arXiv subjects

F. Hussain

Publications and source records attributed to F. Hussain.

13 recordsLinked to original sources

arXiv2021

Study of Generalized Lema\^ıtre-Tolman-Bondi Spacetime in Palatini $f(R)$ Gravity

This paper aims to analyze the generalization of Lema\^ıtre-Tolman-Bondi (LTB) spacetime for dissipative dust under the influence of Palatini $f(R)$ gravity. We explore the modified field equations, kinematical variables, and mass function in this scenario. We construct Bianchi identities using conservation and differential equations for shear, expansion, and curvature scalar in the background of Palatini $f(R)$ gravity. We calculated the scalar functions coming from the orthogonal decomposition of the Riemann tensor in this framework. These scalar functions known as structure scalars have been explored for LTB spacetime using modified field equations. The symmetric properties of LTB spacetime have been discussed using two subcases. We found that generalized LTB spacetime has properties comparable with LTB and obtained structure scalars in both cases which have a similar dependence on a material profile even in Palatini gravity.

gr-qc↗

arXiv2021

Explainable Artificial Intelligence (XAI): An Engineering Perspective

The remarkable advancements in Deep Learning (DL) algorithms have fueled enthusiasm for using Artificial Intelligence (AI) technologies in almost every domain; however, the opaqueness of these algorithms put a question mark on their applications in safety-critical systems. In this regard, the `explainability' dimension is not only essential to both explain the inner workings of black-box algorithms, but it also adds accountability and transparency dimensions that are of prime importance for regulators, consumers, and service providers. eXplainable Artificial Intelligence (XAI) is the set of techniques and methods to convert the so-called black-box AI algorithms to white-box algorithms, where the results achieved by these algorithms and the variables, parameters, and steps taken by the algorithm to reach the obtained results, are transparent and explainable. To complement the existing literature on XAI, in this paper, we take an `engineering' approach to illustrate the concepts of XAI. We discuss the stakeholders in XAI and describe the mathematical contours of XAI from engineering perspective. Then we take the autonomous car as a use-case and discuss the applications of XAI for its different components such as object detection, perception, control, action decision, and so on. This work is an exploratory study to identify new avenues of research in the field of XAI.

cs.LG↗

arXiv2019

Dynamics of fracturing saturated porous media and self-organization of rupture

Analytical solutions and a vast majority of numerical ones for fracture propagation in saturated porous media yield smooth behavior while experiments, field observations and a few numerical solutions reveal stepwise crack advancement and pressure oscillations. To explain this fact, we invoke self-organization of rupture observed in fracturing solids, both dry and fully saturated, when two requirements are satisfied: i) the external drive has a much slower timescale than fracture propagation; and ii) the increment of the external load (drive) is applied only when the internal rearrangement of fracture is over. These requirements are needed to obtain clean Self Organised Criticality (SOC) in quasi-static situations. They imply that there should be no restriction on the fracture velocity i.e. algorithmically the fracture advancement rule should always be independent of the crack velocity. Generally, this is not the case when smooth answers are obtained which are often unphysical. Under the above conditions hints of Self Organized Criticality are evident in heterogeneous porous media in quasi-static conditions using a lattice model, showing stepwise advancement of the fracture and pressure oscillations. We extend this model to incorporate inertia forces and show that this behavior still holds. By incorporating the above requirements in numerical fracture advancement algorithms for cohesive fracture in saturated porous continua we also reproduce stepwise advancements and pressure oscillations both in quasi-static and dynamic situations. Since dynamic tests of dry specimens show that the fracture advancement velocity is not constant we replicate such an effect with a model of a debonding beam on elastic foundation. This is the first step before introducing the interaction with a fluid.

cs.CE↗

arXiv2004

Bounds on Four-Fermion Contact Interactions Induced by String Resonances

Based on tree-level open-string scattering amplitudes in the low string-scale scenario, we derive the massless fermion scattering amplitudes. The amplitudes are required to reproduce those of the Standard Model at tree level in the low energy limit. We then obtain four-fermion contact interactions by expanding in inverse powers of the string scale and explore the constraints on the string scale from low energy data. The Chan-Paton factors and the string scale are treated as free parameters. We find that data from the neutral and charged current processes at HERA, Drell-Yan process at the Tevatron, and from LEP-II put lower bounds on the string scale M_S >= 0.9-1.3 TeV for typical values of the Chan-Paton factors, which are comparable to Tevatron bounds on Z' and W' masses.

hep-ph↗

arXiv2002

Covariant L-S Scheme for the effective N*NM couplings

For excited nucleon states $N^*$ of arbitrary spin coupling to nucleon (N) and meson (M), we propose a Lorentz covariant orbital-spin (L-S) scheme for the effective $N^*NM$ couplings. To be used for the partial wave analysis of various $N^*$ production and decay processes, it combines merits of two conventional schemes, {\sl i.e.}, covariant effective Lagrangian approach and multipole analysis with amplitudes expanded according to angular momentum L. As examples, explicit formulae are given for $N^*\to Nπ$, $N^*\to Nω$ and $ψ\to N^*\bar N$ processes which are under current experimental studies.

