Fast numerical algorithm for the linear canonical transform

The linear canonical transform (LCT) describes the effect of any quadratic phase system (QPS) on an input optical wave field. Special cases of the LCT include the fractional Fourier transform (FRT), the Fourier transform (FT), and the Fresnel transform (FST) describing free-space propagation. Currently there are numerous efficient algorithms used (for purposes of numerical simulation in the area of optical signal processing) to calculate the discrete FT, FRT, and FST. All of these algorithms are based on the use of the fast Fourier transform (FFT). In this paper we develop theory for the discrete linear canonical transform (DLCT), which is to the LCT what the discrete Fourier transform (DFT) is to the FT. We then derive the fast linear canonical transform (FLCT), an N log N algorithm for its numerical implementation by an approach similar to that used in deriving the FFT from the DFT. Our algorithm is significantly different from the FFT, is based purely on the properties of the LCT, and can be used for FFT, FRT, and FST calculations and, in the most general case, for the rapid calculation of the effect of any QPS.     

Improving hydrogen storage capacity of MOF by functionalization of the organic linker with lithium atoms

A combination of quantum and classical calculations have been performed in order to investigate hydrogen storage in metal-organic frameworks (MOFs) modified by lithium alkoxide groups. Ab initio calculations showed that the interaction energies between the hydrogen molecules and this functional group are up to three times larger compared with unmodified MOF. This trend was verified by grand canonical Monte Carlo (GCMC) simulations in various thermodynamic conditions. The gravimetric capacity of the Li-modified MOFs reached the value of 10 wt % at 77 K and 100 bar, while our results are very promising at room temperature, too, with 4.5 wt %.     

Finite-Size Effects of Surface Tension in Two Segregated BECs Confined by Two Hard Walls

The finite-size effects of the surface tension in two segregated Bose–Einstein condensates limited by two hard walls are studied respectively in canonical ensemble and grand canonical ensemble by means of the Gross–Pitaevskii theory in the modified double-parabola approximation. The analytical formulae of surface tensions and their finite-size effects are found together with a new type of long-range forces acting on two walls.     

Consistent linearization and finite element implementation of an incrementally objective canonical form return mapping algorithm for large deformation inelasticity

The present paper focuses on the consistent linearization and finite element implementation of an incrementally objective canonical form return mapping algorithm. A general and modular algorithmic setting, suited for almost any rate constitutive equations, is presented where the finite deformation consistent tangent modulus is obtained as a by‐product of the integration algorithm. Numerical examples illustrate the good performance of the proposed formulation, especially for large deformation increments with noteworthy superimposed rotation, where the consistent formulation converges quadratically in a reasonable number of iterations. Copyright © 2008 John Wiley & Sons, Ltd.     

Generalized hydrodynamics in the transient regime and irreversible thermodynamics

In this article the thermodynamically consistent formulation of generalized hydrodynamics is reviewed and applications to shock-wave structures, ultrasonic wave absorption and dispersion and microchannel flows of the generalized hydrodynamics so formulated are discussed. The kinematic terms of the constitutive equations in the generalized hydrodynamic equations for liquids, which have been calculated by means of non-equilibrium grand canonical ensemble, are also presented.     

Adaptive multi-index collocation for uncertainty quantification and sensitivity analysis

In this paper, we present an adaptive algorithm to construct response surface approximations of high-fidelity models using a hierarchy of lower fidelity models. Our algorithm is based on multi-index stochastic collocation and automatically balances physical discretization error and response surface error to construct an approximation of model outputs. This surrogate can be used for uncertainty quantification (UQ) and sensitivity analysis (SA) at a fraction of the cost of a purely high-fidelity approach. We demonstrate the effectiveness of our algorithm on a canonical test problem from the UQ literature and a complex multiphysics model that simulates the performance of an integrated nozzle for an unmanned aerospace vehicle. We find that, when the input-output response is sufficiently smooth, our algorithm produces approximations that can be over two orders of magnitude more accurate than single fidelity approximations for a fixed computational budget.     

