6,350 research outputs found
NR/HEP: roadmap for the future
Physic in curved spacetime describes a multitude of phenomena, ranging from astrophysics to high-energy physics (HEP). The last few years have witnessed further progress on several fronts, including the accurate numerical evolution of the gravitational field equations, which now allows highly nonlinear phenomena to be tamed. Numerical relativity simulations, originally developed to understand strong-field astrophysical processes, could prove extremely useful to understand HEP processes such as trans-Planckian scattering and gauge–gravity dualities. We present a concise and comprehensive overview of the state-of-the-art and important open problems in the field(s), along with a roadmap for the next years
Uncertain Data in Initial Boundary Value Problems: Impact on Short and Long Time Predictions
We investigate the influence of uncertain data on solutions to initial
boundary value problems. Uncertainty in the forcing function, initial
conditions and boundary conditions are considered and we quantify their
relative influence for short and long time calculations. It is shown that
dissipative boundary conditions leading to energy bounds play a crucial role.
For short time calculations, uncertainty in the initial data dominate. As time
grows, the influence of initial data vanish exponentially fast. For longer time
calculations, the uncertainty in the forcing function and boundary data
dominate, as they grow in time. Errors due to the forcing function grows faster
(linearly in time) than the ones due to the boundary data (grows as the square
root of time). Roughly speaking, the results indicate that for short time
calculations, the initial conditions are the most important, but for longer
time calculations, focus should be on modelling efforts and boundary
conditions. Our findings have impact on predictions where similar mathematical
and numerical techniques are used for both short and long times as for example
in regional weather and climate predictions
Numerical relativity with the conformal field equations
I discuss the conformal approach to the numerical simulation of radiating
isolated systems in general relativity. The method is based on conformal
compactification and a reformulation of the Einstein equations in terms of
rescaled variables, the so-called ``conformal field equations'' developed by
Friedrich. These equations allow to include ``infinity'' on a finite grid,
solving regular equations, whose solutions give rise to solutions of the
Einstein equations of (vacuum) general relativity. The conformal approach
promises certain advantages, in particular with respect to the treatment of
radiation extraction and boundary conditions. I will discuss the essential
features of the analytical approach to the problem, previous work on the
problem - in particular a code for simulations in 3+1 dimensions, some new
results, open problems and strategies for future work.Comment: 34 pages, submitted to the Proceedings of the 2001 Spanish Relativity
meeting, eds. L. Fernandez and L. Gonzalez, to be published by Springer,
Lecture Notes in Physics serie
Roadmap on semiconductor-cell biointerfaces.
This roadmap outlines the role semiconductor-based materials play in understanding the complex biophysical dynamics at multiple length scales, as well as the design and implementation of next-generation electronic, optoelectronic, and mechanical devices for biointerfaces. The roadmap emphasizes the advantages of semiconductor building blocks in interfacing, monitoring, and manipulating the activity of biological components, and discusses the possibility of using active semiconductor-cell interfaces for discovering new signaling processes in the biological world
Stability of Discontinuous Galerkin Spectral Element Schemes for Wave Propagation when the Coefficient Matrices have Jumps
We use the behavior of the L2 norm of the solutions of linear hyperbolic equations with discontinuous coefficient matrices as a surrogate to infer stability of discontinuous Galerkin spectral element methods (DGSEM). Although the L2 norm is not bounded by the initial data for homogeneous and dissipative boundary conditions for such systems, the L2 norm is easier to work with than a norm that discounts growth due to the discontinuities. We show that the DGSEM with an upwind numerical flux that satisfies the Rankine-Hugoniot (or conservation) condition has the same energy bound as the partial differential equation does in the L2 norm, plus an added dissipation that depends on how much the approximate solution fails to satisfy the Rankine-Hugoniot jump
Stability of Correction Procedure via Reconstruction With Summation-by-Parts Operators for Burgers' Equation Using a Polynomial Chaos Approach
In this paper, we consider Burgers' equation with uncertain boundary and
initial conditions. The polynomial chaos (PC) approach yields a hyperbolic
system of deterministic equations, which can be solved by several numerical
methods. Here, we apply the correction procedure via reconstruction (CPR) using
summation-by-parts operators. We focus especially on stability, which is proven
for CPR methods and the systems arising from the PC approach. Due to the usage
of split-forms, the major challenge is to construct entropy stable numerical
fluxes. For the first time, such numerical fluxes are constructed for all
systems resulting from the PC approach for Burgers' equation. In numerical
tests, we verify our results and show also the advantage of the given ansatz
using CPR methods. Moreover, one of the simulations, i.e. Burgers' equation
equipped with an initial shock, demonstrates quite fascinating observations.
The behaviour of the numerical solutions from several methods (finite volume,
finite difference, CPR) differ significantly from each other. Through careful
investigations, we conclude that the reason for this is the high sensitivity of
the system to varying dissipation. Furthermore, it should be stressed that the
system is not strictly hyperbolic with genuinely nonlinear or linearly
degenerate fields
Measure What Should be Measured: Progress and Challenges in Compressive Sensing
Is compressive sensing overrated? Or can it live up to our expectations? What
will come after compressive sensing and sparsity? And what has Galileo Galilei
got to do with it? Compressive sensing has taken the signal processing
community by storm. A large corpus of research devoted to the theory and
numerics of compressive sensing has been published in the last few years.
Moreover, compressive sensing has inspired and initiated intriguing new
research directions, such as matrix completion. Potential new applications
emerge at a dazzling rate. Yet some important theoretical questions remain
open, and seemingly obvious applications keep escaping the grip of compressive
sensing. In this paper I discuss some of the recent progress in compressive
sensing and point out key challenges and opportunities as the area of
compressive sensing and sparse representations keeps evolving. I also attempt
to assess the long-term impact of compressive sensing
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