Abstract: In the present work, we revisit the collapse process of a spherically symmetric homogeneous scalar field (in FRW background) minimally coupled to gravity, when the phase-space deformations are taken into account. Such a deformation is mathematically introduced as a particular type of noncommutativity between the canonical momenta of the scale factor and of the scalar field. In the absence of such deformation, the collapse culminates in a spacetime singularity. However, when the phase-space is deformed, we find that the singularity is removed by a non-singular bounce, beyond which the collapsing cloud re-expands to infinity. More precisely, for negative values of the deformation parameter, we identify the appearance of a negative pressure, which decelerates the collapse to finally avoid the singularity formation. While in the un-deformed case, the horizon curve monotonically decreases to finally cover the singularity, in the deformed case the horizon has a minimum value that this value depends on deformation parameter and initial configuration of the collapse. Such a setting predicts a threshold mass for black hole formation in stellar collapse and manifests the role of non-commutative geometry in physics and especially in stellar collapse and supernova explosion.
Abstract: Understanding how airborne pathogens are
transported through hospital wards is essential for determining the
infection risk to patients and healthcare workers. This study utilizes
Computational Fluid Dynamics (CFD) simulations to explore
possible pathogen transport within a six-bed partitioned Nightingalestyle
hospital ward.
Grid independence of a ward model was addressed using the Grid
Convergence Index (GCI) from solutions obtained using three fullystructured
grids. Pathogens were simulated using source terms in
conjunction with a scalar transport equation and a RANS turbulence
model. Errors were found to be less than 4% in the calculation of air
velocities but an average of 13% was seen in the scalar field.
A parametric study of variations in the pathogen release point
illustrated that its distribution is strongly influenced by the local
velocity field and the degree of air mixing present.
Abstract: This research paper is based upon the simulation of
gradient of mathematical functions and scalar fields using MATLAB.
Scalar fields, their gradient, contours and mesh/surfaces are
simulated using different related MATLAB tools and commands for
convenient presentation and understanding. Different mathematical
functions and scalar fields are examined here by taking their
gradient, visualizing results in 3D with different color shadings and
using other necessary relevant commands. In this way the outputs of
required functions help us to analyze and understand in a better way
as compared to just theoretical study of gradient.