The Lanczos algorithm with selective orthogonalization

A new stable and efficient implementation of the Lanczos algorithm is presented. The algorithm is a powerful method for finding a few eigenvalues and eigenvectors at one or both ends of the spectrum of a symmetric matrix A. The algorithm is particularly effective if A is large and sparse in that the only way in which A enters the calculation is through a subroutine which computes Av for any vector v. Thus the user is free to take advantage of any sparsity structure in A and A need not even be represented as a matrix et al

A short note on the presence of spurious states in finite basis approximations

The genesis of spurious solutions in finite basis approximations to operators which possess a continuum and a point spectrum is discussed and a simple solution for identifying these solutions is suggested

Extending the range of liquids available for NMR cryoporometry studies of porous materials

Nuclear magnetic resonance (NMR) cryoporometry, although well established, can be limited by the inability of any one liquid to probe a broad range of pore sizes, a relatively small number of commonly-used probe liquids and the requirement to match the probe liquid to the chemistry of the material being studied. Here we demonstrate, for the first time, the use of menthol and t-butanol as probe liquids in NMR cryoporometry measurements. Using appropriate estimates for the values of the melting point depression constant, kc, and the non-freezing surface layer, 2sl, NMR melting data was converted into pore size distributions. The melting point depression constant for t-butanol is similar to that of cyclohexane; however due to its functionality, t-butanol may be the preferred liquid used to study the porosity of hydrophilic materials. Menthol, having a larger value of kc, can accurately analyze larger pore sizes up to 100 nm. This represents the first use of menthol and t-butanol to accurately probe pore dimensions in NMR cryoporometry

NMR cryoporometric measurements of porous silica:A method for the determination of melting point depression parameters of probe liquids

Nuclear magnetic resonance (NMR) cryoporometry is a non-invasive method for determining the pore size distributions of materials such as porous silica. Cryoporometry has several advantages over other porometric techniques. It is able to measure the melting process in a series of discrete steps, whereas transient heat flow techniques, such as differential scanning calorimetry (DSC), have a minimum rate of measurement, and, secondly, NMR cryoporometry can analyze pore shapes with any geometry, where nitrogen porosimetry is complicated for samples with spherical pores with narrow necks. However, one key drawback of the method is that, for any one liquid observed in any one material, there is a lack of consensus in the two parameters, kckc andView the MathML source2sl , used to convert experimental NMR melting point depression data into a pore size distribution. By considering two decades worth of literature data, values for both were obtained for water in porous silica supports, in particular an estimate of a non-freezing layer between the solid ice and the inner surface of the pore. These values were used to produce pore size distributions for three silica materials, SBA-15 and KIT-6, both with cylindrical pores but possessing different structures, and SBA-16, which has spherical pores. This represents the first time KIT-6 has been characterized by the NMR method. Furthermore, this work demonstrates a general method for obtaining values for kckc and View the MathML source2sl which can be applied to any liquid for which suitable literature data is available

Negative Impurity Magnetic Susceptibility and Heat Capacity in a Kondo Model with Narrow Peaks in the Local Density of Electron States

Temperature dependencies of the impurity magnetic susceptibility, entropy, and heat capacity have been obtained by the method of numerical renormalization group and exact diagonalization for the Kondo model with peaks in the electron density of states near the Fermi energy (in particular, with logarithmic Van Hove singularities). It is shown that these quantities can be {\it negative}. A new effect has been predicted (which, in principle, can be observed experimentally), namely, the decrease in the magnetic susceptibility and heat capacity of a nonmagnetic sample upon the addition of magnetic impurities into it

Stability of two-dimensional spatial solitons in nonlocal nonlinear media

We discuss existence and stability of two-dimensional solitons in media with spatially nonlocal nonlinear response. We show that such systems, which include thermal nonlinearity and dipolar Bose Einstein condensates, may support a variety of stationary localized structures - including rotating spatial solitons. We also demonstrate that the stability of these structures critically depends on the spatial profile of the nonlocal response function.Comment: 8 pages, 9 figure

Calculation of Densities of States and Spectral Functions by Chebyshev Recursion and Maximum Entropy

