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On the Free Energy Monte Carlo algorithm  [PDF]
M. J. Thill
Physics , 1997,
Abstract: In this paper, I investigate more closely the recently proposed Free Energy Monte Carlo algorithm that is devised in particular for calculations where conventional Monte Carlo simulations struggle with ergodicity problems. The simplest version of the proposed algorithm allows for the determination of the entropy function of statistical systems and/or performs entropy sampling at sufficiently large times. I also show how this algorithm can be used to explore the system's energy space, in particular for minima.
Cost of the Generalised Hybrid Monte Carlo Algorithm for Free Field Theory  [PDF]
A. D. Kennedy,Brian Pendleton
Physics , 2000, DOI: 10.1016/S0550-3213(01)00129-8
Abstract: We study analytically the computational cost of the Generalised Hybrid Monte Carlo (GHMC) algorithm for free field theory. We calculate the Metropolis acceptance probability for leapfrog and higher-order discretisations of the Molecular Dynamics (MD) equations of motion. We show how to calculate autocorrelation functions of arbitrary polynomial operators, and use these to optimise the GHMC momentum mixing angle, the trajectory length, and the integration stepsize for the special cases of linear and quadratic operators. We show that long trajectories are optimal for GHMC, and that standard HMC is more efficient than algorithms based on Second Order Langevin Monte Carlo (L2MC), sometimes known as Kramers Equation. We show that contrary to naive expectations HMC and L2MC have the same volume dependence, but their dynamical critical exponents are z = 1 and z = 3/2 respectively.
Metadynamic sampling of the free energy landscapes of proteins coupled with a Monte Carlo algorithm  [PDF]
F. Marini,C. Camilloni,D. Provasi,R. A. Broglia,G. Tiana
Quantitative Biology , 2007,
Abstract: Metadynamics is a powerful computational tool to obtain the free energy landscape of complex systems. The Monte Carlo algorithm has proven useful to calculate thermodynamic quantities associated with simplified models of proteins, and thus to gain an ever-increasing understanding on the general principles underlying the mechanism of protein folding. We show that it is possible to couple metadynamics and Monte Carlo algorithms to obtain the free energy of model proteins in a way which is computationally very economical.
Efficient calculation of imaginary time displaced correlation functions in the projector auxiliary field quantum Monte-Carlo algorithm  [PDF]
M. Feldbacher,F. F. Assaad
Physics , 2000, DOI: 10.1103/PhysRevB.63.073105
Abstract: The calculation of imaginary time displaced correlation functions with the auxiliary field projector quantum Monte-Carlo algorithm provides valuable insight (such as spin and charge gaps) in the model under consideration. One of the authors and M. Imada [F.F. Assaad and M. Imada, J. Phys. Soc. Jpn. 65 189 (1996).] have proposed a numerically stable method to compute those quantities. Although precise this method is expensive in CPU time. Here, we present an alternative approach which is an order of magnitude quicker, just as precise, and very simple to implement. The method is based on the observation that for a given auxiliary field the equal time Green function matrix, $G$, is a projector: $G^2 = G$.
Stable Quantum Monte Carlo Algorithm for $T=0$ Calculation of Imaginary Time Green Functions  [PDF]
F. F. Assaad,M. Imada
Physics , 1995, DOI: 10.1143/JPSJ.65.189
Abstract: We present a numerically stable Quantum Monte Carlo algorithm to calculate zero-temperature imaginary-time Green functions $ G(\vec{r}, \tau) $ for Hubbard type models. We illustrate the efficiency of the algorithm by calculating the on-site Green function $ G(\vec{r}=0, \tau) $ on $4 \times 4$ to $12 \times 12$ lattices for the two-dimensional half-filled repulsive Hubbard model at $U/t = 4$. By fitting the tail of $ G(\vec{r}=0, \tau) $ at long imaginary time to the form $e^{-\tau \Delta_c}$, we obtain a precise estimate of the charge gap: $\Delta_c = 0.67 \pm 0.02$ in units of the hopping matrix element. We argue that the algorithm provides a powerful tool to study the metal-insulator transition from the insulator side.
