Random Walkers with Shrinking Steps in d-Dimensions and Their Long Term Memory

We study, in d-dimensions, the random walker with geometrically shrinking step sizes at each hop. We emphasize the integrated quantities such as expectation values, cumulants and moments rather than a direct study of the probability distribution. We develop a 1/d expansion technique and study various correlations of the first step to the position as ti me goes to infinity. We also show and substantiate with a study of the cumulants that to order 1/d the system admits a continuum counterpart equation which can be obtained with a generalization of the ordinary technique to obtain the continuum limit. We also advocate that this continuum counterpart equation, which is nothing but the ordinary diffusion equation with a diffusion constant decaying exponentially in continuous time, captures all the qualitative aspects of t he discrete system and is often a good starting point for quantitative approximations

Non-universal behavior for aperiodic interactions within a mean-field approximation

We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following two deterministic aperiodic sequences: Fibonacci or period-doubling ones. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponent $\beta$, $\gamma$ and $\delta$. For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.Comment: 6 pages, 7 figures, to be published in Phys. Rev.

Effectiveness of Neuromotor Task Training for Children with Developmental Coordination Disorder: A Pilot Study

The aim of this pilot study was to evaluate the effectiveness of a Neuromotor Task Training (NTT), recently developed for the treatment of children with Developmental Coordination Disorder (DCD) by pediatric physical therapists in the Netherlands. NTT is a task-oriented treatment program based upon recent insights from motor control and motor learning research. Ten children with DCD (intervention group) were tested before and after 9 and 18 treatment sessions on the Movement ABC and a dysgraphia scale in order to measure the effectiveness of treatment on gross and fine motor skills in general and handwriting in particular. Five children (no-treatment control group) were tested twice with a time lag of nine weeks on the Movement ABC in order to measure spontaneous improvement. No improvement was measured for the children in the notreatment control group, whereas a significant improvement was found for children in the intervention group for both quality of handwriting and performance on the Movement ABC after 18 treatment sessions

An instrument for dimensional diagnosis of a child’s constitution (ICC)

Developmental disorders present themselves with complex problems that may threaten a child’s development. In every child a disorder shows itself in a unique way, which makes it necessary to individualize. The objective of this preliminary study is to develop an instrument that provides a dimensional diagnosis by mapping the degree of (dis)balance in three domains of child development. The instrument is based on anthroposophic anthropology and typology. The instrument will be usable in all kinds of care for children with developmental disorders.The typology of a child’s constitution was operationalized using concept mapping and consensus building with experts. Preliminary tests of the psychometric properties of the instrument were applied on children with developmental disorders in a pilot study in Dutch healthcare. The Instrument for diagnosis of a Child’s Constitution (ICC) developed in this study consists of two parts. Part I contains 36 polar formulated items in three subscales of 12 items and is to be completed by healthcare professionals. Part II consists of three VAS scales (Visual analogue scales) and is to be completed y a practitioner. The outcome (the scores of Part I and II) forms a profile of the child’s constitution, showing the (dis) balance in three domains of child development. A pilot study with 38 children shows positive face validity, and moderate internal consistency and inter-rater reliability of the ICC. The ICC has been developed as a diagnostic instrument to assess individualized dimensional diagnosis of children with a developmental disorder. Future studies will focus on validation of the instrument

Phase diagram of self-assembled rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a two-dimensional system of particles with two bonding sites that, by decreasing temperature or increasing density, polymerize reversibly into chains with discrete orientational degrees of freedom and, at the same time, undergo a continuous isotropic-nematic (IN) transition. A complete phase diagram was obtained as a function of temperature and density. The numerical results were compared with mean field (MF) and real space renormalization group (RSRG) analytical predictions about the IN transformation. While the RSRG approach supports the continuous nature of the transition, the MF solution predicts a first-order transition line and a tricritical point, at variance with the simulation results.Comment: 12 pages, 10 figures, supplementary informatio

