Showing papers on "Monte Carlo method published in 1991"
Book•
01 Jan 1991
TL;DR: This book discusses the construction of tests in non-standard situations testing for randomness of species co-occurences on islands examining time change in niche ovelap probing multivariate data with random skewers other examples.
Abstract: Part 1 Randomization tests and confidence intervals: the idea of a randomization test examples of a randomization test aspects of randomization testing raised by the examples confidence intervals from randomization. Part 2 Monte Carlo and other computer intensive methods: Monte Carlo tests jackknifing bootstrapping bootstrap tests of significance and confidence intervals. Part 3 Some general considerations: power determining how many randomizations are needed determining a randomization distribution exactly the computer generation of pseudo-random numbers generating random permutations. Part 4 One and two sample tests: the paired comparisons design the one sample randomization test the two sample randomization test the comparison of two samples on multiple measurements. Part 5 Analysis of variance: one factor analysis of variance Bartlett's test for constant variance examples of more complicated types of analysis of variance discussion computer program. Part 6 Regrssion analysis: simple regression testing for a non-zero beta value confidence limits for beta multiple linear regression randomizing X variable values. Part 7 Distance matrices and spatial data: testing for association between distance matrices Mantel's test determining significance by sampling randomization distribution confidence limits for a matrix regression coefficient problems involving more than two matrices. Part 8 Other analyses on spatial data: the study of spatial point patterns Mead's randomization test a test based on nearest neighbour distances testing for an association between two point patterns the Besag-Diggle test tests using distances between points. Part 9 Time series: randomization and time series randomization tests for serial correlation randomization tests for trend randomization tests for periodicity irregularly spaced series tests on times of occurence discussion of procedures for irregular series bootstrap and Monte Carlo tests. Part 10 Multivariate data: univariate and multivariate tests sample means and covariance matrices comparison on sample means vectors chi-squared analyses for count data principal component analysis and other one sample methods discriminate function analysis. Part 11 Ad hoc methods: the construction of tests in non-standard situations testing for randomness of species co-occurences on islands examining time change in niche ovelap probing multivariate data with random skewers other examples. Part 12 Conclusion: randomization methods bootstrap and Monte Carlo methods.
1,705 citations
01 Jan 1991
TL;DR: Markov chain Monte Carlo (MCMC) as discussed by the authors is a general tool for simulation of complex stochastic processes useful in many types of statistical inference, including maximum likelihood estimation and maximum pseudo likelihood estimation.
Abstract: Markov chain Monte Carlo (e. g., the Metropolis algorithm and Gibbs sampler) is a general tool for simulation of complex stochastic processes useful in many types of statistical inference. The basics of Markov chain Monte Carlo are reviewed, including choice of algorithms and variance estimation, and some new methods are introduced. The use of Markov chain Monte Carlo for maximum likelihood estimation is explained, and its performance is compared with maximum pseudo likelihood estimation.
1,242 citations
TL;DR: In this paper, particle-in-cell (PIC) combined with Monte Carlo collision (MCC) calculations are used for simulation of partially ionized gases, with many of the features met in low-temperature collision plasmas.
Abstract: Many-particle charged-particle plasma simulations using spatial meshes for the electromagnetic field solutions, particle-in-cell (PIC) merged with Monte Carlo collision (MCC) calculations, are coming into wide use for application to partially ionized gases. The author emphasizes the development of PIC computer experiments since the 1950s starting with one-dimensional (1-D) charged-sheet models, the addition of the mesh, and fast direct Poisson equation solvers for 2-D and 3-D. Details are provided for adding the collisions between the charged particles and neutral atoms. The result is many-particle simulations with many of the features met in low-temperature collision plasmas; for example, with applications to plasma-assisted materials processing, but also related to warmer plasmas at the edges of magnetized fusion plasmas. >
1,115 citations
TL;DR: In this article, a class of multicanonical Monte Carlo algorithms is presented which can reduce the slowing down to a quadratic power law ≈V2. But this algorithm is not suitable for the case of finite volumes.
1,086 citations
TL;DR: If a ‘‘dynamical hierarchy’’ of transition probabilities is created which also satisfy the detailed‐balance criterion, then Monte Carlo methods may be utilized to simulate the Poisson process and both static and dynamic properties of model Hamiltonian systems may be obtained and interpreted consistently.
