7,058 research outputs found
Approximation of probability density functions for PDEs with random parameters using truncated series expansions
The probability density function (PDF) of a random variable associated with
the solution of a partial differential equation (PDE) with random parameters is
approximated using a truncated series expansion. The random PDE is solved using
two stochastic finite element methods, Monte Carlo sampling and the stochastic
Galerkin method with global polynomials. The random variable is a functional of
the solution of the random PDE, such as the average over the physical domain.
The truncated series are obtained considering a finite number of terms in the
Gram-Charlier or Edgeworth series expansions. These expansions approximate the
PDF of a random variable in terms of another PDF, and involve coefficients that
are functions of the known cumulants of the random variable. To the best of our
knowledge, their use in the framework of PDEs with random parameters has not
yet been explored
On connectivity-dependent resource requirements for digital quantum simulation of -level particles
A primary objective of quantum computation is to efficiently simulate quantum
physics. Scientifically and technologically important quantum Hamiltonians
include those with spin-, vibrational, photonic, and other bosonic degrees
of freedom, i.e. problems composed of or approximated by -level particles
(qudits). Recently, several methods for encoding these systems into a set of
qubits have been introduced, where each encoding's efficiency was studied in
terms of qubit and gate counts. Here, we build on previous results by including
effects of hardware connectivity. To study the number of SWAP gates required to
Trotterize commonly used quantum operators, we use both analytical arguments
and automatic tools that optimize the schedule in multiple stages. We study the
unary (or one-hot), Gray, standard binary, and block unary encodings, with
three connectivities: linear array, ladder array, and square grid. Among other
trends, we find that while the ladder array leads to substantial efficiencies
over the linear array, the advantage of the square over the ladder array is
less pronounced. These results are applicable in hardware co-design and in
choosing efficient qudit encodings for a given set of near-term quantum
hardware. Additionally, this work may be relevant to the scheduling of other
quantum algorithms for which matrix exponentiation is a subroutine.Comment: Accepted to QCE20 (IEEE Quantum Week). Corrected erroneous circuits
in Figure
London Penetration Length and String Tension in SU(2) Lattice Gauge Theory
We study the distribution of the color fields due to a static quark-antiquark
pair in SU(2) lattice gauge theory. We find evidence of dual Meissner effect.
We put out a simple relation between the penetration length and the string
tension.Comment: uuencoded compressed Postscript file (text+figures
The deconfining phase transition in full QCD with two dynamical flavors
We investigate the deconfining phase transition in SU(3) pure gauge theory
and in full QCD with two flavors of staggered fermions. The phase transition is
detected by measuring the free energy in presence of an abelian monopole
background field. In the pure gauge case our finite size scaling analysis is in
agreement with the well known presence of a weak first order phase transition.
In the case of 2 flavors full QCD we find, using the standard pure gauge and
staggered fermion actions, that the phase transition is consistent with weak
first order, contrary to the expectation of a crossover for not too large quark
masses and in agreement with results obtained by the Pisa group.Comment: 23 pages, 11 figures, 4 tables (minor typos corrected, references
updated, accepted for publication on JHEP
Mutual Inductance Route to Paramagnetic Meissner Effect in 2D Josephson Junction Arrays
We simulate two-dimensional Josephson junction arrays, including full mutual-
inductance effects, as they are cooled below the transition temperature in a
magnetic field. We show numerical simulations of the array magnetization as a
function of position, as detected by a scanning SQUID which is placed at a
fixed height above the array. The calculated magnetization images show striking
agreement with the experimental images obtained by A. Nielsen et al. The
average array magnetization is found to be paramagnetic for many values of the
applied field, confirming that paramagnetism can arise from magnetic screening
in multiply-connected superconductors without the presence of d-wave
superconductivity.Comment: REVTeX 3.1, 5 pages, 5 figure
Simultaneous Embeddings with Few Bends and Crossings
A simultaneous embedding with fixed edges (SEFE) of two planar graphs and
is a pair of plane drawings of and that coincide when restricted to
the common vertices and edges of and . We show that whenever and
admit a SEFE, they also admit a SEFE in which every edge is a polygonal curve
with few bends and every pair of edges has few crossings. Specifically: (1) if
and are trees then one bend per edge and four crossings per edge pair
suffice (and one bend per edge is sometimes necessary), (2) if is a planar
graph and is a tree then six bends per edge and eight crossings per edge
pair suffice, and (3) if and are planar graphs then six bends per edge
and sixteen crossings per edge pair suffice. Our results improve on a paper by
Grilli et al. (GD'14), which proves that nine bends per edge suffice, and on a
paper by Chan et al. (GD'14), which proves that twenty-four crossings per edge
pair suffice.Comment: Full version of the paper "Simultaneous Embeddings with Few Bends and
Crossings" accepted at GD '1
Renormalization and topological susceptibility on the lattice: SU(2) Yang-Mills theory
The renormalization functions involved in the determination of the
topological susceptibility in the SU(2) lattice gauge theory are extracted by
direct measurements, without relying on perturbation theory. The determination
exploits the phenomenon of critical slowing down to allow the separation of
perturbative and non-perturbative effects. The results are in good agreement
with perturbative computations.Comment: 12 pages + 4 figures (PostScript); report no. IFUP-TH 10/9
Gauge-invariant quark-antiquark nonlocal condensates in lattice QCD
We study, by numerical simulations on a lattice, the behaviour of the
gauge-invariant quark-antiquark nonlocal condensates in the QCD vacuum with
dynamical fermions. A determination is also done in the quenched approximation
and the results are compared with the full-QCD case. The fermionic correlation
length is extracted and compared with the analogous gluonic quantity.Comment: 14 pages, LaTeX file, + 6 PS figure
Ordered Level Planarity, Geodesic Planarity and Bi-Monotonicity
We introduce and study the problem Ordered Level Planarity which asks for a
planar drawing of a graph such that vertices are placed at prescribed positions
in the plane and such that every edge is realized as a y-monotone curve. This
can be interpreted as a variant of Level Planarity in which the vertices on
each level appear in a prescribed total order. We establish a complexity
dichotomy with respect to both the maximum degree and the level-width, that is,
the maximum number of vertices that share a level. Our study of Ordered Level
Planarity is motivated by connections to several other graph drawing problems.
Geodesic Planarity asks for a planar drawing of a graph such that vertices
are placed at prescribed positions in the plane and such that every edge is
realized as a polygonal path composed of line segments with two adjacent
directions from a given set of directions symmetric with respect to the
origin. Our results on Ordered Level Planarity imply -hardness for any
with even if the given graph is a matching. Katz, Krug, Rutter and
Wolff claimed that for matchings Manhattan Geodesic Planarity, the case where
contains precisely the horizontal and vertical directions, can be solved in
polynomial time [GD'09]. Our results imply that this is incorrect unless
. Our reduction extends to settle the complexity of the Bi-Monotonicity
problem, which was proposed by Fulek, Pelsmajer, Schaefer and
\v{S}tefankovi\v{c}.
Ordered Level Planarity turns out to be a special case of T-Level Planarity,
Clustered Level Planarity and Constrained Level Planarity. Thus, our results
strengthen previous hardness results. In particular, our reduction to Clustered
Level Planarity generates instances with only two non-trivial clusters. This
answers a question posed by Angelini, Da Lozzo, Di Battista, Frati and Roselli.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
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