64,118 research outputs found
Osculating and neighbour-avoiding polygons on the square lattice
We study two simple modifications of self-avoiding polygons. Osculating
polygons are a super-set in which we allow the perimeter of the polygon to
touch at a vertex. Neighbour-avoiding polygons are only allowed to have nearest
neighbour vertices provided these are joined by the associated edge and thus
form a sub-set of self-avoiding polygons. We use the finite lattice method to
count the number of osculating polygons and neighbour-avoiding polygons on the
square lattice. We also calculate their radius of gyration and the first
area-weighted moment. Analysis of the series confirms exact predictions for the
critical exponents and the universality of various amplitude combinations. For
both cases we have found exact solutions for the number of convex and
almost-convex polygons.Comment: 14 pages, 5 figure
The Effects of Driving Restrictions on Air Quality: SĂŁo Paulo, BogotĂĄ, Beijing, and Tianjin
In a typical driving restriction, vehicle use is restricted based on the vehicleâs license plate; one cannot drive vehicles with certain license plate numbers on certain days. Driving restrictions have been used as a method to reduce urban air pollution or traffic congestion because they are easy and inexpensive to implement. We investigate whether driving restrictions introduced in SĂŁo Paulo, BogotĂĄ, Beijing and Tianjin have improved air quality. Across different versions of the driving restrictions there is no evidence that the overall air quality at different places has been improved. However, several important results show up in this extensive analysis. Temporal shifting of driving is likely to appear when the restrictions are only effective during certain hours of weekdays. Driving restrictions could potentially reduce the extreme concentrations of air pollutants. Driving restrictions can only be expected to alleviate air pollution when implemented with an extended schedule or in an extended region. The effects of the driving restrictions are primarily on the concentrations of CO and PM10.driving restriction, air quality, Environmental Economics and Policy,
Computing the lower and upper bounds of Laplace eigenvalue problem: by combining conforming and nonconforming finite element methods
This article is devoted to computing the lower and upper bounds of the
Laplace eigenvalue problem. By using the special nonconforming finite elements,
i.e., enriched Crouzeix-Raviart element and extension , we get
the lower bound of the eigenvalue. Additionally, we also use conforming finite
elements to do the postprocessing to get the upper bound of the eigenvalue. The
postprocessing method need only to solve the corresponding source problems and
a small eigenvalue problem if higher order postprocessing method is
implemented. Thus, we can obtain the lower and upper bounds of the eigenvalues
simultaneously by solving eigenvalue problem only once. Some numerical results
are also presented to validate our theoretical analysis.Comment: 19 pages, 4 figure
Exact Scaling Functions for Self-Avoiding Loops and Branched Polymers
It is shown that a recently conjectured form for the critical scaling
function for planar self-avoiding polygons weighted by their perimeter and area
also follows from an exact renormalization group flow into the branched polymer
problem, combined with the dimensional reduction arguments of Parisi and
Sourlas. The result is generalized to higher-order multicritical points,
yielding exact values for all their critical exponents and exact forms for the
associated scaling functions.Comment: 5 pages; v2: factors of 2 corrected; v.3: relation with existing
theta-point results clarified, some references added/update
A synthetic electric force acting on neutral atoms
Electromagnetism is a simple example of a gauge theory where the underlying
potentials -- the vector and scalar potentials -- are defined only up to a
gauge choice. The vector potential generates magnetic fields through its
spatial variation and electric fields through its time-dependence. We
experimentally produce a synthetic gauge field that emerges only at low energy
in a rubidium Bose-Einstein condensate: the neutral atoms behave as charged
particles do in the presence of a homogeneous effective vector potential. We
have generated a synthetic electric field through the time dependence of an
effective vector potential, a physical consequence even though the vector
potential is spatially uniform
Locating regions in a sequence under density constraints
Several biological problems require the identification of regions in a
sequence where some feature occurs within a target density range: examples
including the location of GC-rich regions, identification of CpG islands, and
sequence matching. Mathematically, this corresponds to searching a string of 0s
and 1s for a substring whose relative proportion of 1s lies between given lower
and upper bounds. We consider the algorithmic problem of locating the longest
such substring, as well as other related problems (such as finding the shortest
substring or a maximal set of disjoint substrings). For locating the longest
such substring, we develop an algorithm that runs in O(n) time, improving upon
the previous best-known O(n log n) result. For the related problems we develop
O(n log log n) algorithms, again improving upon the best-known O(n log n)
results. Practical testing verifies that our new algorithms enjoy significantly
smaller time and memory footprints, and can process sequences that are orders
of magnitude longer as a result.Comment: 17 pages, 8 figures; v2: minor revisions, additional explanations; to
appear in SIAM Journal on Computin
Graphene microwave transistors on sapphire substrates
We have developed metal-oxide graphene field-effect transistors (MOGFETs) on
sapphire substrates working at microwave frequencies. For monolayers, we obtain
a transit frequency up to ~ 80 GHz for a gate length of 200 nm, and a power
gain maximum frequency of about ~ 3 GHz for this specific sample. Given the
strongly reduced charge noise for nanostructures on sapphire, the high
stability and high performance of this material at low temperature, our MOGFETs
on sapphire are well suited for a cryogenic broadband low-noise amplifier
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