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This paper considers the use of singular perturbation approximations for general linear quantum systems where the system dynamics are described in terms of both annihilation and creation operators. Results that are related to the physical…
Simulating the dynamics of non-equilibrium matter under extreme conditions lies beyond the capabilities of classical computation alone. Remarkable advances in quantum information science and technology are profoundly changing how we…
On large-scales, comparable to the horizon, the observable clustering properties of galaxies are affected by various general relativistic effects. To calculate these effects one needs to consistently solve for the metric, densities and…
The numerical simulation of turbulence in stars has led to a rich set of possibilities regarding stellar pulsations, asteroseismology, thermonuclear yields, and formation of neutron stars and black holes. The breaking of symmetry by…
The modern study of the dynamics of stellar systems requires the use of high-performance computers. Indeed, an accurate modelization of the structure and evolution of self-gravitating systems like planetary systems, open clusters, globular…
Recently an alternate technique for numerical quantum gravity, dynamical triangulation, has been developed. In this method, the geometry is varied by adding and subtracting equilateral simplices from the simplicial complex. This method…
We review and extend, in a self-contained way, the mathematical foundations of numerical simulation methods that are based on the use of random states. The power and versatility of this simulation technology is illustrated by calculations…
Numerical methods for the simulation of cavitation processes have been developed for more than 50 years. The rich variety of physical phenomena triggered by the collapse of a bubble has several applications in medicine and environmental…
A formalism and its numerical implementation is presented which allows to calculate quantities determining the spacetime structure in the large directly. This is achieved by conformal techniques by which future null infinity ($\Scri{}^+$)…
This paper describes a general-purpose programming technique, called the Simulation of Simplicity, which can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task to provide a…
In the study of the process of cosmic structure formation numerical simulations are crucial tools to interface observational data to theoretical models and to investigate issues otherwise unexplored. Enormous advances have been achieved in…
This is a brief review article of a seminar given at the International Conference on Gravitation, Astrophysics and Cosmology 2024 (ICGAC-2024), Mathura, India. We begin with a historical survey of some singular solutions in the theory of…
Galaxy clusters are sources of gravitational radiation. The main aim of this paper is to give numerical estimates and theoretical description of the relevant features of the gravitational radiation coming from an appropriate spatial…
I review the current state of numerical simulations of stellar feedback in the context of star formation at scales ranging from the formation of individual stars to models of galaxy formation including cosmic reionisation. I survey the…
We review basic computational techniques for simulations of various magnetic properties of solids. Several applications to compute magnetic anisotropy energy, spin wave spectra, magnetic susceptibilities and temperature dependent…
We present a review of the current state of the art of cosmological dark matter simulations, with particular emphasis on the implications for dark matter detection efforts and studies of dark energy. This review is intended both for…
Gravitational collapse is one of the most fruitful subjects in gravitational physics. It is well known that singularity formation is inevitable in complete gravitational collapse. It was conjectured that such a singularity should be hidden…
The simulation of rich star clusters presents challenging problems of several kinds, including the design of suitable hardware and software, and numerous theoretical problems in stellar dynamics and stellar physics. Great progress has been…
We present an overview of recent developments in numerical relativity studies of higher dimensional spacetimes with a focus on time evolutions of black-hole systems. After a brief review of the numerical techniques employed for these…
A remarkable series of breakthroughs in numerical relativity modeling of black hole binary mergers has occurred over the past few years. This paper provides a general overview of these exciting developments, focusing on recent progress in…