Equivalence of finite dimensional input-output models of solute transport and diffusion in geosciences

We show that for a large class of finite dimensional input-output positive systems that represent networks of transport and diffusion of solute in geological media, there exist equivalent multi-rate mass transfer and multiple interacting continua representations, which are quite popular in geo-sciences. Moreover, we provide explicit methods to construct these equivalent representations. The proofs show that controllability property is playing a crucial role for obtaining equivalence. These results contribute to our fundamental understanding on the effect of fine-scale geological structures on the transfer and dispersion of solute, and, eventually, on their interaction with soil microbes and minerals

The Anderson model of localization: a challenge for modern eigenvalue methods

We present a comparative study of the application of modern eigenvalue algorithms to an eigenvalue problem arising in quantum physics, namely, the computation of a few interior eigenvalues and their associated eigenvectors for the large, sparse, real, symmetric, and indefinite matrices of the Anderson model of localization. We compare the Lanczos algorithm in the 1987 implementation of Cullum and Willoughby with the implicitly restarted Arnoldi method coupled with polynomial and several shift-and-invert convergence accelerators as well as with a sparse hybrid tridiagonalization method. We demonstrate that for our problem the Lanczos implementation is faster and more memory efficient than the other approaches. This seemingly innocuous problem presents a major challenge for all modern eigenvalue algorithms.Comment: 16 LaTeX pages with 3 figures include

Spherical Slepian functions and the polar gap in geodesy

The estimation of potential fields such as the gravitational or magnetic potential at the surface of a spherical planet from noisy observations taken at an altitude over an incomplete portion of the globe is a classic example of an ill-posed inverse problem. Here we show that the geodetic estimation problem has deep-seated connections to Slepian's spatiospectral localization problem on the sphere, which amounts to finding bandlimited spherical functions whose energy is optimally concentrated in some closed portion of the unit sphere. This allows us to formulate an alternative solution to the traditional damped least-squares spherical harmonic approach in geodesy, whereby the source field is now expanded in a truncated Slepian function basis set. We discuss the relative performance of both methods with regard to standard statistical measures as bias, variance and mean-square error, and pay special attention to the algorithmic efficiency of computing the Slepian functions on the region complementary to the axisymmetric polar gap characteristic of satellite surveys. The ease, speed, and accuracy of this new method makes the use of spherical Slepian functions in earth and planetary geodesy practical.Comment: 14 figures, submitted to the Geophysical Journal Internationa

An Overview of Polynomially Computable Characteristics of Special Interval Matrices

It is well known that many problems in interval computation are intractable, which restricts our attempts to solve large problems in reasonable time. This does not mean, however, that all problems are computationally hard. Identifying polynomially solvable classes thus belongs to important current trends. The purpose of this paper is to review some of such classes. In particular, we focus on several special interval matrices and investigate their convenient properties. We consider tridiagonal matrices, {M,H,P,B}-matrices, inverse M-matrices, inverse nonnegative matrices, nonnegative matrices, totally positive matrices and some others. We focus in particular on computing the range of the determinant, eigenvalues, singular values, and selected norms. Whenever possible, we state also formulae for determining the inverse matrix and the hull of the solution set of an interval system of linear equations. We survey not only the known facts, but we present some new views as well

Spin-polarized Quantum Transport in Mesoscopic Conductors: Computational Concepts and Physical Phenomena

Mesoscopic conductors are electronic systems of sizes in between nano- and micrometers, and often of reduced dimensionality. In the phase-coherent regime at low temperatures, the conductance of these devices is governed by quantum interference effects, such as the Aharonov-Bohm effect and conductance fluctuations as prominent examples. While first measurements of quantum charge transport date back to the 1980s, spin phenomena in mesoscopic transport have moved only recently into the focus of attention, as one branch of the field of spintronics. The interplay between quantum coherence with confinement-, disorder- or interaction-effects gives rise to a variety of unexpected spin phenomena in mesoscopic conductors and allows moreover to control and engineer the spin of the charge carriers: spin interference is often the basis for spin-valves, -filters, -switches or -pumps. Their underlying mechanisms may gain relevance on the way to possible future semiconductor-based spin devices. A quantitative theoretical understanding of spin-dependent mesoscopic transport calls for developing efficient and flexible numerical algorithms, including matrix-reordering techniques within Green function approaches, which we will explain, review and employ.Comment: To appear in the Encyclopedia of Complexity and System Scienc

Schematic baryon models, their tight binding description and their microwave realization

A schematic model for baryon excitations is presented in terms of a symmetric Dirac gyroscope, a relativistic model solvable in closed form, that reduces to a rotor in the non-relativistic limit. The model is then mapped on a nearest neighbour tight binding model. In its simplest one-dimensional form this model yields a finite equidistant spectrum. This is experimentally implemented as a chain of dielectric resonators under conditions where their coupling is evanescent and good agreement with the prediction is achieved.Comment: 17 pages, 15 figure

Exploring NK Fitness Landscapes Using Imitative Learning

The idea that a group of cooperating agents can solve problems more efficiently than when those agents work independently is hardly controversial, despite our obliviousness of the conditions that make cooperation a successful problem solving strategy. Here we investigate the performance of a group of agents in locating the global maxima of NK fitness landscapes with varying degrees of ruggedness. Cooperation is taken into account through imitative learning and the broadcasting of messages informing on the fitness of each agent. We find a trade-off between the group size and the frequency of imitation: for rugged landscapes, too much imitation or too large a group yield a performance poorer than that of independent agents. By decreasing the diversity of the group, imitative learning may lead to duplication of work and hence to a decrease of its effective size. However, when the parameters are set to optimal values the cooperative group substantially outperforms the independent agents