5,860 research outputs found
Efficient Monte Carlo Calculations of the One-Body Density
An alternative Monte Carlo estimator for the one-body density rho(r) is
presented. This estimator has a simple form and can be readily used in any type
of Monte Carlo simulation. Comparisons with the usual regularization of the
delta-function on a grid show that the statistical errors are greatly reduced.
Furthermore, our expression allows accurate calculations of the density at any
point in space, even in the regions never visited during the Monte Carlo
simulation. The method is illustrated with the computation of accurate
Variational Monte Carlo electronic densities for the Helium atom (1D curve) and
for the water dimer (3D grid containing up to 51x51x51=132651 points).Comment: 12 pages with 3 postscript figure
Zero-Variance Zero-Bias Principle for Observables in quantum Monte Carlo: Application to Forces
A simple and stable method for computing accurate expectation values of
observable with Variational Monte Carlo (VMC) or Diffusion Monte Carlo (DMC)
algorithms is presented. The basic idea consists in replacing the usual
``bare'' estimator associated with the observable by an improved or
``renormalized'' estimator. Using this estimator more accurate averages are
obtained: Not only the statistical fluctuations are reduced but also the
systematic error (bias) associated with the approximate VMC or (fixed-node) DMC
probability densities. It is shown that improved estimators obey a
Zero-Variance Zero-Bias (ZVZB) property similar to the usual Zero-Variance
Zero-Bias property of the energy with the local energy as improved estimator.
Using this property improved estimators can be optimized and the resulting
accuracy on expectation values may reach the remarkable accuracy obtained for
total energies. As an important example, we present the application of our
formalism to the computation of forces in molecular systems. Calculations of
the entire force curve of the H,LiH, and Li molecules are presented.
Spectroscopic constants (equilibrium distance) and (harmonic
frequency) are also computed. The equilibrium distances are obtained with a
relative error smaller than 1%, while the harmonic frequencies are computed
with an error of about 10%
Homogeneous algebras
Various concepts associated with quadratic algebras admit natural
generalizations when the quadratic algebras are replaced by graded algebras
which are finitely generated in degree 1 with homogeneous relations of degree
N. Such algebras are referred to as {\sl homogeneous algebras of degree N}. In
particular it is shown that the Koszul complexes of quadratic algebras
generalize as N-complexes for homogeneous algebras of degree N.Comment: 24 page
Impact of Regulatory Agencies on the Efficiency of Publicly-Owned Utilities
We compare the economic efficiency of a publicly-owned utility directly controlled by the government with a publicly-owned utility regulated by a public utility commission (PUC). Regulation by a PUC is modelled as a Nash equilibrium of a game between two principals, the government and the PUC, each of them having control over a subset of decision variables determining the utility performance. A utility manager, who has private information over a productivity parameter, is the agent. Comparisons of both regulatory regimes are made with respect to output, choice of inputs, manager's information rent and firm's profit. Reasons for which the government should prefer one regulatory regime over the other are discussed. The recent regulatory reform of electricity markets in the province of Quebec (Canada) provides an illustration of the model.Regulation, Public Enterprises
International Competition between Public or Mixed Enterprises
We develop a model in which two firms from different countries compete on each other domestic market. Each firm is jointly owned by the residents and the government of its country. The extent of the government's stake in the public enterprise is endogenous and it determines the weight given to domestic consumers' surplus in the firm's payoff function. We show that the choice of each government's stake depends on a trade-off between allocative efficiency on the domestic market and profitability of foreign markets. We also highlight the fact that the government's stake in one country has an impact on firms' behavior in both countries.Regulation, public enterprises, duopoly
International Competition Between Public or Mixed Enterprises
We develop a model in which two firms from different countries compete on each other domestic market. Each firms is jointly owned by the residents and the government of its country. The extent of the government's stake in the public enterprise is endogenous and it determines the weight given the domestic consumers' surplus inithe firm's payoff function. We show that the choice of each government's stake depends on a trade-off between allocative efficiency on the domestic market and profitability of foreign markets. We also highlight the fact that the government's stake in on country has an impact of firms' behavior in both countries.Regulation, Public Enterprises, Duopoly
Risk aggregation, dependence structure and diversification benefit
Insurance and reinsurance live and die from the diversification benefits or lack of it in their risk portfolio. The new solvency regulations allow companies to include them in their computation of risk-based capital (RBC). The question is how to really evaluate those benefits. To compute the total risk of a portfolio, it is important to establish the rules for aggregating the various risks that compose it. This can only be done through modelling of their dependence. It is a well known fact among traders in financial markets that "diversification works the worst when one needs it the most''. In other words, in times of crisis the dependence between risks increases. Experience has shown that very large loss events almost always affect multiple lines of business simultaneously. September 11, 2001, is an example of such an event: when the claims originated simultaneously from lines of business which are usually uncorrelated, such as property and life, at the same time that the assets of the company were depreciated due to the crisis on the stock markets. In this paper, we explore various methods of modelling dependence and their influence on diversification benefits. We show that the latter strongly depend on the chosen method and that rank correlation grossly overestimates diversification. This has consequences on the RBC for the whole portfolio, which is smaller than it should be when correctly accounting for tail correlation. However, the problem remains to calibrate the dependence for extreme events, which are rare by definition. We analyze and propose possible ways to get out of this dilemma and come up with reasonable estimates.Risk-Based Capital, Hierarchical Copula, Dependence, Calibration
A coupled approximate deconvolution and dynamic mixed scale model for large-eddy simulation
Large-eddy simulations of incompressible Newtonian fluid flows with
approximate deconvolution models based on the van Cittert method are reported.
The Legendre spectral element method is used for the spatial discretization to
solve the filtered Navier--Stokes equations. A novel variant of approximate
deconvolution models blended with a mixed scale model using a dynamic
evaluation of the subgrid-viscosity constant is proposed. This model is
validated by comparing the large-eddy simulation with the direct numerical
simulation of the flow in a lid-driven cubical cavity, performed at a Reynolds
number of 12'000. Subgrid modeling in the case of a flow with coexisting
laminar, transitional and turbulent zones such as the lid-driven cubical cavity
flow represents a challenging problem. Moreover, the coupling with the spectral
element method having very low numerical dissipation and dispersion builds a
well suited framework to analyze the efficiency of a subgrid model. First- and
second-order statistics obtained using this new model are showing very good
agreement with the direct numerical simulation. Filtering operations rely on an
invertible filter applied in a modal basis and preserving the C0-continuity
across elements. No clipping on dynamic parameters was needed to preserve
numerical stability
- âŠ