单壁纳米碳管储氢机制研究

在将单壁纳米碳管当作巨正则系综的基础上,定义了两个序参量,对其储氢机制作了研究。认为纳米碳管之所以能大量会氢的原因是由于解离的氢分子、原子之间形成关联的相互作用会导致中空管内压力下降,气体凝聚成液体状态,储氢增加。     

Pillared graphene: a new 3-D network nanostructure for enhanced hydrogen storage

A multiscale theoretical approach was used to investigate hydrogen storage in a novel three-dimensional carbon nanostructure. This novel nanoporous material has by design tunable pore sizes and surface areas. Its interaction with hydrogen was studied thoroughly via ab initio and grand canonical Monte Carlo calculations. Our results show that, if this material is doped with lithium cations, it can store up to 41 g H2/L under ambient conditions, almost reaching the DOE volumetric requirement for mobile applications.     

Molecular sieving using single wall carbon nanotubes

By using molecular dynamics and grand canonical Monte Carlo simulations, we find that a nanotube with a constriction results in high transport resistance to nitrogen while allowing oxygen to pass at a much higher rate even though these gases have very similar sizes and energetics. This provides an understanding of the reported high permeation rates of oxygen relative to nitrogen in nanoporous carbon membranes and a basis for designing nanotubes with constrictions using available technologies for membrane-based separations.     

Effects of size distribution on the combustion efficiency of a liquid propellant rocket motor

Abstract

A new algorithm is presented to generate the parameters of the Schwarz canonical form. This new algorithm is simpler than the Routh algorithm in evaluating the Schwarz canonical form. The similarity transformation from a state‐space model in the phase‐variable form to that in the Schwarz canonical form is naturally established.     

Exactly Solved Model for 4He Adsorption on Carbon Nanotube Bundles

The thermodynamics of atomic deposit adsorbed in grooves, on outer surface, and into intertube channels of a closed-end carbon nanobundle has been investigated theoretically. The grand canonical partition function for the groove subsystem was found within the transfer-matrix method with regard for interparticle interactions in chains and between the chains. The adsorption isotherms, isosteric heat and heat capacity have been calculated. The proposed theory is in excellent quantitative agreement with the experimental data on thermodynamics of helium adsorbate.     

Digital signal processing for an open-loop fiber-optic gyroscope

Open-loop fiber-optic gyroscopes (FOG's) are generally less stable than closed-loop FOG's, yet they offer simpler implementation. We propose a modification of the harmonic division algorithm for an open-loop FOG, which is more stable and also simpler for implementation than the original one. It is shown that when the analog signal is properly sampled and quantized, the performance of our algorithm reaches that of closed-loop FOG's. Our algorithm may be implemented by the use of off-the-shelf component, and does not require an integrated optics circuit.     

Microscopic studies of fluids in pores: Computer simulation and mean-field theory

The behavior of a simple model of a fluid confined to a single, infinitely long cylindrical pore is investigated by means of both a grand canonical Monte Carlo computer simulation and a mean-field theory. The theory is used to calculate the density profile of the fluid, as well as the grand potential of the system. The effect of the (size of the) pore radius as well as the temperature and pressure on the phase behavior of the fluid is studied in some detail, and the results are compared to those produced by related work in this field. The preliminary results from the simulation indicate that, in pores whose radii are a few molecular diameters in size, the fluid molecules tend to pack in cylindrically concentric shells about the axis of the pore.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

The importance of excited states in the thermodynamics of partially ionized plasma

The expansion of thermodynamic functions into series in terms of degrees of activity in the grand canonical ensemble is used to consistently include the contribution of highly excited states to partial thermodynamic functions of atomic plasma components and to the equation of ionization equilibrium. It is demonstrated that, when the nearest neighbor approximation is used to calculate the atomic partition function, the corrections due to the interaction of charges in continuous spectrum vary considerably compared with the traditionally employed models. No Debye asymptotics are observed either in the decrease of the ionization potential or in the corrections to the charged component pressure.     

