73,654 research outputs found
A Monte Carlo Solution to the Balitsky-Fadin-Kuraev-Lipatov Equation for Resummation in Perturbative QCD
No full textA simple solution to the BFKL equation is obtained as a series in the number of real gluons emitted with transverse momentum greater than some small cutoff ¯. This solution reveals physics inside the BFKL ladder which is hidden in the standard inclusive solution, and lends itself to a straightforward Monte Carlo implementation. With this approach one can explore new useful physical observables, which are shown to be independent of the cutoff ¯. In addition, this approach allows the imposition of kinematic constraints (such as energy conservation) which are important at finite energies. The distribution of P E? of particles in a central rapidity bin between two widely-spaced jets is presented as an example. The BFKL (Balitsky-Fadin-Kuraev-Lipatov) equation [1], which systematically resums powers of ff s times large rapidity intervals or logarithms of Feynman x in perturbative QCD, has recently moved from the purely theoretical realm to the phenomenological arena. The classic predic..
A Hardware Generator of Multi-point Distributed Random Numbers for Monte Carlo Simulation
No full textMonte Carlo simulation of weak approximations of stochastic differential equations constitutes an intensive computational task. In applications such as finance, for instance, to achieve "real time" execution, as often required, one needs highly efficient implementations of the multi-point distributed random number generator underlying the simulations. In this paper a fast and flexible dedicated hardware solution on a field programmable gate array is presented. A comparative performance analysis between a software-only and the proposed hardware solution demonstrates that the hardware solution is bottleneck-free, retains the flexibility of the software solution and significantly increases the computational efficiency. Moreover, simulations in applications such as economics, insurance, physics, population dynamics, epidemiology, structural mechanics, chemistry and biotechnology can benefit from the obtained speedup.random number generators; random bit generators; hardware implementation; field programmable gate arrays (FPGAs); Monte Carlo simulation; weak Taylor schemes; multi-point distributed random variables
Proxy simulation schemes using likelihood ratio weighted Monte Carlo for generic robust Monte-Carlo sensitivities and high accuracy drift approximation (with applications to the LIBOR Market Model)
No full textWe consider a generic framework for generating likelihood ratio weighted Monte Carlo simulation paths, where we use one simulation scheme K° (proxy scheme) to generate realizations and then reinterpret them as realizations of another scheme K* (target scheme) by adjusting measure (via likelihood ratio) to match the distribution of K° such that E( f(K*) | F_t ) = E( f(K°) w | F_t ). This is done numerically in every time step, on every path. This makes the approach independent of the product (the function f) and even of the model, it only depends on the numerical scheme. The approach is essentially a numerical version of the likelihood ratio method [Broadie & Glasserman, 1996] and Malliavin's Calculus [Fournie et al., 1999; Malliavin, 1997] reconsidered on the level of the discrete numerical simulation scheme. Since the numerical scheme represents a time discrete stochastic process sampled on a discrete probability space the essence of the method may be motivated without a deeper mathematical understanding of the time continuous theory (e.g. Malliavin's Calculus). The framework is completely generic and may be used for high accuracy drift approximations and the robust calculation of partial derivatives of expectations w.r.t. model parameters (i.e. sensitivities, aka. Greeks) by applying finite differences by reevaluating the expectation with a model with shifted parameters. We present numerical results using a Monte-Carlo simulation of the LIBOR Market Model for benchmarking.Monte-Carlo, Likelihood Ratio, Malliavin Calculus, Sensitivities, Greeks
A Monte Carlo solution of the Liouville Equaion for quantum transport in semiconductors
No full textAn original Monte Carlo solution of the Liouville equation for quantum transport in semiconductors is presented
The Monte Carlo method for the solution of charge transport in semiconductors with applications to cavalent materials
No full textThe review presents in a comprehensive and tutorial form the basic principles of the Monte Carlo method, as applied to the solution of transport problems in semiconductors. A collection of results obtained with Monte Carlo simulations is presented for covalent semiconductors
Analysis of quantum features in transport theory from a quantum monte carlo approach
No full textWE PRESENT A mONTE cARLO APPROACH TO THE SOLUTION OF THE Liouvlle equation for an ensemble of carriers in semiconductors
Crossed source-detector geometry for a novel spray diagnostic: Monte Carlo simulation and analytical results
No full textSprays and other industrially relevant turbid media can be quantitatively
characterized by light scattering. However, current optical diagnostic
techniques generate errors in the intermediate scattering regime where the
average number of light scattering is too great for the single scattering to be
assumed, but too few for the diffusion approximation to be applied. Within this
transitional single-to-multiple scattering regime, we consider a novel crossed
source-detector geometry that allows the intensity of single scattering to be
measured separately from the higher scattering orders. We verify Monte Carlo
calculations that include the imperfections of the experiment against analytical
results. We show quantitatively the influence of the detector numerical aperture
and the angle between the source and the detector on the relative intensity of
the scattering orders in the intermediate single-to-multiple scattering regime.
