arXiv subjects

Omar El Deeb

Publications and source records attributed to Omar El Deeb.

11 recordsLinked to original sources

arXiv2026

Dual-moon forced dynamics and nonlinear aggregation in Saturn's F ring: From quasi-periodicity to modulated oscillations

We develop a minimal nonlinear model to investigate the oscillatory dynamics of Saturn's F ring under dual-moon forcing from Prometheus and Pandora. The model extends classical predator--prey dynamics by incorporating both a nonlinear mass aggregation term $kM^n$ and explicit dual-frequency forcing, capturing how higher-order coagulation physics interacts with multi-moon perturbations. Through systematic numerical integration and dynamical-systems tools, including time-series, spectral, stroboscopic, and rotation number analysis, we identify distinct dynamical regimes controlled by the parameters $n$ and $k$. For moderate nonlinearity $(n=1.28,k=0.54)$, the numerical diagnostics are consistent with bounded quasiperiodic motion, characterized by smooth amplitude modulation, thin stroboscopic loops, and discrete spectral peaks. For stronger nonlinearity $(n=1.30,k=0.62)$, the same diagnostics indicate a transition toward strongly modulated oscillations, with broadened stroboscopic bands and sideband-rich spectra. A projected rotation-number diagnostic reveals organized regions in parameter space, including smooth quasiperiodic-like domains and near-locking bands analogous to Arnold tongues. Our results show that a reduced deterministic dual-forcing model can generate bounded quasiperiodic-like and strongly modulated aggregation-fragmentation cycles with timescales comparable to relevant moon-ring forcing periods, providing a possible low-dimensional mechanism contributing to F-ring variability.

physics.gen-ph↗

arXiv2024

Higher order mass aggregation terms in a nonlinear predator-prey model maintain limit cycle stability in Saturn's F ring

We consider a generic higher order mass aggregation term for interactions between particles exhibiting oscillatory clumping and disaggregation behavior in the F ring of Saturn, using a novel predator-prey model that relates the mean mass aggregate (prey) and the square of the relative dispersion velocity (predator) of the interacting particles. The resulting cyclic dynamic behavior is demonstrated through time series plots, phase portraits and their stroboscopic phase maps. Employing an eigenvalue stability analysis of the Jacobian of the system, we find out that there are two distinct regimes depending on the exponent and the amplitude of the higher order interactions of the nonlinear mass term. In particular, the system exhibits a limit cycle oscillatory stable behavior for a range of values of these parameters and a non-cyclic behavior for another range, separated by a curve across which phase transitions would occur between the two regimes. This shows that the observed clumping dynamics in Saturn's F ring, corresponding to a limit cycle stability regime, can be systematically maintained in presence of physical higher order mass aggregation terms in the introduced model.

physics.gen-ph↗

arXiv2024

Synchronization in a market model with time delays

We examine a system of N=2 coupled non-linear delay-differential equations representing financial market dynamics. In such time delay systems, coupled oscillations have been derived. We linearize the system for small time delays and study its collective dynamics. Using analytical and numerical solutions, we obtain the bifurcation diagrams and analyze the corresponding regions of amplitude death, phase locking, limit cycles and market synchronization in terms of the system frequency-like parameters and time delays. We further numerically explore higher order systems with N>2, and demonstrate that limit cycles can be maintained for coupled N-asset models with appropriate parameterization.

physics.soc-ph↗

arXiv2023

Discrete physical states and correction terms in the Supersymmetric c=1 Model of String Theory

In this article, we investigate the supersymmetric c=1 model of superstring theory and demonstrate how the spectrum of states is expanded and new symmetries of the theory are generated by the existence of ghost cohomologies. As a result, we establish significant connections between two-dimensional supergravity and physical theories in higher dimensions. Additionally, we provide a comprehensive guide for constructing BRST-invariant and nontrivial vertex operators and carry out explicit computations to determine the correction terms needed to maintain BRST invariance of the corresponding currents.

physics.gen-ph↗

arXiv2023

Entropic Spatial Auto-correlation of Voter Uncertainty and Voter Transitions in Parliamentary Elections

This paper studies a novel spatial auto-correlation model of voter uncertainty across districts. We use the Moran $I$ index to measure the auto-correlation of Shannon, relative Shannon, Tsallis and relative Tsallis entropies of regional electoral outcomes with respect to geographic adjacency, proximity and sectarian adjacency. Using data from the Lebanese parliamentary elections, we find strong geographic and gravitational adjacency correlations. More importantly, there is a notably strong correlation in sectarian adjacency in both $2018$ and $2022$ elections, with a very high level of confidence. This result asserts the dominance of the sectarian factor in Lebanese politics. We also introduce the method of maximized general entropy estimation that allows us to determine the Markov transition matrix of voters between consecutive elections.

