13,673 research outputs found

    On the use of a Modified Latin Hypercube Sampling (MLHS) approach in the estimation of a Mixed Logit model for vehicle choice

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    Quasi-random number sequences have been used extensively for many years in the simulation of integrals that do not have a closed-form expression, such as Mixed Logit and Multinomial Probit choice probabilities. Halton sequences are one example of such quasi-random number sequences, and various types of Halton sequences, including standard, scrambled, and shuffled versions, have been proposed and tested in the context of travel demand modeling. In this paper, we propose an alternative to Halton sequences, based on an adapted version of Latin Hypercube Sampling. These alternative sequences, like scrambled and shuffled Halton sequences, avoid the undesirable correlation patterns that arise in standard Halton sequences. However, they are easier to create than scrambled or shuffled Halton sequences. They also provide more uniform coverage in each dimension than any of the Halton sequences. A detailed analysis, using a 16-dimensional Mixed Logit model for choice between alternative-fuelled vehicles in California, was conducted to compare the performance of the different types of draws. The analysis shows that, in this application, the Modified Latin Hypercube Sampling (MLHS) outperforms each type of Halton sequence. This greater accuracy combined with the greater simplicity make the MLHS method an appealing approach for simulation of travel demand models and simulation-based models in general

    Ground state properties of the bond alternating spin-12\frac{1}{2} anisotropic Heisenberg chain

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    Ground state properties, dispersion relations and scaling behaviour of spin gap of a bond alternating spin-12\frac{1}{2} anisotropic Heisenberg chain have been studied where the exchange interactions on alternate bonds are ferromagnetic (FM) and antiferromagnetic (AFM) in two separate cases. The resulting models separately represent nearest neighbour (NN) AFM-AFM and AFM-FM bond alternating chains. Ground state energy has been estimated analytically by using both bond operator and Jordan-Wigner representations and numerically by using exact diagonalization. Dispersion relations, spin gap and several ground state orders have been obtained. Dimer order and string orders are found to coexist in the ground state. Spin gap is found to develop as soon as the non-uniformity in alternating bond strength is introduced in the AFM-AFM chain which further remains non-zero for the AFM-FM chain. This spin gap along with the string orders attribute to the Haldane phase. The Haldane phase is found to exist in most of the anisotropic region similar to the isotropic point.Comment: 16 pages, 6 figures, 1 tabl

    Simple mechanisms that impede the Berry phase identification from magneto-oscillations

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    The phase of quantum magneto-oscillations is often associated with the Berry phase and is widely used to argue in favor of topological nontriviality of the system (Berry phase 2πn+π2\pi n+\pi). Nevertheless, the experimentally determined value may deviate from 2πn+π2\pi n+\pi arbitrarily, therefore more care should be made analyzing the phase of magneto-oscillations to distinguish trivial systems from nontrivial. In this paper we suggest two simple mechanisms dramatically affecting the experimentally observed value of the phase in three-dimensional topological insulators: (i) magnetic field dependence of the chemical potential, and (ii) possible nonuniformity of the system. These mechanisms are not limited to topological insulators and can be extended to other topologically trivial and non-trivial systems.Comment: 9 pages, 4 figures, in published version the title was change

    Characterizing Pixel and Point Patterns with a Hyperuniformity Disorder Length

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    We introduce the concept of a hyperuniformity disorder length that controls the variance of volume fraction fluctuations for randomly placed windows of fixed size. In particular, fluctuations are determined by the average number of particles within a distance hh from the boundary of the window. We first compute special expectations and bounds in dd dimensions, and then illustrate the range of behavior of hh versus window size LL by analyzing three different types of simulated two-dimensional pixel pattern - where particle positions are stored as a binary digital image in which pixels have value zero/one if empty/contain a particle. The first are random binomial patterns, where pixels are randomly flipped from zero to one with probability equal to area fraction. These have long-ranged density fluctuations, and simulations confirm the exact result h=L/2h=L/2. Next we consider vacancy patterns, where a fraction ff of particles on a lattice are randomly removed. These also display long-range density fluctuations, but with h=(L/2)(f/d)h=(L/2)(f/d) for small ff. For a hyperuniform system with no long-range density fluctuations, we consider Einstein patterns where each particle is independently displaced from a lattice site by a Gaussian-distributed amount. For these, at large LL, hh approaches a constant equal to about half the root-mean-square displacement in each dimension. Then we turn to grayscale pixel patterns that represent simulated arrangements of polydisperse particles, where the volume of a particle is encoded in the value of its central pixel. And we discuss the continuum limit of point patterns, where pixel size vanishes. In general, we thus propose to quantify particle configurations not just by the scaling of the density fluctuation spectrum but rather by the real-space spectrum of h(L)h(L) versus LL. We call this approach Hyperuniformity Disorder Length Spectroscopy
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