Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userComputing Gowdy spacetimes via spectral evolution in future and past directions
79
0
0.0
(
0
)
Added by
Philippe G. LeFloch
Publication date
2008
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We consider a system of nonlinear wave equations with constraints that arises from the Einstein equations of general relativity and describes the geometry of the so-called Gowdy symmetric spacetimes on T3. We introduce two numerical methods, which are based on pseudo-spectral approximation. The first approach relies on marching in the future time-like direction and toward the coordinate singularity t=0. The second approach is designed from asymptotic formulas that are available near this singularity; it evolves the solutions in the past timelike direction from final data given at t=0. This backward method relies a novel nonlinear transformation, which allows us to reduce the nonlinear source terms to simple quadratic products of the unknown variables. Numerical experiments are presented in various regimes, including cases where spiky structures are observed as the coordinate singularity is approached. The proposed backward strategy leads to a robust numerical method which allows us to accurately simulate the long-time behavior of a large class of Gowdy spacetimes.
rate research
Read More
Model-based evaluation in cybersecurity has a long history. Attack Graphs (AGs) and Attack Trees (ATs) were the earlier developed graphical security models for cybersecurity analysis. However, they have limitations (e.g., scalability problem, state-space explosion problem, etc.) and lack the ability to capture other security features (e.g., countermeasures). To address the limitations and to cope with various security features, a graphical security model named attack countermeasure tree (ACT) was developed to perform security analysis by taking into account both attacks and countermeasures. In our research, we have developed different variants of a hierarchical graphical security model to solve the complexity, dynamicity, and scalability issues involved with security models in the security analysis of systems. In this paper, we summarize and classify security models into the following; graph-based, tree-based, and hybrid security models. We discuss the development of a hierarchical attack representation model (HARM) and different variants of the HARM, its applications, and usability in a variety of domains including the Internet of Things (IoT), Cloud, Software-Defined Networking, and Moving Target Defenses. We provide the classification of the security metrics, including their discussions. Finally, we highlight existing problems and suggest future research directions in the area of graphical security models and applications. As a result of this work, a decision-maker can understand which type of HARM will suit their network or security analysis requirements.
We study the phase space of the quintom cosmologies for a class of exponential potentials. We combine normal forms expansions and the center manifold theory in order to describe the dynamics near equilibrium sets. Furthermore, we construct the unstable and center manifold of the massless scalar field cosmology motivated by the numerical results given in Lazkoz and Leon (Phys Lett B 638:303. arXiv:astro-ph/0602590, 2006). We study the role of the curvature on the dynamics. Several monotonic functions are defined on relevant invariant sets for the quintom cosmology. Finally, conservation laws of the cosmological field equations and algebraic solutions are determined by using the symmetry analysis and the singularity analysis.
We study the propagation of bubbles of new vacuum in a radially inhomogeneous background filled with dust or radiation, and including a cosmological constant, as a first step in the analysis of the influence of inhomogeneities in the evolution of an inflating region. We also compare the cases with dust and radiation backgrounds and show that the evolution of the bubble in radiation environments is notably different from that in the corresponding dust cases, both for homogeneous and inhomogeneous ambients, leading to appreciable differences in the evolution of the proper radius of the bubble.
The effects which quantum fields and an $alpha_0 R^2$ term in the gravitational Lagrangian have on future singularities are investigated. While all values of $alpha_0$ are considered, an emphasis is placed on those values which are compatible with the universe having undergone Starobinsky inflation in the past. These are also values which lead to stable solutions to the semiclassical backreaction equations in the present universe. The dark energy is modeled as a perfect fluid, and the focus is on type I-IV singularities and little rips which result when the classical Einstein equations are solved with various types of dark energy as a source. First, evidence is provided that the energy densities of massive conformally coupled scalar fields approach that of the conformally invariant scalar field as a type III singularity is approached. Then, solutions to the semiclassical backreaction equations are investigated when conformally invariant fields and the $ alpha_0 R^2$ term in the gravitational Lagrangian are present. General proofs regarding the behaviors of the solutions are given. The proofs are illustrated by analytic and numerical calculations in specific cases.
Quantum computing is an emerging paradigm with the potential to offer significant computational advantage over conventional classical computing by exploiting quantum-mechanical principles such as entanglement and superposition. It is anticipated that this computational advantage of quantum computing will help to solve many complex and computationally intractable problems in several areas such as drug design, data science, clean energy, finance, industrial chemical development, secure communications, and quantum chemistry. In recent years, tremendous progress in both quantum hardware development and quantum software/algorithm have brought quantum computing much closer to reality. Indeed, the demonstration of quantum supremacy marks a significant milestone in the Noisy Intermediate Scale Quantum (NISQ) era - the next logical step being the quantum advantage whereby quantum computers solve a real-world problem much more efficiently than classical computing. As the quantum devices are expected to steadily scale up in the next few years, quantum decoherence and qubit interconnectivity are two of the major challenges to achieve quantum advantage in the NISQ era. Quantum computing is a highly topical and fast-moving field of research with significant ongoing progress in all facets. This article presents a comprehensive review of quantum computing literature, and taxonomy of quantum computing. Further, the proposed taxonomy is used to map various related studies to identify the research gaps. A detailed overview of quantum software tools and technologies, post-quantum cryptography and quantum computer hardware development to document the current state-of-the-art in the respective areas. We finish the article by highlighting various open challenges and promising future directions for research.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
