rolling, bending extrusion and stamping. The author highlights recent developments of metal forming technologies and explains sound, new and powerful expert system techniques for solving advanced engineering problems in metal forming. In addition, the basics of expert systems, their importance and applications to metal forming processes, computer-aided analysis of metalworking processes, formability analysis, mathematical modeling and case studies of individual processes are presented
Architecture‑aware modeling of pedestrian dynamics
No full textThe spread of infectious diseases arises from complex interactions between disease dynamics and human behavior. Predicting the outcome of this complex system is difficult. Consequently, there has been a recent emphasis on comparing the relative risks of different policy
options rather than precise predictions. Here, one performs a parameter sweep to generate a large number of possible scenarios for human behavior under different policy options and identifies the relative risks of different decisions regarding policy or design choices. In particular, this approach has been used to identify effective approaches to social distancing in crowded locations, with pedestrian dynamics used to simulate the movement of individuals. This incurs a large computational load, though. The traditional approach of optimizing the implementation of existing mathematical models on parallel systems leads to a moderate improvement in computational performance. In contrast, we show that when dealing with human behavior, we can create a model from scratch that takes computer architectural features into account, yielding much higher performance without requiring complicated parallelization efforts. Our solution is based on two key observations. (i) Models do not capture human behavior as precisely as models for scientific phenomena describe natural processes. Consequently, there is some leeway in designing a model to suit the computational architecture. (ii) The result of a parameter sweep, rather than a single simulation, is the semantically meaningful result. Our model leverages these features to perform efficiently on CPUs and GPUs. We obtain a speedup factor of around 60 using this new model on two Xeon Platinum 8280 CPUs and a factor 125 speedup on 4 NVIDIA Quadro RTX 5000 GPUs over a parallel implementation of the existing model. The careful design of a GPU implementation makes it fast enough for real-time decision-making. We illustrate it on an application to COVID-19.Journal ArticleFinal article publishe
