407 research outputs found
Using Elimination Theory to construct Rigid Matrices
The rigidity of a matrix A for target rank r is the minimum number of entries
of A that must be changed to ensure that the rank of the altered matrix is at
most r. Since its introduction by Valiant (1977), rigidity and similar
rank-robustness functions of matrices have found numerous applications in
circuit complexity, communication complexity, and learning complexity. Almost
all nxn matrices over an infinite field have a rigidity of (n-r)^2. It is a
long-standing open question to construct infinite families of explicit matrices
even with superlinear rigidity when r = Omega(n).
In this paper, we construct an infinite family of complex matrices with the
largest possible, i.e., (n-r)^2, rigidity. The entries of an n x n matrix in
this family are distinct primitive roots of unity of orders roughly exp(n^2 log
n). To the best of our knowledge, this is the first family of concrete (but not
entirely explicit) matrices having maximal rigidity and a succinct algebraic
description.
Our construction is based on elimination theory of polynomial ideals. In
particular, we use results on the existence of polynomials in elimination
ideals with effective degree upper bounds (effective Nullstellensatz). Using
elementary algebraic geometry, we prove that the dimension of the affine
variety of matrices of rigidity at most k is exactly n^2-(n-r)^2+k. Finally, we
use elimination theory to examine whether the rigidity function is
semi-continuous.Comment: 25 Pages, minor typos correcte
Three-dimensional numerical modeling of flow field in rectangular shallow reservoirs
Flow field in shallow waters, which is characterized by its complex mixing process and inherent dynamic nature, is interesting mainly due to its practical importance (e. g. in free flushing operation and sedimentation in large reservoirs). 3D numerical models make it possible to track two-dimensional large turbulence coherent structures, which are the dominant phenomenon in shallow reservoirs flow field. In the present study a fully three-dimensional numerical model SSIIM that employs the Finite Volume Approach (FVM) was utilized to reproduce the 3D flow field. Various shallow reservoir geometries with fixed and deformed equilibrium bed were considered. The measurements by Large-Scale Particle Image Velocimetry techniques (LSPIV) and Ultrasonic Doppler Velocity Profiler (UVP) over the flow depth were used for model validation. Outcomes revealed reasonable agreement between the simulated and measured flow velocity field even when an asymmetric flow pattern exists in the reservoir
Simulation of the aluminum alloy A356 solidification cast in cylindrical permanent molds
Counter-propagating radiative shock experiments on the Orion laser and the formation of radiative precursors
We present results from new experiments to study the dynamics of radiative
shocks, reverse shocks and radiative precursors. Laser ablation of a solid
piston by the Orion high-power laser at AWE Aldermaston UK was used to drive
radiative shocks into a gas cell initially pressurised between and $1.0 \
bar with different noble gases. Shocks propagated at {80 \pm 10 \ km/s} and
experienced strong radiative cooling resulting in post-shock compressions of {
\times 25 \pm 2}. A combination of X-ray backlighting, optical self-emission
streak imaging and interferometry (multi-frame and streak imaging) were used to
simultaneously study both the shock front and the radiative precursor. These
experiments present a new configuration to produce counter-propagating
radiative shocks, allowing for the study of reverse shocks and providing a
unique platform for numerical validation. In addition, the radiative shocks
were able to expand freely into a large gas volume without being confined by
the walls of the gas cell. This allows for 3-D effects of the shocks to be
studied which, in principle, could lead to a more direct comparison to
astrophysical phenomena. By maintaining a constant mass density between
different gas fills the shocks evolved with similar hydrodynamics but the
radiative precursor was found to extend significantly further in higher atomic
number gases (\sim4$ times further in xenon than neon). Finally, 1-D and 2-D
radiative-hydrodynamic simulations are presented showing good agreement with
the experimental data.Comment: HEDLA 2016 conference proceeding
Evaluation of cyclone geometry and its influence on performance parameters by computational fluid dynamics (CFD)
The effects of sample position and gas flow pattern on the sintering of a 7xxx aluminum alloy
The effects of sample position and gas flow pattern on the sintering of a 7xxx aluminum alloy Al-7Zn-2.5Mg-1Cu in flowing nitrogen have been investigated both experimentally and numerically. The near-surface pore distribution and sintered density of the samples show a strong dependency on the sample separation distance over the range from 2 mm to 40 mm. The open porosity in each sample increases with increasing separation distance while the closed porosity remains essentially unchanged. A two-dimensional computational fluid dynamics (CFD) model has been developed to analyze the gas flow behavior near the sample surfaces during isothermal sintering. The streamlines, velocity profile, and volume flow rate in the cavity between each two samples are presented as a function of the sample separation distance at a fixed nitrogen flow rate of 6 L/min. The CFD modeling results provide essential details for understanding the near-surface pore distribution and density of the sintered samples. It is proposed that the different gas flow patterns near the sample surfaces result in variations of the oxygen content from the incoming nitrogen flow in the local sintering atmosphere, which affects the self-gettering process of the aluminum compacts during sintering. This leads to the development of different near-surface pore distributions and sintered densities
Formation of radiatively cooled, supersonically rotating, plasma flows in Z-pinch experiments: Towards the development of an experimental platform to study accretion disk physics in the laboratory
International audienc
Theoretical and numerical studies of coupling multizone and CFD models for building air distribution simulations
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