Calculation of the Density of States Using Discrete Variable Representation and Toeplitz Matrices

A direct and exact method for calculating the density of states for systems with localized potentials is presented. The method is based on explicit inversion of the operator $E-H$. The operator is written in the discrete variable representation of the Hamiltonian, and the Toeplitz property of the asymptotic part of the obtained {\it infinite} matrix is used. Thus, the problem is reduced to the inversion of a {\it finite} matrix

Investigation of the Multiple Method Adaptive Control (MMAC) method for flight control systems

The stochastic adaptive control of the NASA F-8C digital-fly-by-wire aircraft using the multiple model adaptive control (MMAC) method is presented. The selection of the performance criteria for the lateral and the longitudinal dynamics, the design of the Kalman filters for different operating conditions, the identification algorithm associated with the MMAC method, the control system design, and simulation results obtained using the real time simulator of the F-8 aircraft at the NASA Langley Research Center are discussed

Superdiffusion of massive particles induced by multi-scale velocity fields

We study drag-induced diffusion of massive particles in scale-free velocity fields, where superdiffusive behavior emerges due to the scale-free size distribution of the vortices of the underlying velocity field. The results show qualitative resemblance to what is observed in fluid systems, namely the diffusive exponent for the mean square separation of pairs of particles and the preferential concentration of the particles, both as a function of the response time.Comment: 5 pages, 5 figures. Accepted for publication in EP

Self-similar disk packings as model spatial scale-free networks

The network of contacts in space-filling disk packings, such as the Apollonian packing, are examined. These networks provide an interesting example of spatial scale-free networks, where the topology reflects the broad distribution of disk areas. A wide variety of topological and spatial properties of these systems are characterized. Their potential as models for networks of connected minima on energy landscapes is discussed.Comment: 13 pages, 12 figures; some bugs fixed and further discussion of higher-dimensional packing

Path-integral representation for a stochastic sandpile

We introduce an operator description for a stochastic sandpile model with a conserved particle density, and develop a path-integral representation for its evolution. The resulting (exact) expression for the effective action highlights certain interesting features of the model, for example, that it is nominally massless, and that the dynamics is via cooperative diffusion. Using the path-integral formalism, we construct a diagrammatic perturbation theory, yielding a series expansion for the activity density in powers of the time.Comment: 22 pages, 6 figure

Prenatal Maternal Mood Patterns Predict Child Temperament and Adolescent Mental Health

Background This study quantifies the dynamics of maternal mood focusing on unpredictability, and to assess if greater unpredictability of prenatal maternal mood predicts child temperament and internalizing symptoms through early adolescence. Methods The association between prenatal mood predictability and child internalizing symptoms were assessed in two longitudinal cohorts (N’s = 227 and 180). Maternal mood was assessed repeatedly during pregnancy as early as 15 weeks’ gestation. Predictability of maternal mood was calculated by applying Shannon’s entropy to the distribution of responses on mood questionnaires. Maternal reports of child negative affectivity (a predictor of later internalizing) were collected at 6, 12, 24 months and 7 years of age. Child self-reports of anxiety symptoms were collected at 10 years and reports of depression symptoms at 13 years. Results Fetal exposure to more elevated maternal mood entropy predicted higher levels of child negative affectivity at 12 months (r = .36; p \u3c 01), 24 months (r = .31; p \u3c 01) and 7 years (r = .32; p \u3c 01) of age. In addition, children exposed to higher prenatal maternal mood entropy, reported higher levels of anxiety symptoms at 10 years (r = .24; p \u3c 01) and elevated depressive symptoms at 13 years (r = .29; p \u3c .01). These associations persisted after adjusting for maternal pre and postnatal mood valence (e.g. depression levels) and for other relevant demographic characteristics. Conclusions Our findings provide strong support for the notion that patterns of maternal mood influence the developing brain. More specifically, they suggest that prenatal maternal mood predictability may be a critical predictor of developmental mental health trajectories and should be considered when assessing early life influences on lifespan mental health