physics.soc-ph↗

arXiv2022

Efficacy versus abundancy: Comparing vaccination schemes

We introduce a novel compartmental model accounting for the effects of vaccine efficacy, deployment rates and timing of initiation of deployment. We simulate different scenarios and initial conditions, and we find that higher abundancy and rate of deployment of low efficacy vaccines lowers the cumulative number of deaths in comparison to slower deployment of high efficacy vaccines. We also forecast that, at the same daily deployment rate, the earlier introduction of vaccination schemes with lower efficacy would also lower the number of deaths with respect to a delayed introduction of high efficacy vaccines, which can however, still achieve lower numbers of infections and better herd immunity.

q-bio.PE↗

arXiv2020

Spatial autocorrelation and the dynamics of the mean center of COVID-19 infections in Lebanon

In this paper we study the spatial spread of the COVID-19 infection in Lebanon. We inspect the spreading of the daily new infections across the 26 administrative districts of the country, and implement Moran's $I$ statistics in order to analyze the tempo-spatial clustering of the infection in relation to various variables parameterized by adjacency, proximity, population, population density, poverty rate and poverty density, and we find out that except for the poverty rate, the spread of the infection is clustered and associated to those parameters with varying magnitude for the time span between July (geographic adjacency and proximity) or August (population, population density and poverty density) through October. We also determine the temporal dynamics of geographic location of the mean center of new and cumulative infections since late March. The results obtained allow for regionally and locally adjusted health policies and measures that would provide higher levels of public health safety in the country.

q-bio.PE↗

arXiv2020

The Dynamics of COVID-19 spread: Evidence from Lebanon

We explore the spread of the Coronavirus disease 2019 (COVID-19) in Lebanon by adopting two different approaches: the STEIR model, which is a modified SEIR model accounting for the effect of travel, and a repeated iterations model. We fit available daily data since the first diagnosed case until the end of June 2020 and we forecast possible scenarios of contagion associated with different levels of social distancing measures and travel inflows. We determine the initial reproductive transmission rate in Lebanon and all subsequent dynamics. In the repeated iterations (RI) model we iterate the available data of currently infected people to forecast future infections under several possible scenarios of contagion. In both models, our results suggest that tougher mitigation measures would slow down the spread of the disease. On the other hand, the current relaxation of measures and partial resumption of international flights, as the STEIR reveals, would trigger a second outbreak of infections, with severity depending on the extent of relaxation. We recommend strong institutional and public commitment to mitigation measures to avoid uncontrolled spread.

physics.soc-ph↗

arXiv2018

Analytic structures of unitary RSOS models with integrable boundary conditions

In this paper, we consider the unitary critical restricted-solid-on-solid (RSOS) lattice $\mathcal{M}(5,6)$ model with integrable boundary conditions. We introduce its commuting double row transfer matrix satisfying the universal functional relations, and we use it in order to study the analytic structure of the transfer matrix eigenvalues and plot representative zero configurations of sample eigenvalues of the transfer matrix. We finally conclude with a comparative analysis with the critical and tricritical Ising models with integrable boundary conditions.

hep-th↗

arXiv2016

On the critical boundary RSOS \mathcal{M}(3,5) model

We consider the critical non-unitary minimal model {\cal M}(3,5) with integrable boundaries. We analyze the patterns of zeros of the eigenvalues of the transfer matrix and then determine the spectrum of the critical theory through the Thermodynamic Bethe Ansatz (TBA) equations. By solving the TBA functional equation satisfied by the transfer matrices of the associated A_{4} RSOS lattice model of Forrester and Baxter in Regime III in the continuum scaling limit, we derive the integral TBA equations for all excitations in the (r=1,s=1) sector then determine their corresponding energies. The excitations are classified in terms of (m,n) systems.

hep-th↗

arXiv2015

Lee-Yang Model in Presence of Defects

I choose the Lee-Yang model and go through different approaches to analyze it using the form factor approach and the bootstrap program, the lattice description and the lattice TBA equations for a full understanding of the model. The bootstrap program aims to explicitly solve 1+1 dimensional integrable quantum field theories. In the first step, called the S-matrix bootstrap, the scattering matrix, is determined from its properties. In developing a defect form factor program the first step is the T-matrix bootstrap. Interacting integrable defect theories are purely transmitting and topological. We analyze both operators localized in the bulk and also on the defect. By finding their solutions, the spectral representation of any correlator can be determined. Next we consider the model on the lattice. The lattice approach allows to obtain both massive and massless excited TBA equations by studying the continuum scaling limit of the associated integrable lattice models. The most important input from the lattice approach is an insight into the analytic structure of the excited state solutions of the TBA equations. Previously this structure had to be guessed. In this thesis we turn our attention to the simplest example of a non-unitary minimal theory, namely, the Lee-Yang minimal model M(2,5). We study the Lee-Yang model on the lattice. We analyze the periodic, boundary and the seam cases in both massive and massless regimes. We derive their ground state TBA equations and analyze the flows between different boundary and defect conditions. Finally, in the large volume limit, we calculate the Lüscher correction terms of the TBA energy of a one-particle state. We display those ideas in the end of the thesis as this is an important direction of work in string theory, particularly in the AdS/CFT correspondence.

hep-th↗