We present an efficient algorithm for calculating spectral properties of large sparse Hamiltonian matrices such as densities of states and spectral functions. The combination of Chebyshev recursion and maximum entropy achieves high energy resolution without significant roundoff error, machine precision or numerical instability limitations. If controlled statistical or systematic errors are acceptable, cpu and memory requirements scale linearly in the number of states. The inference of spectral properties from moments is much better conditioned for Chebyshev moments than for power moments. We adapt concepts from the kernel polynomial approximation, a linear Chebyshev approximation with optimized Gibbs damping, to control the accuracy of Fourier integrals of positive non-analytic functions. We compare the performance of kernel polynomial and maximum entropy algorithms for an electronic structure example.Comment: 8 pages RevTex, 3 postscript figure

Detection and imaging in strongly backscattering randomly layered media

Abstract. Echoes from small reflectors buried in heavy clutter are weak and difficult to distinguish from the medium backscatter. Detection and imaging with sensor arrays in such media requires filtering out the unwanted backscatter and enhancing the echoes from the reflectors that we wish to locate. We consider a filtering and detection approach based on the singular value decomposition of the local cosine transform of the array response matrix. The algorithm is general and can be used for detection and imaging in heavy clutter, but its analysis depends on the model of the cluttered medium. This paper is concerned with the analysis of the algorithm in finely layered random media. We obtain a detailed characterization of the singular values of the transformed array response matrix and justify the systematic approach of the filtering algorithm for detecting and refining the time windows that contain the echoes that are useful in imaging

Restarted Q-Arnoldi-type methods exploiting symmetry in quadratic eigenvalue problems

The final publication is available at Springer via http://dx.doi.org/ 10.1007/s10543-016-0601-5.We investigate how to adapt the Q-Arnoldi method for the case of symmetric quadratic eigenvalue problems, that is, we are interested in computing a few eigenpairs of with M, C, K symmetric matrices. This problem has no particular structure, in the sense that eigenvalues can be complex or even defective. Still, symmetry of the matrices can be exploited to some extent. For this, we perform a symmetric linearization , where A, B are symmetric matrices but the pair (A, B) is indefinite and hence standard Lanczos methods are not applicable. We implement a symmetric-indefinite Lanczos method and enrich it with a thick-restart technique. This method uses pseudo inner products induced by matrix B for the orthogonalization of vectors (indefinite Gram-Schmidt). The projected problem is also an indefinite matrix pair. The next step is to write a specialized, memory-efficient version that exploits the block structure of A and B, referring only to the original problem matrices M, C, K as in the Q-Arnoldi method. This results in what we have called the Q-Lanczos method. Furthermore, we define a stabilized variant analog of the TOAR method. We show results obtained with parallel implementations in SLEPc.This work was supported by the Spanish Ministry of Economy and Competitiveness under Grant TIN2013-41049-P. Carmen Campos was supported by the Spanish Ministry of Education, Culture and Sport through an FPU Grant with reference AP2012-0608.Campos, C.; Román Moltó, JE. (2016). Restarted Q-Arnoldi-type methods exploiting symmetry in quadratic eigenvalue problems. BIT Numerical Mathematics. 56(4):1213-1236. https://doi.org/10.1007/s10543-016-0601-5S12131236564Bai, Z., Su, Y.: SOAR: a second-order Arnoldi method for the solution of the quadratic eigenvalue problem. SIAM J. Matrix Anal. 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Humin Formation on SBA-15-pr-SO3H Catalysts during the Alcoholysis of Furfuryl Alcohol to Ethyl Levulinate: Effect of Pore Size on Catalyst Stability, Transport, and Adsorption

Herein, the alcoholysis of furfuryl alcohol in a series of SBA-15-pr-SO3H catalysts with different pore sizes is reported. Elemental analysis and NMR relaxation/diffusion methods show that changes in pore size have a significant effect on catalyst activity and durability. In particular, the decrease in catalyst activity after catalyst reuse is mainly due to carbonaceous deposition, whereas leaching of sulfonic acid groups is not significant. This effect is more pronounced in the largest-pore-size catalyst C3, which rapidly deactivates after one reaction cycle, whereas catalysts with a relatively medium and small average pore size (named, respectively, C2 and C1) deactivate after two reaction cycles and to a lesser extent. CHNS elemental analysis showed that C1 and C3 experience a similar amount of carbonaceous deposition, suggesting that the increased reusability of the small-pore-size catalyst can be attributed to the presence of SO3H groups mostly present on the external surface, as corroborated by results on pore clogging obtained by NMR relaxation measurements. The increased reusability of the C2 catalyst is attributed to a lower amount of humin being formed and, at the same time, reduced pore clogging, which helps to maintain accessible the internal pore space