Abstract: Monte Carlo methods are utilized as computational tools in many areas of chemical physics. In this paper, we present the theoretical basis for a dynamical Monte Carlo method in terms of the theory of Poisson processes. We show that if: (1) a ‘‘dynamical hierarchy’’ of transition probabilities is created which also satisfy the detailed‐balance criterion; (2) time increments upon successful events are calculated appropriately; and (3) the effective independence of various events comprising the system can be achieved, then Monte Carlo methods may be utilized to simulate the Poisson process and both static and dynamic properties of model Hamiltonian systems may be obtained and interpreted consistently.
1,039 citations
TL;DR: In this paper, a general fractal decomposition of exponential operators is presented in any order m. The decomposition exp[x(A+B)]=[Sm(x/n)]n +O(xm+1/nm) yields a new efficient approach to quantum Monte Carlo simulations.
Abstract: A general scheme of fractal decomposition of exponential operators is presented in any order m. Namely, exp[x(A+B)]=Sm(x)+O(xm+1) for any positive integer m, where Sm(x)=et1A et2B et3A et4B⋅⋅⋅etMA with finite M depending on m. A general recursive scheme of construction of {tj} is given explicitly. It is proven that some of {tj} should be negative for m≥3 and for any finite M (nonexistence theorem of positive decomposition). General systematic decomposition criterions based on a new type of time‐ordering are also formulated. The decomposition exp[x(A+B)]=[Sm(x/n)]n +O(xm+1/nm) yields a new efficient approach to quantum Monte Carlo simulations.
612 citations
IBM1
TL;DR: In this article, Monte Carlo simulations of electron transport in seven semiconductors of the diamond and zinc-blende structure (Ge, Si, GaAs, InP, AlAs, AlP, InAs, GaP) and some of their alloys were performed at two lattice temperatures (77 and 300 K).
Abstract: Monte Carlo simulations of electron transport in seven semiconductors of the diamond and zinc-blende structure (Ge, Si, GaAs, InP, AlAs, InAs, GaP) and some of their alloys (Al/sub x/Ga/sub 1-x/As, In/sub x/Ga/sub 1-x/As, Ga/sub x/In/sub 1-x/P) and hole transport in Si were performed at two lattice temperatures (77 and 300 K). The model uses band structures obtained from local empirical pseudopotential calculations and particle-lattice scattering rates computed from the Fermi golden rule to account for band-structure effects. Intervalley deformation potentials significantly lower than those which have been previously reported are needed to reproduce available experimental data. This is attributed to the more complicated band structures, particularly around the L- and X-symmetry points in most materials. Satisfactory agreement is obtained between Monte Carlo results and some experiments. >
572 citations
TL;DR: The author's main purpose is to review the techniques and applications of the Monte Carlo method in medical radiation physics since Raeside's review article in 1976, with emphasis on applications where proton and/or electron transport in matter is simulated.
Abstract: The author's main purpose is to review the techniques and applications of the Monte Carlo method in medical radiation physics since Raeside's review article in 1976. Emphasis is given to applications where proton and/or electron transport in matter is simulated. Some practical aspects of Monte Carlo practice, mainly related to random numbers and other computational details, are discussed in connection with common computing facilities available in hospital environments. Basic aspects of electron and photon transport are reviewed, followed by the presentation of the Monte Carlo codes widely available in the public domain. Applications in different areas of medical radiation physics, such as nuclear medicine, diagnostic X-rays, radiotherapy physics (including dosimetry), and radiation protection, and also microdosimetry and electron microscopy, are presented. Actual and future trends in the field, like Inverse Monte Carlo methods, vectorization of codes and parallel processors calculations are also discussed.
554 citations
Book•
22 Mar 1991
TL;DR: In this article, the authors present a book which discusses the same topics in the three levels known from the literature and gives useful information for both beginners and experienced readers, both well-established old techniques and also newest findings.
Abstract: With this book we try to reach several more-or-less unattainable goals namely: To compromise in a single book all the most important achievements of Monte Carlo calculations for solving neutron and photon transport problems. To present a book which discusses the same topics in the three levels known from the literature and gives us useful information for both beginners and experienced readers. It lists both well-established old techniques and also newest findings.
470 citations
TL;DR: An algorithm is described that prices European average options and a closed-form solution is derived for European geometric average options that is comparable to the Black-Scholes algorithm.
Abstract: An algorithm is described that prices European average options. The algorithm is tested against Monte Carlo estimates and is shown to be accurate. The speed of the algorithm is comparable to the Black-Scholes algorithm. A closed-form solution is derived for European geometric average options.
