Optimal conditions for the numerical calculation of the largest Lyapunov exponent for systems of ordinary differential equations

A general indicator of the presence of chaos in a dynamical system is the largest Lyapunov exponent. This quantity provides a measure of the mean exponential rate of divergence of nearby orbits. In this paper, we show that the so-called two-particle method introduced by Benettin et al. could lead to spurious estimations of the largest Lyapunov exponent. As a comparator method, the maximum Lyapunov exponent is computed from the solution of the variational equations of the system. We show that the incorrect estimation of the largest Lyapunov exponent is based on the setting of the renormalization time and the initial distance between trajectories. Unlike previously published works, we here present three criteria that could help to determine correctly these parameters so that the maximum Lyapunov exponent is close to the expected value. The results have been tested with four well known dynamical systems: Ueda, Duffing, R\"ossler and Lorenz.Comment: 12 pages, 8 figures. Accepted in the International Journal of Modern Physics

Geometrical and spectral study of beta-skeleton graphs

We perform an extensive numerical analysis of beta-skeleton graphs, a particular type of proximity graphs. In beta-skeleton graph (BSG) two vertices are connected if a proximity rule, that depends of the parameter beta is an element of (0, infinity), is satisfied. Moreover, for beta > 1 there exist two different proximity rules, leading to lune-based and circle-based BSGs. First, by computing the average degree of large ensembles of BSGs we detect differences, which increase with the increase of beta, between lune-based and circle-based BSGs. Then, within a random matrix theory (RMT) approach, we explore spectral and eigenvector properties of random BSGs by the use of the nearest-neighbor energy-level spacing distribution and the entropic eigenvector localization length, respectively. The RMT analysis allows us to conclude that a localization transition occurs at beta = 1

Literature review of physical and chemical pretreatment processes for lignocellulosic biomass

Different pretreatment technologies published in public literature are described in terms of the mechanisms involved, advantages and disadvantages, and economic assessment. Pretreatment technologies for lignocellulosic biomass include biological, mechanical, chemical methods and various combinations thereof. The choice of the optimum pretreatment process depends very much on the objective of the biomass pretreatment, its economic assessment and environmental impact. Only a small number of pretreatment methods has been reported as being potentially cost-effective thus far. These include steam explosion, liquid hot water, concentrated acid hydrolysis and dilute acid pretreatments

Long-range Heisenberg models in quasi-periodically driven crystals of trapped ions

We introduce a theoretical scheme for the analog quantum simulation of long-range XYZ models using current trapped-ion technology. In order to achieve fully-tunable Heisenberg-type interactions, our proposal requires a state-dependent dipole force along a single vibrational axis, together with a combination of standard resonant and detuned carrier drivings. We discuss how this quantum simulator could explore the effect of long-range interactions on the phase diagram by combining an adiabatic protocol with the quasi-periodic drivings and test the validity of our scheme numerically. At the isotropic Heisenberg point, we show that the long-range Hamiltonian can be mapped onto a non-linear sigma model with a topological term that is responsible for its low-energy properties, and we benchmark our predictions with Matrix-Product-State numerical simulations.Comment: closer to published versio

Correlates of Poverty and Participation in Food Assistance Programs among Hispanic Elders in Massachusetts

Hispanics are a rapidly growing population in Massachusetts, but little is known about the health, nutrition, and economic situation of the elder segment of these groups. In this report, we examine factors associated with poverty and the use of food assistance programs, using data from an NIA-funded project on Hispanic elders in Massachusetts. Poverty is shown to be a major problem with differences across Hispanic subgroups. Puerto Rican and Dominican elders have lower incomes, on average, than other Hispanics—mainly Cubans, and Central and South Americans—or than non-Hispanic whites living in the same neighborhoods. Older age, lower education, and living alone are associated with poverty within this population. Limited income sources and recent immigration are also important factors. Hispanic elders are more likely to receive SSI benefits, but are much less likely to have pension income. Financial insecurity in old age among Hispanics is associated with more chronic ailment and mobility limitations. Puerto Rican and Dominican elders have the highest poverty and disability rates and report the most food insecurity. However, with the exception of the Food Stamp program, participation in food programs tends to be very low for these Hispanic elders. Given the prevalence of problems demonstrated by these groups, more attention to program outreach and adaptation for Hispanic elders is needed.

