2,293 research outputs found
Moduli spaces of d-connections and difference Painleve equations
We show that difference Painleve equations can be interpreted as isomorphisms
of moduli spaces of d-connections on the projective line with given singularity
structure. We also derive a new difference equation. It is the most general
difference Painleve equation known so far, and it degenerates to both
difference Painleve V and classical (differential) Painleve VI equations.Comment: 30 pages (LaTeX
Nonlocal transport in the charge density waves of -TaS
We studied the nonlocal transport of a quasi-one dimensional conductor
-TaS. Electric transport phenomena in charge density waves include the
thermally-excited quasiparticles, and collective motion of charge density waves
(CDW). In spite of its long-range correlation, the collective motion of a CDW
does not extend far beyond the electrodes, where phase slippage breaks the
correlation. We found that nonlocal voltages appeared in the CDW of
-TaS, both below and above the threshold field for CDW sliding. The
temperature dependence of the nonlocal voltage suggests that the observed
nonlocal voltage originates from the CDW even below the threshold field.
Moreover, our observation of nonlocal voltages in both the pinned and sliding
states reveals the existence of a carrier with long-range correlation, in
addition to sliding CDWs and thermally-excited quasiparticles.Comment: 8 pages, 4 figure
The Ginibre ensemble of real random matrices and its scaling limits
We give a closed form for the correlation functions of ensembles of a class
of asymmetric real matrices in terms of the Pfaffian of an antisymmetric matrix
formed from a matrix kernel associated to the ensemble. We apply
this result to the real Ginibre ensemble and compute the bulk and edge scaling
limits of its correlation functions as the size of the matrices becomes large.Comment: 47 pages, 8 figure
Exact Domain Integration in the Boundary Element Method for 2D Poisson Equation
Boundary value problems for Poisson equation often
appear in electrical engineering applications, such as magnetic
and electric field modeling and so on. In such context, effective
techniques of solving such equations are subject of continuous
development. This article reports an exact formula for domain
integral in boundary-integral form of 2D Poisson Equation. This
formula is derived for rectangle domain element
τ-function of discrete isomonodromy transformations and probability
We introduce the τ-function of a difference rational connection (d-connection) and its isomonodromy transformations. We show that in a continuous limit ourτ-function agrees with the Jimbo–Miwa–Ueno τ-function. We compute the τ-function for the isomonodromy transformations leading to difference Painlevé V and difference Painlevé VI equations. We prove that the gap probability for a wide class of discrete random matrix type models can be viewed as the τ-function for an associated d-connection
Effects of Particle Shape on Growth Dynamics at Edges of Evaporating Colloidal Drops
We study the influence of particle shape on growth processes at the edges of
evaporating drops. Aqueous suspensions of colloidal particles evaporate on
glass slides, and convective flows during evaporation carry particles from drop
center to drop edge, where they accumulate. The resulting particle deposits
grow inhomogeneously from the edge in two-dimensions, and the deposition front,
or growth line, varies spatio-temporally. Measurements of the fluctuations of
the deposition front during evaporation enable us to identify distinct growth
processes that depend strongly on particle shape. Sphere deposition exhibits a
classic Poisson like growth process; deposition of slightly anisotropic
particles, however, belongs to the Kardar-Parisi-Zhang (KPZ) universality
class, and deposition of highly anisotropic ellipsoids appears to belong to a
third universality class, characterized by KPZ fluctuations in the presence of
quenched disorder
Ewens measures on compact groups and hypergeometric kernels
On unitary compact groups the decomposition of a generic element into product
of reflections induces a decomposition of the characteristic polynomial into a
product of factors. When the group is equipped with the Haar probability
measure, these factors become independent random variables with explicit
distributions. Beyond the known results on the orthogonal and unitary groups
(O(n) and U(n)), we treat the symplectic case. In U(n), this induces a family
of probability changes analogous to the biassing in the Ewens sampling formula
known for the symmetric group. Then we study the spectral properties of these
measures, connected to the pure Fisher-Hartvig symbol on the unit circle. The
associated orthogonal polynomials give rise, as tends to infinity to a
limit kernel at the singularity.Comment: New version of the previous paper "Hua-Pickrell measures on general
compact groups". The article has been completely re-written (the presentation
has changed and some proofs have been simplified). New references added
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