459 citations
TL;DR: Using the QCD coherent branching algorithm, the authors compute the Deep Inelastic Scattering and Drell-Yan hard cross sections in the semi-inclusive region of large χ and compare the results with known analytical expressions to the same accuracy in the MS subtraction scheme.
TL;DR: In this article, a library of Monte Carlo programs for leptonic and semileptonic decays of the τ lepton is presented, which can be easily attached to any Monte Carlo program simulating the production of τ's.
02 Nov 1991
TL;DR: The ITS system as discussed by the authors is a powerful and user-friendly software package permitting state-of-the-art Monte Carlo solution of linear time-independent coupled electron/photon radiation transport problems, with or without the presence of macroscopic electric and magnetic fields of arbitrary spatial dependence.
Abstract: The ITS system is a powerful and user-friendly software package permitting state-of-the-art Monte Carlo solution of linear time-independent coupled electron/photon radiation transport problems, with or without the presence of macroscopic electric and magnetic fields of arbitrary spatial dependence. Version 3.0 is a major upgrade of the system with important improvements in the physical model, variance reduction, I/O, and user friendliness. Improvements to the cross-section generator include the replacement of Born-approximation bremsstrahlung cross section with the results of numerical phase-shift calculations, the addition of coherent scattering and binding effects in incoherent scattering, an upgrade of collisional and radiative stopping powers, and a complete rewrite to Fortran 77 standards emphasizing Block-IF structure. Improvements in the Monte Carlo codes are also described. >
TL;DR: In this paper, the applicability of genetic algorithms to the inversion of plane-wave seismograms was investigated, where a random walk in model space and a transition probability rule were used to help guide their search.
Abstract: Seismic waveform inversion is one of many geophysical problems which can be identified as a nonlinear multiparameter optimization problem. Methods based on local linearization fail if the starting model is too far from the true model. We have investigated the applicability of “Genetic Algorithms” (GA) to the inversion of plane‐wave seismograms. Like simulated annealing, genetic algorithms use a random walk in model space and a transition probability rule to help guide their search. However, unlike a single simulated annealing run, the genetic algorithms search from a randomly chosen population of models (strings) and work with a binary coding of the model parameter set. Unlike a pure random search, such as in a “Monte Carlo” method, the search used in genetic algorithms is not directionless. Genetic algorithms essentially consist of three operations, selection, crossover, and mutation, which involve random number generation, string copies, and some partial string exchanges. The choice of the initial popul...
TL;DR: This article presents the vectorization and ensuing optimization of VENUS on the CRAY‐YMP and IBM‐3090 in terms of both global strategies and technical details, and proposes a switching algorithm designed to enhance the vector performance and to minimize the memory storage.
Abstract: The general chemical dynamics computer program VENUS is used to perform classical trajectory simulations for large polyatomic systems, with many atoms and complicated potential energy functions. To simulate an ensemble of many trajectories requires a large amount of CPU time. Since each trajectory is independent, it is possible to parallel process a large set of trajectories instead of processing the trajectories by the conventional sequential approach. This enhances the vectorizability of the VENUS program, since the integration of Hamilton's equations of motion and the gradient evaluation, which comprise 97.8% of the CPU, can each be parallel processed. In this article, the vectorization and ensuing optimization of VENUS on the CRAY‐YMP and IBM‐3090 are presented in terms of both global strategies and technical details. A switching algorithm is designed to enhance the vector performance and to minimize the memory storage. A performance of 140 MFLOPS and a vector/scalar execution rate ratio of 10.6 are observed when this new version of VENUS is used to study the association of CH3 with the H(Ar)12 cluster on the CRAY‐YMP.
CERN1
TL;DR: In this article, an algorithm for the Monte Carlo simulation of QED single-photon radiative corrections in decays is presented, which is implemented in an independent package written in FORTRAN 77.
TL;DR: In this article, the variable soft sphere (VSS) model was introduced for both the viscosity and diffusion cross sections (coefficients) to be consistent with those of the inverse power law (IPL) or Lennard Jones (LJ) potential.
Abstract: The variable soft sphere (VSS) molecular model is introduced for both the viscosity and diffusion cross sections (coefficients) to be consistent with those of the inverse‐power‐law (IPL) or Lennard‐Jones (LJ) potential. The VSS model has almost the same analytical and computational simplicity (computation time) as the variable hard sphere (VHS) model in the Monte Carlo simulation of rarefied gas flows. The null‐collision Monte Carlo method is used to make comparative calculations for the molecular diffusion in a heat‐bath gas and the normal shock wave structure in a simple gas. For the most severe test of the VSS model for the IPL potential, the softest practical model corresponding to the Maxwell molecule is chosen. The agreement in the molecular diffusion and shock wave structure between the VSS model and the IPL or LJ potential is remarkably good.