hep-ph↗

arXiv1999

One-pion transitions between heavy baryons in the constituent quark model

Single pion transitions of S wave to S wave, P wave to S wave and P wave to P wave heavy baryons are analyzed in the framework of the Heavy Quark Symmetry limit (HQS). We use a constituent quark model picture for the light diquark system with an underlying SU(2N_{f}) X O(3) symmetry to reduce the number of the HQS coupling factors required to describe these transitions. We also use the quantum theory of angular momentum to rewrite the one-pion transitions constituent quark model results in a more general form using the 6j- and 9j-symbols. We finally estimate the decay rates of some single pion transitions between charm baryon states.

hep-ph↗

arXiv1998

Black hole - D-brane correspondence: An example

We explore the connection between D-branes and black holes in one particular case: a $D3$-brane compactified to four dimensions on $T^6/Z_3$. Using the $D$-brane boundary state description we show the equivalence with a double extremal N=2 black hole solution of four dimensional supergravity.

hep-th↗

arXiv1995

$SU(2N_{f})\otimes O(3)$ light diquark symmetry and current-induced heavy baryon transition form factors

We study the current-induced bottom baryon to charm baryon transitions in the Heavy Quark Symmetry limit as $m_{q}\rightarrow \infty$. Our discussion involves $s$-wave to $s$-wave as well as $s$-wave to $p$-wave transitions. Using a constituent quark model picture for the light diquark system with an underlying $SU(2N_{f})\otimes O(3)$ symmetry and the heavy quark symmetry we arrive at a number of new predictions for the reduced form factors that describe these transitions.

hep-ph↗

arXiv1995

On the Form Factors of the $D_{s}^{+}\to ϕμ^{+}ν_μ decay

We apply the infinite mass effective theory, when a heavy quark mass tends to infinity, and Chiral perturbation theory at the quark level, based on the extended Nambu -- Jona -- Lasinio model with linear realization of chiral $U(3)\times U(3)$ symmetry, to calculate the form factors of the $D^{\,+}_{\,s}\toϕ~μ^+~ν_{\,μ}$ decay up to the first order in current $s$ -- quark mass. The theoretical results are compared with experimental data and found to be in good agreement.

hep-ph↗

arXiv1995

Current s-Quark Mass Corrections to the Form Factors of D-Meson Semileptonic Decays

The infinite mass effective theory, when a heavy quark mass tends to infinity, and Chiral perturbation theory at the quark level, based on the extended Nambu -- Jona -- Lasinio model with linear realization of chiral $U(3)\times U(3)$ symmetry, are applied to the calculation of current $s$ -- quark mass corrections to the form factors of the $D\to\bar K~e^+~ν_e$ and $D\to\bar K^{\ast}~e^+~ν_e$ decays. These corrections turn out to be quite significant, of the order of $7-20\%$. The theoretical results are compared with experimental data.

hep-ph↗

arXiv1995

An Introduction to the Heavy Quark Effective Theory

These lecture notes begin with a brief survey of the physics of heavy quark systems. This discusion motivates the introduction of the Heavy Quark Effective theory (HQET) which captures a great deal of the intuition developed. A derivation of the HQET from QCD is presented as well as an analysis of its special properties. The effective theory can be seen to amount to a one-dimensional field theory in the quark sector. The heavy quark flavour- and spin- symmetry of the effective lagrangian is an offspring of this. Other topics covered include the question of covariance of the theory, the construction of interpolating fields for the heavy hadron states, the application of LSZ reduction theorems to determine the (reduced) number of form factors in flavour changing transitions, a complete verification of Luke's theorem, plus the matching conditions between QCD and the HQET beyond tree level. These are an expanded version of lectures presented during the Trieste 1994 Summer school on High Energy physics.

hep-ph↗

arXiv1994

Heavy Quark Effective Theory, Interpolating Fields and Bethe-Salpeter Amplitudes

We use the LSZ reduction theorem and interpolating fields, alongwith the heavy quark effective theory, to investigate the structure of the Bethe-Salpeter amplitude for heavy hadrons. We show how a simple form of this amplitude, used extensively in heavy hadron decay calculations, follows naturally upto $O(1/M)$ from these field theoretic considerations.

hep-ph↗

arXiv1993

Hadrons of Arbitrary Spin and Heavy Quark Symmetry

We present a general construction of the spin content of the Bethe-Salpeter amplitudes (covariant wave functions) for heavy hadrons with arbitrary orbital excitations, using representations of the Lorentz group. These wave functions incorporate the symmetries manifest in the heavy quark limit. In the baryonic sector we clearly differentiate between the $Λ$ and $Σ$ type excited baryons. We then use the trace formalism to evaluate the weak transitions of ground state heavy hadrons to arbitrary excited heavy hadrons. The contributions of excited states to the Bjorken sum rule are also worked out in detail.

hep-ph↗