14,660 research outputs found
Sensitivity analysis and parameter estimation for distributed hydrological modeling: potential of variational methods
Variational methods are widely used for the analysis and control of computationally intensive spatially distributed systems. In particular, the adjoint state method enables a very efficient calculation of the derivatives of an objective function (response function to be analysed or cost function to be optimised) with respect to model inputs. In this contribution, it is shown that the potential of variational methods for distributed catchment scale hydrology should be considered. A distributed flash flood model, coupling kinematic wave overland flow and Green Ampt infiltration, is applied to a small catchment of the Thoré basin and used as a relatively simple (synthetic observations) but didactic application case. It is shown that forward and adjoint sensitivity analysis provide a local but extensive insight on the relation between the assigned model parameters and the simulated hydrological response. Spatially distributed parameter sensitivities can be obtained for a very modest calculation effort (~6 times the computing time of a single model run) and the singular value decomposition (SVD) of the Jacobian matrix provides an interesting perspective for the analysis of the rainfall-runoff relation. For the estimation of model parameters, adjoint-based derivatives were found exceedingly efficient in driving a bound-constrained quasi-Newton algorithm. The reference parameter set is retrieved independently from the optimization initial condition when the very common dimension reduction strategy (i.e. scalar multipliers) is adopted. Furthermore, the sensitivity analysis results suggest that most of the variability in this high-dimensional parameter space can be captured with a few orthogonal directions. A parametrization based on the SVD leading singular vectors was found very promising but should be combined with another regularization strategy in order to prevent overfitting
Spin-orbital Kondo decoherence by environmental effects in capacitively coupled quantum dot devices
Strong correlation effects in a capacitively coupled double quantum-dot setup
were previously shown to provide the possibility of both entangling spin-charge
degrees of freedom and realizing efficient spin-filtering operations by static
gate-voltage manipulations. Motivated by the use of such a device for quantum
computing, we study the influence of electromagnetic noise on a general
spin-orbital Kondo model, and investigate the conditions for observing
coherent, unitary transport, crucial to warrant efficient spin manipulations.
We find a rich phase diagram, where low-energy properties sensitively depend on
the impedance of the external environment and geometric parameters of the
system. Relevant energy scales related to the Kondo temperature are also
computed in a renormalization-group treatment, allowing to assess the
robustness of the device against environmental effects.Comment: 13 pages, 13 figures. Minor modifications in V
Non-equilibrium umbrella sampling applied to force spectroscopy of soft matter
Physical systems often respond on a timescale which is longer than that of the measurement. This is particularly true in soft matter where direct experimental measurement, for example in force spectroscopy, drives the soft system out of equilibrium and provides a non-equilibrium measure. Here we demonstrate experimentally for the first time that equilibrium physical quantities (such as the mean square displacement) can be obtained from non-equilibrium measurements via umbrella sampling. Our model experimental system is a bead fluctuating in a time-varying optical trap. We also show this for simulated force spectroscopy on a complex soft molecule--a piston-rotaxane
Description of Pairing correlation in Many-Body finite systems with density functional theory
Different steps leading to the new functional for pairing based on natural
orbitals and occupancies proposed in ref. [D. Lacroix and G. Hupin,
arXiv:1003.2860] are carefully analyzed. Properties of quasi-particle states
projected onto good particle number are first reviewed. These properties are
used (i) to prove the existence of such a functional (ii) to provide an
explicit functional through a 1/N expansion starting from the BCS approach
(iii) to give a compact form of the functional summing up all orders in the
expansion. The functional is benchmarked in the case of the picked fence
pairing Hamiltonian where even and odd systems, using blocking technique are
studied, at various particle number and coupling strength, with uniform and
random single-particle level spacing. In all cases, a very good agreement is
found with a deviation inferior to 1% compared to the exact energy.Comment: 14 pages, 9 figure
Entanglement and Quantum Noise Due to a Thermal Bosonic Field
We analyze the indirect exchange interaction between two two-state systems,
e.g., spins 1/2, subject to a common finite-temperature environment modeled by
bosonic modes. The environmental modes, e.g., phonons or cavity photons, are
also a source of quantum noise. We analyze the coherent vs noise-induced
features of the two-spin dynamics and predict that for low enough temperatures
the induced interaction is coherent over time scales sufficient to create
entanglement. A nonperturbative approach is utilized to obtain an exact
solution for the onset of the induced interaction, whereas for large times, a
Markovian scheme is used. We identify the time scales for which the spins
develop entanglement for various spatial separations. For large enough times,
the initially created entanglement is erased by quantum noise. Estimates for
the interaction and the level of quantum noise for localized impurity electron
spins in Si-Ge type semiconductors are given.Comment: 12 pages, 9 figures; typos correcte
Regression on particle systems connected to mean-field SDEs with applications
In this note we consider the problem of using regression on interacting particles to compute conditional expectations for McKean-Vlasov SDEs. We prove general result on convergence of linear regression algorithms and establish the corresponding rates of convergence. Application to optimal stopping and variance reduction are considered
Projected particle methods for solving McKean--Vlaslov equations
We study a novel projection-based particle method to the solution of the corresponding McKean-Vlasov equation. Our approach is based on the projection-type estimation of the marginal density of the solution in each time step. The projection-based particle method can profit from additional smoothness of the underlying density and leads in many situation to a significant reduction of numerical complexity compared to kernel density estimation algorithms. We derive strong convergence rates and rates of density estimation. The case of linearly growing coefficients of the McKean-Vlasov equation turns out to be rather challenging and requires some new type of averaging technique. This case is exemplified by explicit solutions to a class of McKean-Vlasov equations with affine drift
Multilevel dual approach for pricing American style derivatives
In this article we propose a novel approach to reduce the computational complexity of the dual method for pricing American options. We consider a sequence of martingales that converges to a given target martingale and decompose the original dual representation into a sum of representations that correspond to different levels of approximation to the target martingale. By next replacing in each representation true conditional expectations with their Monte Carlo estimates, we arrive at what one may call a multilevel dual Monte Carlo algorithm. The analysis of this algorithm reveals that the computational complexity of getting the corresponding target upper bound, due to the target martingale, can be significantly reduced. In particular, it turns out that using our new approach, we may construct a multilevel version of the well-known nested Monte Carlo algorithm of Andersen and Broadie (2004) that is, regarding complexity, virtually equivalent to a non-nested algorithm. The performance of this multilevel algorithm is illustrated by a numerical example
Field momentum and gyroscopic dynamics of classical systems with topological defects
The standard relation between the field momentum and the force is generalized
for the system with a field singularity: in addition to the regular force,
there appear the singular one. This approach is applied to the description of
the gyroscopic dynamics of the classical field with topological defects. The
collective variable Lagrangian description is considered for gyroscopical
systems with account of singularities. Using this method we describe the
dynamics of two-dimensional magnetic solitons. We establish a relation between
the gyroscopic force and the singular one. An effective Lagrangian description
is discussed for the magnetic soliton dynamics.Comment: LaTeX, 19 page
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