TL;DR: This paper sets out a Bayesian representation of the model in the spirit of Kalbfleisch (1978) and discusses inference using Monte Carlo methods.
Abstract: Many analyses in epidemiological and prognostic studies and in studies of event history data require methods that allow for unobserved covariates or "frailties." Clayton and Cuzick (1985, Journal of the Royal Statistical Society, Series A 148, 82-117) proposed a generalization of the proportional hazards model that implemented such random effects, but the proof of the asymptotic properties of the method remains elusive, and practical experience suggests that the likelihoods may be markedly nonquadratic. This paper sets out a Bayesian representation of the model in the spirit of Kalbfleisch (1978, Journal of the Royal Statistical Society, Series B 40, 214-221) and discusses inference using Monte Carlo methods.
TL;DR: The average protonation of residues as a function of pH from an equilibrium distribution of states generated by random sampling and the shape of the resulting curve agreed fairly well with experiment, but the proton uptake from which the free energy was calculated agreed only to within a factor of two with the observed values.
Abstract: We used Monte Carlo methods to treat statistical problem of electrostatic interactions among many titrating amino acids and applied these methods to lysozyme and the photosynthetic reaction center of Rhodobacter sphaeroides, including all titrating sites. We computed the average protonation of residues as a function of pH from an equilibrium distribution of states generated by random sampling. Electrostatic energies were calculated from a finite difference solution to the linearized Poisson-Boltzmann equation using the coordinates from solved protein structures. For most calculations we used the Metropolis algorithm to sample protonation states; for strongly coupled sites, we substantially reduced sampling errors by using a modified algorithm that allows multiple site transitions. The Monte Carlo method agreed with calculations for a small test system, lysozyme, for which the complete partition function was calculated. We also calculated the pH dependence of the free energy change associated with electron transfer from the primary to the secondary quinone in the photosynthetic reaction center. The shape of the resulting curve agreed fairly well with experiment, but the proton uptake from which the free energy was calculated agreed only to within a factor of two with the observed values. We believe that this discrepancy resulted from errors in the individual electrostatic energy calculations rather than from errors in the Monte Carlo sampling.
Book•
01 Aug 1991
TL;DR: In this article, the DAMOCLES Monte Carlo Device Simulation Program (DMCDPS) is implemented for Semiconductor Heterostructure Devices and Monte Carlo Simulation of Quasi-One-Dimensional Systems.
Abstract: 1. Numerical Aspects and Implementation of the DAMOCLES Monte Carlo Device Simulation Program.- 2. Scattering Mechanisms for Semiconductor Transport Calculations.- 3. Evaluating Photoexcitation Experiments Using Monte Carlo Simulations.- 4. Extensions of the Monte Carlo Simulation in Semiconductors to Fast Processes.- 5. Theory and Calculation of the Deformation Potential Electron-Phonon Scattering Rates in Semiconductors.- 6. Ensemble Monte Carlo Investigation of Nonlinear Transport Effects in Semiconductor Heterostructure Devices.- 7. Monte Carlo Simulation of Quasi-One-Dimensional Systems.- 8. The Application of Monte Carlo Techniques in Advanced Hydrodynamic Transport Models.- 9. Vectorization of Monte Carlo Algorithms for Semiconductor Simulation.- 10. Full Band Monte Carlo Program for Electrons in Silicon.
CERN1
TL;DR: A hamiltonian-guided Monte Carlo algorithm for simulations of lattice field theories allowing the trajectory length to be shrunk to the step-size without losing on the speed of configuration decorrelation is presented.
TL;DR: In this article, the authors present analytical representations of the six-dimensional potential energy hypersurface for (HF)2, the parameters of which are closely adjusted to low energy experimental properties such as hydrogen bond dissociation energy (D0=1062 cm−1 ) and vibrational-rotational spectra in the far and mid infrared.
Abstract: We report analytical representations of the six‐dimensional potential energy hypersurface for (HF)2, the parameters of which are closely adjusted to low energy experimental properties such as hydrogen bond dissociation energy (D0=1062 cm−1 ) and vibrational–rotational spectra in the far and mid infrared. We present a detailed analysis of properties of the hypersurface in terms of its stationary points, harmonic normal mode amplitudes, and frequencies for the Cs minimum and C2h saddle point and effective Morse parameters and anharmonic overtone vibrational structure for the hydrogen bond and the HF stretching vibrations. The comparison between experimental data and the potential energy surface is carried out by means of accurate solutions of the rotational–vibrational Schrodinger equation with quantum Monte Carlo techniques, which include anharmonic interactions between all modes for the highly flexible dimer. Two extensions of the quantum Monte Carlo technique are presented, which are based on the clamped...
