480,939 research outputs found
Volume and complexity for warped AdS black holes
We study the Complexity=Volume conjecture for Warped AdS black holes. We
compute the spatial volume of the Einstein-Rosen bridge and we find that its
growth rate is proportional to the Hawking temperature times the
Bekenstein-Hawking entropy. This is consistent with expectations about
computational complexity in the boundary theory.Comment: 18 pages, 3 figures, V2: refs adde
Numerical modelling of heat transfer and experimental validation in Powder-Bed Fusion with the Virtual Domain Approximation
Among metal additive manufacturing technologies, powder-bed fusion features
very thin layers and rapid solidification rates, leading to long build jobs and
a highly localized process. Many efforts are being devoted to accelerate
simulation times for practical industrial applications. The new approach
suggested here, the virtual domain approximation, is a physics-based rationale
for spatial reduction of the domain in the thermal finite-element analysis at
the part scale. Computational experiments address, among others, validation
against a large physical experiment of 17.5 of deposited
volume in 647 layers. For fast and automatic parameter estimation at such level
of complexity, a high-performance computing framework is employed. It couples
FEMPAR-AM, a specialized parallel finite-element software, with Dakota, for the
parametric exploration. Compared to previous state-of-the-art, this formulation
provides higher accuracy at the same computational cost. This sets the path to
a fully virtualized model, considering an upwards-moving domain covering the
last printed layers
A Fully Polynomial-Time Approximation Scheme for Speed Scaling with Sleep State
We study classical deadline-based preemptive scheduling of tasks in a
computing environment equipped with both dynamic speed scaling and sleep state
capabilities: Each task is specified by a release time, a deadline and a
processing volume, and has to be scheduled on a single, speed-scalable
processor that is supplied with a sleep state. In the sleep state, the
processor consumes no energy, but a constant wake-up cost is required to
transition back to the active state. In contrast to speed scaling alone, the
addition of a sleep state makes it sometimes beneficial to accelerate the
processing of tasks in order to transition the processor to the sleep state for
longer amounts of time and incur further energy savings. The goal is to output
a feasible schedule that minimizes the energy consumption. Since the
introduction of the problem by Irani et al. [16], its exact computational
complexity has been repeatedly posed as an open question (see e.g. [2,8,15]).
The currently best known upper and lower bounds are a 4/3-approximation
algorithm and NP-hardness due to [2] and [2,17], respectively. We close the
aforementioned gap between the upper and lower bound on the computational
complexity of speed scaling with sleep state by presenting a fully
polynomial-time approximation scheme for the problem. The scheme is based on a
transformation to a non-preemptive variant of the problem, and a discretization
that exploits a carefully defined lexicographical ordering among schedules
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Adaptive smoothing techniques for 3-D unstructured meshes
To correctly capture the behavior of deforming material volumes in 3-D, the Los Alamos unstructured grid code X3D has access to a variety of moving mesh algorithms. The authors present two such algorithms which markedly differ in their computational complexity. The first algorithm, Moving finite Elements for Surfaces, has only 2-D computational complexity, in that they only solve for interface motions and obtain volume point motions through interpolation. The second algorithm, Minimum Error Gradient Adaption, has 3-D complexity, since the volume tetrahedral deformations must be computed. Naturally, the 3-D complexity algorithm can model realistically a larger class of physical problems than the lower complexity approach. They present examples in metallic grain growth and semiconductor process modeling
The supernova-regulated ISM. I. The multi-phase structure
We simulate the multi-phase interstellar medium randomly heated and stirred
by supernovae, with gravity, differential rotation and other parameters of the
solar neighbourhood. Here we describe in detail both numerical and physical
aspects of the model, including injection of thermal and kinetic energy by SN
explosions, radiative cooling, photoelectric heating and various transport
processes. With 3D domain extending 1 kpc^2 horizontally and 2 kpc vertically,
the model routinely spans gas number densities 10^-5 - 10^2 cm^-3, temperatures
10-10^8 K, local velocities up to 10^3 km s^-1 (with Mach number up to 25).
The thermal structure of the modelled ISM is classified by inspection of the
joint probability density of the gas number density and temperature. We confirm
that most of the complexity can be captured in terms of just three phases,
separated by temperature borderlines at about 10^3 K and 5x10^5 K. The
probability distribution of gas density within each phase is approximately
lognormal. We clarify the connection between the fractional volume of a phase
and its various proxies, and derive an exact relation between the fractional
volume and the filling factors defined in terms of the volume and probabilistic
averages. These results are discussed in both observational and computational
contexts. The correlation scale of the random flows is calculated from the
velocity autocorrelation function; it is of order 100 pc and tends to grow with
distance from the mid-plane. We use two distinct parameterizations of radiative
cooling to show that the multi-phase structure of the gas is robust, as it does
not depend significantly on this choice.Comment: 28 pages, 22 figures and 8 table
Tenfold your photons -- a physically-sound approach to filtering-based variance reduction of Monte-Carlo-simulated dose distributions
X-ray dose constantly gains interest in the interventional suite. With dose
being generally difficult to monitor reliably, fast computational methods are
desirable. A major drawback of the gold standard based on Monte Carlo (MC)
methods is its computational complexity. Besides common variance reduction
techniques, filter approaches are often applied to achieve conclusive results
within a fraction of time. Inspired by these methods, we propose a novel
approach. We down-sample the target volume based on the fraction of mass,
simulate the imaging situation, and then revert the down-sampling. To this end,
the dose is weighted by the mass energy absorption, up-sampled, and distributed
using a guided filter. Eventually, the weighting is inverted resulting in
accurate high resolution dose distributions. The approach has the potential to
considerably speed-up MC simulations since less photons and boundary checks are
necessary. First experiments substantiate these assumptions. We achieve a
median accuracy of 96.7 % to 97.4 % of the dose estimation with the proposed
method and a down-sampling factor of 8 and 4, respectively. While maintaining a
high accuracy, the proposed method provides for a tenfold speed-up. The overall
findings suggest the conclusion that the proposed method has the potential to
allow for further efficiency.Comment: 6 pages, 3 figures, Bildverarbeitung f\"ur die Medizin 202
Complexity change under conformal transformations in AdS/CFT
Using the volume proposal, we compute the change of complexity of holographic
states caused by a small conformal transformation in AdS/CFT. This
computation is done perturbatively to second order. We give a general result
and discuss some of its properties. As operators generating such conformal
transformations can be explicitly constructed in CFT terms, these results allow
for a comparison between holographic methods of defining and computing
computational complexity and purely field-theoretic proposals. A comparison of
our results to one such proposal is given.Comment: v2: 23 pages, 5 figures, added references and one entirely new
section about a comparison to a field theory proposal v3: 27 pages, 5
figures, minor improvements. Matches published versio
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