6,220 research outputs found
Continuity for self-destructive percolation in the plane
A few years ago two of us introduced, motivated by the study of certain
forest-fireprocesses, the self-destructive percolation model (abbreviated as
sdp model). A typical configuration for the sdp model with parameters p and
delta is generated in three steps: First we generate a typical configuration
for the ordinary percolation model with parameter p. Next, we make all sites in
the infinite occupied cluster vacant. Finally, each site that was already
vacant in the beginning or made vacant by the above action, becomes occupied
with probability delta (independent of the other sites).
Let theta(p, delta) be the probability that some specified vertex belongs, in
the final configuration, to an infinite occupied cluster. In our earlier paper
we stated the conjecture that, for the square lattice and other planar
lattices, the function theta has a discontinuity at points of the form (p_c,
delta), with delta sufficiently small. We also showed remarkable consequences
for the forest-fire models.
The conjecture naturally raises the question whether the function theta is
continuous outside some region of the above mentioned form. We prove that this
is indeed the case. An important ingredient in our proof is a (somewhat
stronger form of a) recent ingenious RSW-like percolation result of
Bollob\'{a}s and Riordan
Pumped current and voltage for an adiabatic quantum pump
We consider adiabatic pumping of electrons through a quantum dot. There are
two ways to operate the pump: to create a dc current or to create a
dc voltage . We demonstrate that, for very slow pumping,
and are not simply related via the dc conductance as . For the case of a chaotic quantum dot, we consider the statistical
distribution of . Results are presented for the limiting
cases of a dot with single channel and with multichannel point contacts.Comment: 6 pages, 4 figure
On the order of a non-abelian representation group of a slim dense near hexagon
We show that, if the representation group of a slim dense near hexagon
is non-abelian, then is of exponent 4 and ,
, where is the near polygon
embedding dimension of and is the dimension of the universal
representation module of . Further, if , then
is an extraspecial 2-group (Theorem 1.6)
Long-range elastic guidance mechanisms for electrostatic comb-drive actuators
The range of motion and output force of the often used electrostatic comb-drive with folded flexure straight guidance, as shown in Figure 1, is limited by sideways instability due to poor sideways stiffness of the folded flexure at relatively large deflections [1]
Single-mask thermal displacement sensor in MEMS
In this work we describe a one degree-of-freedom microelectromechanical thermal\ud
displacement sensor integrated with an actuated stage. The system was fabricated in the device layer of a silicon-on-insulator wafer using a single-mask process. The sensor is based on the temperature dependent electrical resistivity of silicon and the heat transfer by conduction through a thin layer of air. On a measurement range of 50 μm and using a measurement bandwidth of 30 Hz, the 1-sigma noise corresponds to 3.47 nm. The power consumption of the sensor is 209 mW, almost completely independent of stage position. The drift of the sensor over a measurement period of 32 hours was 32 nm
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