Book•
01 Oct 1991
TL;DR: General Schemes for Constructing Scalar and Vector Monte Carlo Algorithms for Solving Boundary Value Problems: Random Walks on Boundary and Inside the Domain Algorithm and Numerical Experiments.
Abstract: General Schemes for Constructing Scalar and Vector Monte Carlo Algorithms for Solving Boundary Value Problems: Random Walks on Boundary and Inside the Domain Algorithms. Random Walks and Approximations of Random Processes. Monte Carlo Algorithms for Solving Integral Equations: Algorithms Based on Numerical Analytical Continuation. Asymptotically Unbiased Estimates Based on Singular Approximation of the Kernel. The Eigen-Value Problems for Integral Operators. Alternative Constructions of the Resolvent: Modifications and Numerical Experiments. Monte Carlo Algorithms for Solving Boundary Value Problems of the Potential Theory: The Walk on Boundary Algorithms for Solving Interior and Exterior Boundary Value Problems. Walk Inside the Domain Algorithms. Numerical Solution of Test and Applied Problems of Potential Theory in Deterministic. Monte Carlo Algorithms for Solving High-order Equations and Problems in Elasticity: Biharmonic Problem. Metaharmonic Equations. Spatial Problems of Elasticity Theory. Applications to Stochastic Elasticity Problems. Diffusion Problems: Walk on Boundary Algorithms for the Heat Equation. The Walk Inside the Domain Algorithms. Particle Diffusion in Random Velocity Fields. Applications to Diffusion Problems.
TL;DR: In this paper, the Coulomb forces over a charged particle by other charged particles are derived for the sums over Coulomb force exerted on a charge by other charge particles, the central cell system being repeated to infinity by periodic boundary conditions.
Abstract: Formulae are derived for the sums over Coulomb forces exerted on a charged particle by other charged particles, the central cell system being repeated to infinity by periodic boundary conditions. Such sums are needed in molecular dynamics simulations involving either ions or neutral molecules represented as bound conglomerates of charges, and in astrophysical simulations of gravitating masses. The derived sums are rapidly convergent, being expressed in terms of Bessel functions Kr(z), which decrease exponentially with z. The force expressions are integrated analytically to give the potential function, which may be used in Monte Carlo simulations. The geometries considered are: (i) systems confined between two parallel walls, and (ii) unconfined three-dimensional systems.
TL;DR: Results of Monte Carlo simulations of folding of a model ``protein,'' which is a freely joined 27-monomer chain on a simple cubic lattice with nearest-neighbor interactions, are reported, finding only one out of thirty sequences folds and finds the global minimum.
Abstract: Results of Monte Carlo simulations of folding of a model ``protein,'' which is a freely joined 27-monomer chain on a simple cubic lattice with nearest-neighbor interactions, are reported. All compact self-avoiding conformations on this chain have been enumerated, and the conformation (``native'') corresponding to the global minimum of energy is known for each sequence. Only one out of thirty sequences folds and finds the global minimum. For this sequence, the folding process has a two-stage character, with a rapid noncooperative compactization followed by a slower transition over a free-energy barrier to the global minimum. The evolutionary implications of the results are discussed.
TL;DR: In this paper, the authors applied the technique of evaluating a nonlocal pseudopotential with a trial function to give an approximate, local many-body pseudopoential which was used in a valence-only diffusion Monte Carlo (DMC) calculation.
Abstract: We have applied the technique of evaluating a nonlocal pseudopotential with a trial function to give an approximate, local many‐body pseudopotential which was used in a valence‐only diffusion Monte Carlo (DMC) calculation. The pair and triple correlation terms in the trial function have been carefully optimized to minimize the effect of the locality approximation. We discuss the accuracy and computational demands of the nonlocal pseudopotential evaluation for the DMC method. Calculations of Si, Sc, and Cu ionic and atomic states and the Si2 dimer are reported. In most cases ∼90% of the correlation energy was recovered at the variational level and excellent estimations of the ground state energies were obtained by the DMC simulations. The small statistical error allowed us to determine the quality of the assumed pseudopotentials by comparison of the DMC results with experimental values.