Monte Carlo and analytical calculations of double light-scattering intensity are
made with small particles that exhibit isotropic scattering. The agreement
between Monte Carlo and analytical techniques validates use of the Monte Carlo
approach in the intermediate scattering regime. Monte Carlo calculations are
then performed for typical parameters of sprays and aerosols with anisotropic
(Mie) scattering in the intermediate single-to-multiple scattering regime
Geodesic Monte Carlo on Embedded Manifolds
No full textMarkov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing geodesic flows in the Hamilton–Jacobi representation. This paper takes the differential geometric basis of Markov chain Monte Carlo further by considering methods to simulate from probability distributions that themselves are defined on a manifold, with common examples being classes of distributions describing directional statistics. Proposal mechanisms are developed based on the geodesic flows over the manifolds of support for the distributions, and illustrative examples are provided for the hypersphere and Stiefel manifold of orthonormal matrices
Monte Carlo studies of BFKL Physics
No full textWe study the properties of the BFKL evolution of a (-channel gluon exchange in the high-energy limit. In particular we formulate a solution to the BFKL evolution equation in terms of an explicit sum over emitted gluons, which allows for a Monte Carlo integration of the resulting rapidity ordered multi-gluon phase space. This formulation allows for an introduction of the running of the coupling to the BFKL evolution. More importantly, the Monte Carlo implementation of the solution to the BFKL evolution equation allows for studies of the exclusive final states resulting from the exchange. The full control over the gluon radiation allows for energy and momentum conservation to be observed when calculating the hadronic cross sections. This is in contrast to the standard analytic approach to BFKL physics, which solves the BFKL equation by effectively summing over any number of gluons emitted and integrating over the full rapidity ordered allowed phase space. It is therefore impossible to reconstruct the parton momentum fractions exactly, and thus energy and longitudinal momentum conservation is violated. Although the effect is indeed formally subleading, we show that the numerical impact at present and planned collider energies is very significant. The reduction in parton flux due to the increased energy consumption by the BFKL evolution is sufficient to change the parton level result of an exponential rise of the dijet cross section as a function of the rapidity separation of the leading dijets to a situation much like the LO case. However, we identify the azimuthal correlation between the dijets as an observable sensitive to BFKL effects but more stable under the observation of energy and momentum conservation. We also apply the BFKL MC to a study of dijets at the Tevatron. Finally we consider W + 2-jet production, a process which in the limit of large rapidity separation between the two jets exhibit the same factorisation into two impact factors and a (-channel gluon exchange as dijet production. We identify observables in this setup, for which BFKL effects could be important
Density estimators through Zero Variance Markov Chain Monte Carlo
No full textA Markov Chain Monte Carlo method is proposed for the pointwise evaluation of a density whose normalizing constant is not known. This method was introduced in the physics literature by Assaraf et al (2007). Conditions for unbiasedness of the estimator are derived. A central limit theorem is also proved under regularity conditions. The new idea is tested on some toy-examples.Density estimator, Fundamental solution, MCMC simulation
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