35 research outputs found
Quantified Derandomization of Linear Threshold Circuits
One of the prominent current challenges in complexity theory is the attempt
to prove lower bounds for , the class of constant-depth, polynomial-size
circuits with majority gates. Relying on the results of Williams (2013), an
appealing approach to prove such lower bounds is to construct a non-trivial
derandomization algorithm for . In this work we take a first step towards
the latter goal, by proving the first positive results regarding the
derandomization of circuits of depth .
Our first main result is a quantified derandomization algorithm for
circuits with a super-linear number of wires. Specifically, we construct an
algorithm that gets as input a circuit over input bits with
depth and wires, runs in almost-polynomial-time, and
distinguishes between the case that rejects at most inputs
and the case that accepts at most inputs. In fact, our
algorithm works even when the circuit is a linear threshold circuit, rather
than just a circuit (i.e., is a circuit with linear threshold gates,
which are stronger than majority gates).
Our second main result is that even a modest improvement of our quantified
derandomization algorithm would yield a non-trivial algorithm for standard
derandomization of all of , and would consequently imply that
. Specifically, if there exists a quantified
derandomization algorithm that gets as input a circuit with depth
and wires (rather than wires), runs in time at
most , and distinguishes between the case that rejects at
most inputs and the case that accepts at most
inputs, then there exists an algorithm with running time
for standard derandomization of .Comment: Changes in this revision: An additional result (a PRG for quantified
derandomization of depth-2 LTF circuits); rewrite of some of the exposition;
minor correction
Numerical Investigation of Wind Turbine Airfoils under Clean and Dusty Air Conditions
This paper focuses on the simulation of the airflow around wind turbine airfoils (S809 and S814) under both clean and dusty air conditions by using Computational Fluid Dynamics (CFD). The physical geometries of the airfoils and the meshing processes are completed in the ANSYS Mesh package ICEM. The simulation is done by ANSYS FLUENT. For clean air condition, Spalart– Allmaras (SA) model and realizable k-ε model are used. The results are compared with the experimental data to test which model agrees better. For dusty air condition, simulation of the two-phase flow is operated by realizable k-ε model and discrete phase model (DPM) in different concentration of dust particles (1% and 10% in volume). The results are compared with the data of clean air to illustrate the effect of dust contamination on the lift and drag characteristics of the airfoil