TL;DR: The details of an application of the method of maximum entropy to the extraction of spectral and transport properties from the imaginary-time correlation functions generated from quantum Monte Carlo simulations of the nondegenerate, symmetric, single-impurity Anderson model are reported.
Abstract: We report the details of an application of the method of maximum entropy to the extraction of spectral and transport properties from the imaginary-time correlation functions generated from quantum Monte Carlo simulations of the nondegenerate, symmetric, single-impurity Anderson model. We find that these physical properties are approximately universal functions of temperature and frequency when these parameters are scaled by the Kondo temperature. We also found that important details for successful extractions included the generation of statistically independent, Gaussian-distributed data, and a good choice of a default model to represent the state of our prior knowledge about the result in the absence of data. We suggest that our techniques are not restricted to the Hamiltonian and quantum Monte Carlo algorithm used here, but that maximum entropy and these techniques lay the general groundwork for the extraction of dynamical information from imaginary-time data generated by other quantum Monte Carlo simulations.
TL;DR: In this paper, a complete formulation of scattered wave energy propagation in a random isotropic scattering medium is provided, which is based on the stationary energy transport theory studied by Wu (1985) to the time dependent case, and an iterative solution of this equation gives us a general expression of temporal variation of scattered energy density at arbitrary source and receiver locations as a Neumann series expansion characterized by powers of the scattering coefficient.
Abstract: In this paper we provide a complete formulation of scattered wave energy propagation in a random isotropic scattering medium. First, we formulate the scattered wave energy equation by extending the stationary energy transport theory studied by Wu (1985) to the time dependent case. The iterative solution of this equation gives us a general expression of temporal variation of scattered energy density at arbitrary source and receiver locations as a Neumann series expansion characterized by powers of the scattering coefficient. The first term of this series leads to the first-order scattering formula obtained by Sato (1977). For the source and receiver coincident case, our solution gives the corrected version of high-order formulas obtained by Gao et al. (1983b). Solving the scattered wave energy equation using a Fourier transform technique, we obtain a compact integral solution for the temporal decay of scattered wave energy which includes all multiple scattering contributions and can be easily computed numerically. Examples of this solution are presented and compared with that of the single scattering, energy flux, and diffusion models. We then discuss the energy conservation for our system by starting with our fundamental scattered wave energy equation and then demonstrating that our formulas satisfy the energy conservation when the contributions from all orders of scattering are summed up. We also generalize our scattered wave energy equations to the case of nonuniformly distributed isotropic scattering and absorption coefficients. To solve these equations, feasible numerical procedures, such as a Monte Carlo simulation scheme, are suggested. Our Monte Carlo approach to solve the wave energy equation is different from previous works (Gusev and Abubakirov, 1987; Hoshiba, 1990) based on the ray theoretical approach.
TL;DR: In this article, a concrete model for hierarchically constrained dynamics in the sense proposed by Palmer et al. (Phys. Rev. Lett.53, 958 (1984)) is presented.
Abstract: A concrete model for hierarchically constrained dynamics in the sense proposed by Palmer et al. (Phys. Rev. Lett.53, 958 (1984)) is presented. The model is a kinetic Ising chain with an asymmetric kinetic constraint, allowing a spin to flip only if its neighbour to the right is in the up spin state. The spin autocorrelation function is obtained by numerically exact calculation for finite chain length up toL=9 and by Monte Carlo simulation for effectively infinite chain length. The Kohlrausch-Williams-Watts formula is found to fit the results only with limited accuracy, and within limited time intervals. We also performed an analytical calculation using an effective-medium approximation. The approximation leads to a spurious blocking transition at a critical up spin concentrationc=0.5.
TL;DR: In this article, the authors considered the problem of estimating the parameters of a complex linear FM signal from a finite number of noisy discrete-time observations, and proposed an estimation algorithm consisting of two fast Fourier transforms (FFTs) accompanied by one-dimensional searches for maxima.
Abstract: The authors consider the problem of estimating the parameters of a complex linear FM signal from a finite number of noisy discrete-time observations An estimation algorithm is proposed, and its asymptotic (large sample) performance is analyzed The algorithm is computationally simple, consisting of two fast Fourier transforms (FFTs) accompanied by one-dimensional searches for maxima The variance of the estimates is shown to be close to the Cramer-Rao lower bound when the signal-to-noise ratio is 0 dB and above The authors applied the algorithm to the problem of estimating the kinematic parameters of an accelerating target by pulse-Doppler radar A representative test case was used to exhibit the usefulness of the algorithm for this problem, and to verify the analytical results by Monte Carlo simulations >