Thermal transport of the XXZ chain in a magnetic field

We study the heat conduction of the spin-1/2 XXZ chain in finite magnetic fields where magnetothermal effects arise. Due to the integrability of this model, all transport coefficients diverge, signaled by finite Drude weights. Using exact diagonalization and mean-field theory, we analyze the temperature and field dependence of the thermal Drude weight for various exchange anisotropies under the condition of zero magnetization-current flow. First, we find a strong magnetic field dependence of the Drude weight, including a suppression of its magnitude with increasing field strength and a non-monotonic field-dependence of the peak position. Second, for small exchange anisotropies and magnetic fields in the massless as well as in the fully polarized regime the mean-field approach is in excellent agreement with the exact diagonalization data. Third, at the field-induced quantum critical line between the para- and ferromagnetic region we propose a universal low-temperature behavior of the thermal Drude weight.Comment: 9 pages REVTeX4 including 5 figures, revised version, refs. added, typos correcte

m-Path:An easy-to-use and highly tailorable platform for ecological momentary assessment and intervention in behavioral research and clinical practice

In this paper, we present m-Path (www.m-Path.io), an online platform that provides an easy-to-use and highly tailorable framework for implementing smartphone-based ecological momentary assessment (EMA) and intervention (EMI) in both research and clinical practice in the context of blended care. Because real-time monitoring and intervention in people's everyday lives have unparalleled benefits compared to traditional data collection techniques (e.g., retrospective surveys or lab-based experiments), EMA and EMI have become popular in recent years. Although a surge in the use of these methods has led to a myriad of EMA and EMI applications, many existing platforms only focus on a single aspect of daily life data collection (e.g., assessment vs. intervention, active self-report vs. passive mobile sensing, research-dedicated vs. clinically-oriented tools). With m-Path, we aim to integrate all of these facets into a single platform, as it is exactly this all-in-one approach that fosters the clinical utility of accumulated scientific knowledge. To this end, we offer a comprehensive platform to set up complex and highly adjustable EMA and EMI designs with advanced functionalities, using an intuitive point-and click web interface that is accessible for researchers and clinicians with limited programming skills. We discuss the strengths of daily life data collection and intervention in general and m-Path in particular. We describe the regular workflow to set up an EMA or EMI design within the m-Path framework, and summarize both the basic functionalities and more advanced features of our software

A comparison between rate-and-state friction and microphysical models, based on numerical simulations of fault slip

Rate-and-state friction (RSF) is commonly used for the characterisation of laboratory friction experiments, such as velocity-step tests. However, the RSF framework provides little physical basis for the extrapolation of these results to the scales and conditions of natural fault systems, and so open questions remain regarding the applicability of the experimentally obtained RSF parameters for predicting seismic cycle transients. As an alternative to classical RSF, microphysics-based models offer means for interpreting laboratory and field observations, but are generally over-simplified with respect to heterogeneous natural systems. In order to bridge the temporal and spatial gap between the laboratory and nature, we have implemented existing microphysical model formulations into an earthquake cycle simulator. Through this numerical framework, we make a direct comparison between simulations exhibiting RSF-controlled fault rheology, and simulations in which the fault rheology is dictated by the microphysical model. Even though the input parameters for the RSF simulation are directly derived from the microphysical model, the microphysics-based simulations produce significantly smaller seismic event sizes than the RSF-based simulation, and suggest a more stable fault slip behaviour. Our results reveal fundamental limitations in using classical rate-and-state friction for the extrapolation of laboratory results. The microphysics-based approach offers a more complete framework in this respect, and may be used for a more detailed study of the seismic cycle in relation to material properties and fault zone pressure-temperature conditions

Dynamical structure factor of the anisotropic Heisenberg chain in a transverse field

We consider the anisotropic Heisenberg spin-1/2 chain in a transverse magnetic field at zero temperature. We first determine all components of the dynamical structure factor by combining exact results with a mean-field approximation recently proposed by Dmitriev {\it et al}., JETP 95, 538 (2002). We then turn to the small anisotropy limit, in which we use field theory methods to obtain exact results. We discuss the relevance of our results to Neutron scattering experiments on the 1D Heisenberg chain compound ${\rm Cs_2CoCl_4}$.Comment: 13 pages, 14 figure

Exact two-spinon dynamical correlation function of the Heisenberg model

We derive the exact contribution of two spinons to the dynamical correlation function of the spin-1/2 Heisenberg model. For this, we use the isotropic limits of the exact form factors that have been recently computed through the quantum affine symmetry of the anisotropic Heisenberg model $XXZ$Comment: 9 pages, Latex, 2 corrections of coefficient