Monte Carlo simulation algorithm for pileup effect of pulses in gamma spectroscopy and pileup distortion calculation on 137Cs pulse height spectrum in NaI(Tl) detector  [cached]
AA Mowlavi
Iranian Journal of Physics Research , 2011,
Abstract: In this paper, an algorithm base on Monte Carlo simulation for pileup effect in gamma spectrum of a detection system is presented whose its code was written in FORTRAN language. The code can be run in paralayzable and nonparalazable mode to obtain the pileup distortion and value of pulses pileup for any detection system. The result show, that the computed spectrum of 137Cs is in good agreement with the experimental spectrum in NaI(Tl) detector. The free of pileup free spectrum and sub-spectra with different degrees of pulses of pileup are calculated. Also, we can apply it to different sources and detectors for pileup correction.
Monte Carlo calculation of ion, electron, and photon spectra of xenon atoms in x-ray free-electron laser pulses  [PDF]
Sang-Kil Son,Robin Santra
Physics , 2012, DOI: 10.1103/PhysRevA.85.063415
Abstract: When atoms and molecules are irradiated by an x-ray free-electron laser (XFEL), they are highly ionized via a sequence of one-photon ionization and relaxation processes. To describe the ionization dynamics during XFEL pulses, a rate equation model has been employed. Even though this model is straightforward for the case of light atoms, it generates a huge number of coupled rate equations for heavy atoms like xenon, which are not trivial to solve directly. Here, we employ the Monte Carlo method to address this problem and we investigate ionization dynamics of xenon atoms induced by XFEL pulses at a photon energy of 4500 eV. Charge state distributions, photo-/Auger electron spectra, and fluorescence spectra are presented for x-ray fluences of up to $10^{13}$ photons/$\mu$m$^2$. With the photon energy of 4500 eV, xenon atoms can be ionized up to +44 through multiphoton absorption characterized by sequential one-photon single-electron interactions.
Parallelization of a Dynamic Monte Carlo Algorithm: a Partially Rejection-Free Conservative Approach  [PDF]
G. Korniss,M. A. Novotny,P. A. Rikvold
Physics , 1998, DOI: 10.1006/jcph.1999.6291
Abstract: We experiment with a massively parallel implementation of an algorithm for simulating the dynamics of metastable decay in kinetic Ising models. The parallel scheme is directly applicable to a wide range of stochastic cellular automata where the discrete events (updates) are Poisson arrivals. For high performance, we utilize a continuous-time, asynchronous parallel version of the n-fold way rejection-free algorithm. Each processing element carries an lxl block of spins, and we employ the fast SHMEM-library routines on the Cray T3E distributed-memory parallel architecture. Different processing elements have different local simulated times. To ensure causality, the algorithm handles the asynchrony in a conservative fashion. Despite relatively low utilization and an intricate relationship between the average time increment and the size of the spin blocks, we find that for sufficiently large l the algorithm outperforms its corresponding parallel Metropolis (non-rejection-free) counterpart. As an example application, we present results for metastable decay in a model ferromagnetic or ferroelectric film, observed with a probe of area smaller than the total system.
Algorithmic differentiation and the calculation of forces by quantum Monte Carlo  [PDF]
Sandro Sorella,Luca Capriotti
Physics , 2010, DOI: 10.1063/1.3516208
Abstract: We describe an efficient algorithm to compute forces in quantum Monte Carlo using adjoint algorithmic differentiation. This allows us to apply the space warp coordinate transformation in differential form, and compute all the 3M force components of a system with M atoms with a computational effort comparable with the one to obtain the total energy. Few examples illustrating the method for an electronic system containing several water molecules are presented. With the present technique, the calculation of finite-temperature thermodynamic properties of materials with quantum Monte Carlo will be feasible in the near future.
Monte Carlo Calculation of the Surface Free Energy for the 2d 7-state Potts Model, and an Estimate for 4d SU(3) Gauge Theory  [PDF]
Wolfhard Janke,Bernd A. Berg,Mohammad Katoot
Physics , 1992, DOI: 10.1016/0550-3213(92)90663-V
Abstract: Using the recently proposed multicanonical ensemble, we perform Monte Carlo simulation for the 2d 7-state Potts model and calculate its surface free energy density (surface tension) to be $2 f^s = 0.0241 \pm 0.0010$. This is an order of magnitude smaller than other estimates in the recent literature. Relying on existing Monte Carlo data, we also give a preliminary estimate for the surface tension of 4d SU(3) lattice gauge theory with $L_t=2$.
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