6,401 research outputs found
Universal Jump in the Helicity Modulus of the Two-Dimensional Quantum XY Model
The helicity modulus of the S=1/2 XY model is precisely estimated through a
world line quantum Monte Carlo method enhanced by a cluster update algorithm.
The obtained estimates for various system sizes and temperatures are well
fitted by a scaling form with L replaced by \log(L/L_0), which is inferred from
the solution of the Kosterlitz renormalization group equation. The validity of
the Kosterlitz-Thouless theory for this model is confirmed.Comment: 4 pages, 3 figure
Application of Bayesian graphs to SN Ia data analysis and compression
Bayesian graphical models are an efficient tool for modelling complex data
and derive self-consistent expressions of the posterior distribution of model
parameters. We apply Bayesian graphs to perform statistical analyses of Type Ia
supernova (SN Ia) luminosity distance measurements from the joint light-curve
analysis (JLA) data set. In contrast to the approach used in previous
studies, the Bayesian inference allows us to fully account for the
standard-candle parameter dependence of the data covariance matrix. Comparing
with analysis results, we find a systematic offset of the marginal
model parameter bounds. We demonstrate that the bias is statistically
significant in the case of the SN Ia standardization parameters with a maximal
6 shift of the SN light-curve colour correction. In addition, we find
that the evidence for a host galaxy correction is now only 2.4 .
Systematic offsets on the cosmological parameters remain small, but may
increase by combining constraints from complementary cosmological probes. The
bias of the analysis is due to neglecting the parameter-dependent
log-determinant of the data covariance, which gives more statistical weight to
larger values of the standardization parameters. We find a similar effect on
compressed distance modulus data. To this end, we implement a fully consistent
compression method of the JLA data set that uses a Gaussian approximation of
the posterior distribution for fast generation of compressed data. Overall, the
results of our analysis emphasize the need for a fully consistent Bayesian
statistical approach in the analysis of future large SN Ia data sets.Comment: 14 pages, 13 figures, 5 tables. Submitted to MNRAS. Compression
utility available at https://gitlab.com/congma/libsncompress/ and example
cosmology code with machine-readable version of Tables A1 & A2 at
https://gitlab.com/congma/sn-bayesian-model-example/ v2: corrected typo in
author's name. v3: 15 pages, incl. corrections, matches the accepted versio
A FIC-based stabilized mixed finite element method with equal order interpolation for solidâpore fluid interaction problems
This is the peer reviewed version of the following article: [de-Pouplana, I., and Oñate, E. (2017) A FIC-based stabilized mixed finite element method with equal order interpolation for solidâpore fluid interaction problems. Int. J. Numer. Anal. Meth. Geomech., 41: 110â134. doi: 10.1002/nag.2550], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nag.2550/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."A new mixed displacement-pressure element for solving solidâpore fluid interaction problems is presented. In the resulting coupled system of equations, the balance of momentum equation remains unaltered, while the mass balance equation for the pore fluid is stabilized with the inclusion of higher-order terms multiplied by arbitrary dimensions in space, following the finite calculus (FIC) procedure. The stabilized FIC-FEM formulation can be applied to any kind of interpolation for the displacements and the pressure, but in this work, we have used linear elements of equal order interpolation for both set of unknowns. Examples in 2D and 3D are presented to illustrate the accuracy of the stabilized formulation for solidâpore fluid interaction problems.Peer ReviewedPostprint (author's final draft
q-State Potts model metastability study using optimized GPU-based Monte Carlo algorithms
We implemented a GPU based parallel code to perform Monte Carlo simulations
of the two dimensional q-state Potts model. The algorithm is based on a
checkerboard update scheme and assigns independent random numbers generators to
each thread. The implementation allows to simulate systems up to ~10^9 spins
with an average time per spin flip of 0.147ns on the fastest GPU card tested,
representing a speedup up to 155x, compared with an optimized serial code
running on a high-end CPU. The possibility of performing high speed simulations
at large enough system sizes allowed us to provide a positive numerical
evidence about the existence of metastability on very large systems based on
Binder's criterion, namely, on the existence or not of specific heat
singularities at spinodal temperatures different of the transition one.Comment: 30 pages, 7 figures. Accepted in Computer Physics Communications.
