1,666 research outputs found
Phase field approximation of cohesive fracture models
We obtain a cohesive fracture model as a -limit of scalar damage
models in which the elastic coefficient is computed from the damage variable
through a function of the form , with diverging for close to the value describing undamaged
material. The resulting fracture energy can be determined by solving a
one-dimensional vectorial optimal profile problem. It is linear in the opening
at small values of and has a finite limit as . If the
function is allowed to depend on the index , for specific choices we
recover in the limit Dugdale's and Griffith's fracture models, and models with
surface energy density having a power-law growth at small openings
Partition into heapable sequences, heap tableaux and a multiset extension of Hammersley's process
We investigate partitioning of integer sequences into heapable subsequences
(previously defined and established by Mitzenmacher et al). We show that an
extension of patience sorting computes the decomposition into a minimal number
of heapable subsequences (MHS). We connect this parameter to an interactive
particle system, a multiset extension of Hammersley's process, and investigate
its expected value on a random permutation. In contrast with the (well studied)
case of the longest increasing subsequence, we bring experimental evidence that
the correct asymptotic scaling is . Finally
we give a heap-based extension of Young tableaux, prove a hook inequality and
an extension of the Robinson-Schensted correspondence
Generalized transition fronts for one-dimensional almost periodic Fisher-KPP equations
This paper investigates the existence of generalized transition fronts for
Fisher-KPP equations in one-dimensional, almost periodic media. Assuming that
the linearized elliptic operator near the unstable steady state admits an
almost periodic eigenfunction, we show that such fronts exist if and only if
their average speed is above an explicit threshold. This hypothesis is
satisfied in particular when the reaction term does not depend on x or (in some
cases) is small enough. Moreover, except for the threshold case, the fronts we
construct and their speeds are almost periodic, in a sense. When our hypothesis
is no longer satisfied, such generalized transition fronts still exist for an
interval of average speeds, with explicit bounds. Our proof relies on the
construction of sub and super solutions based on an accurate analysis of the
properties of the generalized principal eigenvalues
Expected length of the longest common subsequence for large alphabets
We consider the length L of the longest common subsequence of two randomly
uniformly and independently chosen n character words over a k-ary alphabet.
Subadditivity arguments yield that the expected value of L, when normalized by
n, converges to a constant C_k. We prove a conjecture of Sankoff and Mainville
from the early 80's claiming that C_k\sqrt{k} goes to 2 as k goes to infinity.Comment: 14 pages, 1 figure, LaTe
Long -zero-free sequences in finite cyclic groups
A sequence in the additive group of integers modulo is
called -zero-free if it does not contain subsequences with length and
sum zero. The article characterizes the -zero-free sequences in of length greater than . The structure of these sequences is
completely determined, which generalizes a number of previously known facts.
The characterization cannot be extended in the same form to shorter sequence
lengths. Consequences of the main result are best possible lower bounds for the
maximum multiplicity of a term in an -zero-free sequence of any given length
greater than in , and also for the combined
multiplicity of the two most repeated terms. Yet another application is finding
the values in a certain range of a function related to the classic theorem of
Erd\H{o}s, Ginzburg and Ziv.Comment: 11 page
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