28,786 research outputs found
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%
Origin of Spin Ice Behavior in Ising Pyrochlore Magnets with Long Range Dipole Interactions: an Insight from Mean-Field Theory
Recent experiments suggest that the Ising pyrochlore magnets and display qualitative
properties of the ferromagnetic nearest neighbor spin ice model proposed by
Harris {\it et al.}, Phys. Rev. Lett. {\bf 79}, 2554 (1997). The manifestation
of spin ice behavior in these systems {\it despite} the energetic constraints
introduced by the strength and the long range nature of dipole-dipole
interactions, remains difficult to understand. We report here results from a
mean field analysis that shed some light on the origin of spin ice behavior in
(111) Ising pyrochlores. Specifically, we find that there exist a large
frustrating effect of the dipolar interactions beyond the nearest neighbor, and
that the degeneracy established by effective ferromagnetic nearest neighbor
interactions is only very weakly lifted by the long range interactions. Such
behavior only appears beyond a cut-off distance corresponding to
nearest neighbor. Our mean field analysis shows that truncation of dipolar
interactions leads to spurious ordering phenomena that change with the
truncation cut-off distance.Comment: 7 Color POSTSCRIPT figures included. To appear in Canadian Journal of
Physics for the Proceedings of the {\it Highly Frustrated Magnetism 2000
Conference}, Waterloo, Ontario, Canada, June 11-15, 2000 Contact:
[email protected]
Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces
In this paper we present computational techniques to investigate the
solutions of two-component, nonlinear reaction-diffusion (RD) systems on
arbitrary surfaces. We build on standard techniques for linear and nonlinear
analysis of RD systems, and extend them to operate on large-scale meshes for
arbitrary surfaces. In particular, we use spectral techniques for a linear
stability analysis to characterize and directly compose patterns emerging from
homogeneities. We develop an implementation using surface finite element
methods and a numerical eigenanalysis of the Laplace-Beltrami operator on
surface meshes. In addition, we describe a technique to explore solutions of
the nonlinear RD equations using numerical continuation. Here, we present a
multiresolution approach that allows us to trace solution branches of the
nonlinear equations efficiently even for large-scale meshes. Finally, we
demonstrate the working of our framework for two RD systems with applications
in biological pattern formation: a Brusselator model that has been used to
model pattern development on growing plant tips, and a chemotactic model for
the formation of skin pigmentation patterns. While these models have been used
previously on simple geometries, our framework allows us to study the impact of
arbitrary geometries on emerging patterns.Comment: This paper was submitted at the Journal of Mathematical Biology,
Springer on 07th July 2015, in its current form (barring image references on
the last page and cosmetic changes owning to rebuild for arXiv). The complete
body of work presented here was included and defended as a part of my PhD
thesis in Nov 2015 at the University of Ber
Experimental analysis of the boundary layer transition with zero and positive pressure gradient
The influence of a positive pressure gradient on the boundary layer transition is studied. The mean velocity and turbulence profiles of four cases are examined. As the intensity of the pressure gradient is increased, the Reynolds number of the transition onset and the length of the transition region are reduced. The Tollmein-Schlichting waves disturb the laminar regime; the amplification of these waves is in good agreement with the stability theory. The three dimensional deformation of the waves leads finally to the appearance of turbulence. In the case of zero pressure gradient, the properties of the turbulent spots are studied by conditional sampling of the hot-wire signal; in the case of positive pressure gradient, the turbulence appears in a progressive manner and the turbulent spots are much more difficult to characterize
Experimental analysis and computation of the onset and development of the boundary layer transition
The transition of an incompressible boundary layer, with zero pressure gradient and low free-stream turbulence is studied. Mean velocity, turbulence and Reynolds shear stress profiles are presented. The development of the Tollmien-Schlichting waves is clearly shown until the turbulent spots appear. The intermittency phenomenon is studied by conditional sampling of the hotwire signal. The comparison with calculation results obtained by resolution of a set of transport equations shows a good agreement for the mean characteristics of the flow; discrepancies observed for the turbulent quantities evolution are due to the intermittency phenomenon
The Power of Axisymmetric Pulsar
Stationary force-free magnetosphere of an axisymmetric pulsar is shown to
have a separatrix inclination angle of 77.3. The electromagnetic field
has an singularity inside the separatrix near the light cylinder. A
numerical simulation of the magnetosphere which crudely reproduces these
properties is presented. The numerical results are used to estimate the power
of an axisymmetric pulsar: . A need for a better
numerical simulation is pointed out.Comment: 9 page
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