code available at:
http://www.famaf.unc.edu.ar/grupos/GPGPU/Potts/CUDAPotts.htm
Slow sedimentation and deformability of charged lipid vesicles
The study of vesicles in suspension is important to understand the
complicated dynamics exhibited by cells in vivo and in vitro. We developed a
computer simulation based on the boundary-integral method to model the three
dimensional gravity-driven sedimentation of charged vesicles towards a flat
surface. The membrane mechanical behavior was modeled using the Helfrich
Hamiltonian and near incompressibility of the membrane was enforced via a model
which accounts for the thermal fluctuations of the membrane. The simulations
were verified and compared to experimental data obtained using suspended
vesicles labelled with a fluorescent probe, which allows visualization using
fluorescence microscopy and confers the membrane with a negative surface
charge. The electrostatic interaction between the vesicle and the surface was
modeled using the linear Derjaguin approximation for a low ionic concentration
solution. The sedimentation rate as a function of the distance of the vesicle
to the surface was determined both experimentally and from the computer
simulations. The gap between the vesicle and the surface, as well as the shape
of the vesicle at equilibrium were also studied. It was determined that
inclusion of the electrostatic interaction is fundamental to accurately predict
the sedimentation rate as the vesicle approaches the surface and the size of
the gap at equilibrium, we also observed that the presence of charge in the
membrane increases its rigidity
Quantum fidelity and quantum phase transitions in matrix product states
Matrix product states, a key ingredient of numerical algorithms widely
employed in the simulation of quantum spin chains, provide an intriguing tool
for quantum phase transition engineering. At critical values of the control
parameters on which their constituent matrices depend, singularities in the
expectation values of certain observables can appear, in spite of the
analyticity of the ground state energy. For this class of generalized quantum
phase transitions we test the validity of the recently introduced fidelity
approach, where the overlap modulus of ground states corresponding to slightly
different parameters is considered. We discuss several examples, successfully
identifying all the present transitions. We also study the finite size scaling
of fidelity derivatives, pointing out its relevance in extracting critical
exponents.Comment: 7 pages, 3 figure
Applied Koopman Operator Theory for Power Systems Technology
Koopman operator is a composition operator defined for a dynamical system
described by nonlinear differential or difference equation. Although the
original system is nonlinear and evolves on a finite-dimensional state space,
the Koopman operator itself is linear but infinite-dimensional (evolves on a
function space). This linear operator captures the full information of the
dynamics described by the original nonlinear system. In particular, spectral
properties of the Koopman operator play a crucial role in analyzing the
original system. In the first part of this paper, we review the so-called
Koopman operator theory for nonlinear dynamical systems, with emphasis on modal
decomposition and computation that are direct to wide applications. Then, in
the second part, we present a series of applications of the Koopman operator
theory to power systems technology. The applications are established as
data-centric methods, namely, how to use massive quantities of data obtained
numerically and experimentally, through spectral analysis of the Koopman
operator: coherency identification of swings in coupled synchronous generators,
precursor diagnostic of instabilities in the coupled swing dynamics, and
stability assessment of power systems without any use of mathematical models.
Future problems of this research direction are identified in the last
concluding part of this paper.Comment: 31 pages, 11 figure
Randomly Charged Polymers, Random Walks, and Their Extremal Properties
Motivated by an investigation of ground state properties of randomly charged
polymers, we discuss the size distribution of the largest Q-segments (segments
with total charge Q) in such N-mers. Upon mapping the charge sequence to
one--dimensional random walks (RWs), this corresponds to finding the
probability for the largest segment with total displacement Q in an N-step RW
to have length L. Using analytical, exact enumeration, and Monte Carlo methods,
we reveal the complex structure of the probability distribution in the large N
limit. In particular, the size of the longest neutral segment has a
distribution with a square-root singularity at l=L/N=1, an essential
singularity at l=0, and a discontinuous derivative at l=1/2. The behavior near
l=1 is related to a another interesting RW problem which we call the "staircase
problem". We also discuss the generalized problem for d-dimensional RWs.Comment: 33 pages, 19 Postscript figures, RevTe
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