1,255 research outputs found
Analysis of a tensor POD-ROM for parameter dependent parabolic problems
A space-time-parameters structure of the parametric parabolic PDEs motivates
the application of tensor methods to define reduced order models (ROMs). Within
a tensor-based ROM framework, the matrix SVD -- a traditional dimension
reduction technique -- yields to a low-rank tensor decomposition (LRTD). Such
tensor extension of the Galerkin proper orthogonal decomposition ROMs
(POD-ROMs) benefits both the practical efficiency of the ROM and its
amenability for the rigorous error analysis when applied to parametric PDEs.
The paper addresses the error analysis of the Galerkin LRTD-ROM for an abstract
linear parabolic problem that depends on multiple physical parameters. An error
estimate for the LRTD-ROM solution is proved, which is uniform with respect to
problem parameters and extends to parameter values not in a sampling/training
set. The estimate is given in terms of discretization and sampling mesh
properties, and LRTD accuracy. The estimate depends on the smoothness rather
than on the Kolmogorov n-widths of the parameterized manifold of solutions.
Theoretical results are illustrated with several numerical experiments
Interpolatory tensorial reduced order models for parametric dynamical systems
The paper introduces a reduced order model (ROM) for numerical integration of
a dynamical system which depends on multiple parameters. The ROM is a
projection of the dynamical system on a low dimensional space that is both
problem-dependent and parameter-specific. The ROM exploits compressed tensor
formats to find a low rank representation for a sample of high-fidelity
snapshots of the system state. This tensorial representation provides ROM with
an orthogonal basis in a universal space of all snapshots and encodes
information about the state variation in parameter domain. During the online
phase and for any incoming parameter, this information is used to find a
reduced basis that spans a parameter-specific subspace in the universal space.
The computational cost of the online phase then depends only on tensor
compression ranks, but not on space or time resolution of high-fidelity
computations. Moreover, certain compressed tensor formats enable to avoid the
adverse effect of parameter space dimension on the online costs (known as the
curse of dimension). The analysis of the approach includes an estimate for the
representation power of the acquired ROM basis. We illustrate the performance
and prediction properties of the ROM with several numerical experiments, where
tensorial ROM's complexity and accuracy is compared to those of conventional
POD-ROM
Tensorial parametric model order reduction of nonlinear dynamical systems
For a nonlinear dynamical system that depends on parameters, the paper
introduces a novel tensorial reduced-order model (TROM). The reduced model is
projection-based, and for systems with no parameters involved, it resembles
proper orthogonal decomposition (POD) combined with the discrete empirical
interpolation method (DEIM). For parametric systems, TROM employs low-rank
tensor approximations in place of truncated SVD, a key dimension-reduction
technique in POD with DEIM. Three popular low-rank tensor compression formats
are considered for this purpose: canonical polyadic, Tucker, and tensor train.
The use of multilinear algebra tools allows the incorporation of information
about the parameter dependence of the system into the reduced model and leads
to a POD-DEIM type ROM that (i) is parameter-specific (localized) and predicts
the system dynamics for out-of-training set (unseen) parameter values, (ii)
mitigates the adverse effects of high parameter space dimension, (iii) has
online computational costs that depend only on tensor compression ranks but not
on the full-order model size, and (iv) achieves lower reduced space dimensions
compared to the conventional POD-DEIM ROM. The paper explains the method,
analyzes its prediction power, and assesses its performance for two specific
parameter-dependent nonlinear dynamical systems
Neutrino wave function and oscillation suppression
We consider a thought experiment, in which a neutrino is produced by an
electron on a nucleus in a crystal. The wave function of the oscillating
neutrino is calculated assuming that the electron is described by a wave
packet. If the electron is relativistic and the spatial size of its wave packet
is much larger than the size of the crystal cell, then the wave packet of the
produced neutrino has essentially the same size as the wave packet of the
electron. We investigate the suppression of neutrino oscillations at large
distances caused by two mechanisms: 1) spatial separation of wave packets
corresponding to different neutrino masses; 2) neutrino energy dispersion for
given neutrino mass eigenstates. We resolve contributions of these two
mechanisms.Comment: 7 page
Experience in Developing Early Warning System for Financial Crises and the Forecast of Russian Banking Sector Dynamic in 2012
The article summarizes the key results of researches in the field of early warning systems for financial crises, conducted by the Center for Macroeconomic Analysis and Short-Term Forecasting (CMASF) since 2005. The proposed early warning system consists of three major blocks: the leading indicators of certain types of risks and the composite leading indicator of a systemic banking crisis; the medium-term scenario forecasting of key macroeconomic and financial indicators; stress testing of credit and liquidity risks of banks. On the basis of this early warning system we estimate the risks of financial crisis and some kinds of systemic risks in the different scenarios for the Russian economy in 2012. The analysis, in particular, revealed a sensitivity threshold of the domestic financial sector to changes in the world oil prices. Furthermore, it was found that the greatest destabilizing effect on the Russian financial sector may be caused by systemic credit risk.systemic financial crises, credit risks, liquidity risks, currency risks, early warning system, leading indicators, stress testing
Self-energy limited ion transport in sub-nanometer channels
The current-voltage characteristics of the alpha-Hemolysin protein pore
during the passage of single-stranded DNA under varying ionic strength, C, are
studied experimentally. We observe strong blockage of the current, weak
super-linear growth of the current as a function of voltage, and a minimum of
the current as a function of C. These observations are interpreted as the
result of the ion electrostatic self-energy barrier originating from the large
difference in the dielectric constants of water and the lipid bilayer. The
dependence of DNA capture rate on C also agrees with our model.Comment: more experimental material is added. 4 pages, 7 figure
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