Hydrogen storage inside graphene-oxide frameworks

In this paper, we use applied mathematical modelling to investigate the storage of hydrogen molecules inside graphene-oxide frameworks, which comprise two parallel graphenes rigidly separated by perpendicular ligands. Hydrogen uptake is calculated for graphene-oxide frameworks using the continuous approximation and an equation of state for both the bulk and adsorption gas phases. We first validate our approach by obtaining results for two parallel graphene sheets. This result agrees well with an existing theoretical result, namely 1.85 wt% from our calculations, and 2 wt% arising from an ab initio and grand canonical Monte Carlo calculation. This provides confidence to the determination of the hydrogen uptake for the four graphene-oxide frameworks, GOF-120, GOF-66, GOF-28 and GOF-6, and we obtain 1.68, 2, 6.33 and 0 wt%, respectively. The high value obtained for GOF-28 may be partly explained by the fact that the benzenediboronic acid pillars between graphene sheets not only provide mechanical support and porous spaces for the molecular structure but also provide the higher binding energy to enhance the hydrogen storage inside graphene-oxide frameworks. For the other three structures, this binding energy is not as large in comparison to that of GOF-28 and this effect diminishes as the ligand density decreases. In the absence of conflicting data, the present work indicates GOF-28 as a likely contender for practical hydrogen storage.     

Estimation of thermodynamic properties of solutes in silicon II

This paper proposes a computational method for estimating activity coefficients and interaction parameters of solutes in dilute solution taking into consideration the excess entropy of mixing using the grand canonical Monte Carlo simulation. The proposed method was applied to oxygen in silicon solution and its activity coefficient was estimated where a three-body potential was used as inter atomic potentials to reduce computational time. The solubility limit of oxygen was obtained by the reciprocal of the calculated activity coefficient. The calculated value was significantly changed by taking into consideration the excess entropy of mixing.     

The Algorithm of Chemical Species Analysis for <i>Ab Intio</i> Molecular Dynamics Simulations and Its Application

In ab initio molecular dynamics (AIMD) simulations of chemical reactions, it is important but difficult to identify the chemical species in the trajectory automatically and quickly. In this paper, based on the chemical graph theory, an algorithm for molecular species identification, according to the molecular coordinates and empirical bond length database, is presented. As an example, the chemical species in condensed glycine at room temperature are investigated with our algorithm in detail. The chemical species, including canonical and zwitterionic glycine, their protonated and de-protonated states, and the free protons, are all identified, counted and recorded correctly. Potential applications and further development of the algorithm are also discussed.     

Prediction of CH4/H2 Mixture Selectivity in Zn(tbip) from Computer Simulations

We have computed CH₄/H₂ mixture adsorption isotherms and mixture self-diffusivities in Zn(tbip), a nanoporous metal organic material, at 298 K using grand canonical Monte Carlo and equilibrium molecular dynamics simulations. We calculated the adsorption and diffusion selectivities from our simulation results. An approximate model was used to estimate the maximum membrane selectivities. The adsorption selectivity very strongly favors CH₄ over H₂, whereas the diffusion selectivity favors H₂ over CH₄. We find that the adsorption selectivity dominates the mixture selectivity, giving values in the range of 6–50 CH₄/H₂. This indicates that Zn(tbip) may be useful for separating CH₄/H₂ mixtures.     

A new proposed algorithm of arbitrary radix for the computation of the 2D DFT

In this paper, we propose a new approach for computing 2D FFT's that are suitable for implementation on a systolic array architecture. Our algorithm is derived in this paper from a Cooley decimation‐in‐time algorithm by using an appropriate indexing process. It is proved that the number of multiplications necessary to compute our proposed algorithm is significantly reduced while the number of additions remains almost identical to that of conventional 2D FFT's. Comparison results show the good performance of the proposed 2D FFT algorithm against the row‐column FFT transform. Copyright © 1999 John Wiley & Sons, Ltd.