Topology induced anomalous defect production by crossing a quantum critical point

We study the influence of topology on the quench dynamics of a system driven across a quantum critical point. We show how the appearance of certain edge states, which fully characterise the topology of the system, dramatically modifies the process of defect production during the crossing of the critical point. Interestingly enough, the density of defects is no longer described by the Kibble-Zurek scaling, but determined instead by the non-universal topological features of the system. Edge states are shown to be robust against defect production, which highlights their topological nature.Comment: Phys. Rev. Lett. (to be published

Weighted random--geometric and random--rectangular graphs: Spectral and eigenfunction properties of the adjacency matrix

Within a random-matrix-theory approach, we use the nearest-neighbor energy level spacing distribution $P(s)$ and the entropic eigenfunction localization length $\ell$ to study spectral and eigenfunction properties (of adjacency matrices) of weighted random--geometric and random--rectangular graphs. A random--geometric graph (RGG) considers a set of vertices uniformly and independently distributed on the unit square, while for a random--rectangular graph (RRG) the embedding geometry is a rectangle. The RRG model depends on three parameters: The rectangle side lengths $a$ and $1/a$, the connection radius $r$, and the number of vertices $N$. We then study in detail the case $a=1$ which corresponds to weighted RGGs and explore weighted RRGs characterized by $a\sim 1$, i.e.~two-dimensional geometries, but also approach the limit of quasi-one-dimensional wires when $a\gg1$. In general we look for the scaling properties of $P(s)$ and $\ell$ as a function of $a$, $r$ and $N$. We find that the ratio $r/N^\gamma$, with $\gamma(a)\approx -1/2$, fixes the properties of both RGGs and RRGs. Moreover, when $a\ge 10$ we show that spectral and eigenfunction properties of weighted RRGs are universal for the fixed ratio $r/{\cal C}N^\gamma$, with ${\cal C}\approx a$.Comment: 8 pages, 6 figure

Topology induced anomalous defect production by crossing a quantum critical point

We study the influence of topology on the quench dynamics of a system driven across a quantum critical point. We show how the appearance of certain edge states, which fully characterise the topology of the system, dramatically modifies the process of defect production during the crossing of the critical point. Interestingly enough, the density of defects is no longer described by the Kibble-Zurek scaling, but determined instead by the non-universal topological features of the system. Edge states are shown to be robust against defect production, which highlights their topological nature.Comment: Phys. Rev. Lett. (to be published

Wilson Fermions and Axion Electrodynamics in Optical Lattices

The formulation of massless relativistic fermions in lattice gauge theories is hampered by the fundamental problem of species doubling, namely, the rise of spurious fermions modifying the underlying physics. A suitable tailoring of the fermion masses prevents such abundance of species, and leads to the so-called Wilson fermions. Here we show that ultracold atoms provide us with the first controllable realization of these paradigmatic fermions, thus generating a quantum simulator of fermionic lattice gauge theories. We describe a novel scheme that exploits laser-assisted tunneling in a cubic optical superlattice to design the Wilson fermion masses. The high versatility of this proposal allows us to explore a variety of interesting phases in three-dimensional topological insulators, and to test the remarkable predictions of axion electrodynamics.Comment: RevTex4 file, color figures, slightly longer than the published versio

An Optical-Lattice-Based Quantum Simulator For Relativistic Field Theories and Topological Insulators

We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine states of the same alkaline atom, to which the different degrees of freedom of the field theory to be simulated are then mapped. We show that the combination of bi-chromatic optical lattices with Raman transitions can allow the engineering of a spin-dependent tunneling of the atoms between neighboring lattice sites. These assisted-hopping processes can be employed for the quantum simulation of various interesting models, ranging from non-interacting relativistic fermionic theories to topological insulators. We present a toolbox for the realization of different types of relativistic lattice fermions, which can then be exploited to synthesize the majority of phases in the periodic table of topological insulators.Comment: 24 pages, 6 figure