Dimensional Reduction for Directed Branched Polymers

Dimensional reduction occurs when the critical behavior of one system can be related to that of another system in a lower dimension. We show that this occurs for directed branched polymers (DBP) by giving an exact relationship between DBP models in D+1 dimensions and repulsive gases at negative activity in D dimensions. This implies relations between exponents of the two models: $\gamma(D+1)=\alpha(D)$ (the exponent describing the singularity of the pressure), and $\nu_{\perp}(D+1)=\nu(D)$ (the correlation length exponent of the repulsive gas). It also leads to the relation $\theta(D+1)=1+\sigma(D)$, where $\sigma(D)$ is the Yang-Lee edge exponent. We derive exact expressions for the number of DBP of size N in two dimensions.Comment: 7 pages, 1 eps figure, ref 24 correcte

Fundamental measure theory for lattice fluids with hard core interactions

We present the extension of Rosenfeld's fundamental measure theory to lattice models by constructing a density functional for d-dimensional mixtures of parallel hard hypercubes on a simple hypercubic lattice. The one-dimensional case is exactly solvable and two cases must be distinguished: all the species with the same lebgth parity (additive mixture), and arbitrary length parity (nonadditive mixture). At the best of our knowledge, this is the first time that the latter case is considered. Based on the one-dimensional exact functional form, we propose the extension to higher dimensions by generalizing the zero-dimensional cavities method to lattice models. This assures the functional to have correct dimensional crossovers to any lower dimension, including the exact zero-dimensional limit. Some applications of the functional to particular systems are also shown.Comment: 22 pages, 7 figures, needs IOPP LaTeX styles file

Kinetics and Jamming Coverage in a Random Sequential Adsorption of Polymer Chains

Using a highly efficient Monte Carlo algorithm, we are able to study the growth of coverage in a random sequential adsorption (RSA) of self-avoiding walk (SAW) chains for up to 10^{12} time steps on a square lattice. For the first time, the true jamming coverage (theta_J) is found to decay with the chain length (N) with a power-law theta_J propto N^{-0.1}. The growth of the coverage to its jamming limit can be described by a power-law, theta(t) approx theta_J -c/t^y with an effective exponent y which depends on the chain length, i.e., y = 0.50 for N=4 to y = 0.07 for N=30 with y -> 0 in the asymptotic limit N -> infinity.Comment: RevTeX, 5 pages inclduing figure

Measuring Novel Antecedents of Mental Illness: The Questionnaire of Unpredictability in Childhood

Increasing evidence indicates that, in addition to poverty, maternal depression, and other well-established factors, unpredictability of maternal and environmental signals early in life influences trajectories of brain development, determining risk for subsequent mental illness. However, whereas most risk factors for later vulnerability to mental illness are readily measured using existing, clinically available tools, there are no similar measures for assessing early-life unpredictability. Here we validate the Questionnaire of Unpredictability in Childhood (QUIC) and examine its associations with mental health in the context of other indicators of childhood adversity (e.g., traumatic life events, socioeconomic status, and parenting quality). The QUIC was initially validated through administration to a cohort of adult females (N = 116) and then further refined in two additional independent cohorts (male Veterans, N = 95, and male and female adolescents, N = 175). The QUIC demonstrated excellent internal (α = 0.89) and test–retest reliability (r = 92). Scores on the QUIC were positively correlated with other prospective indicators of exposures to unpredictable maternal inputs in infancy and childhood (unpredictable maternal mood and sensory signals), and accuracy of recall also was confirmed with prospective data. Importantly, the QUIC predicted symptoms of anxiety, depression, and anhedonia in the three study cohorts, and these effects persisted after adjusting for other previously established risk factors. The QUIC, a reliable and valid self-report assessment of exposure to unpredictability in the social, emotional, and physical domains during early life, is a brief, comprehensive, and promising instrument for predicting risk for mental illness