Front propagation into unstable and metastable states in Smectic C* liquid crystals: linear and nonlinear marginal stability analysis

We discuss the front propagation in ferroelectric chiral smectics (SmC*) subjected to electric and magnetic fields applied parallel to smectic layers. The reversal of the electric field induces the motion of domain walls or fronts that propagate into either an unstable or a metastable state. In both regimes, the front velocity is calculated exactly. Depending on the field, the speed of a front propagating into the unstable state is given either by the so-called linear marginal stability velocity or by the nonlinear marginal stability expression. The cross-over between these two regimes can be tuned by a magnetic field. The influence of initial conditions on the velocity selection problem can also be studied in such experiments. SmC$^*$ therefore offers a unique opportunity to study different aspects of front propagation in an experimental system

Understanding parental concerns related to their child’s development and factors influencing their decisions to seek help from health care professionals: Results of a qualitative study.

Background: Early identification of children at risk of developmental delay is crucial to promote healthy development. Assessing parental concerns about development is often part of identification processes. However, we currently do not understand well how and why parents become concerned, and, how and why they access early identification and intervention services. The purpose of this study was to explore parental perceptions about their child’s development, and the factors influencing their reported professional help-seeking behaviours. Methods: This exploratory study was part of a larger study describing child development in children aged 2-5 in a small Canadian city. We conducted semi-structured interviews with 16 parents whose children were at risk of developmental delay to examine their perceptions of their child’s development, their use of community services promoting development, and their recommendations to optimize those services. Results: Four themes were identified: 1) Vision of child development influencing help-seeking behaviours: Natural or Supported?, 2) Internal and external sources contributing to parents’ level of developmental concern, 3) Using internal resources and struggling to access external resources, and 4) Satisfaction with services accessed and recommendations to access more support. Parents’ vision of child development along with sources of parental concern appeared to influence the level of concern, enhancing our understanding of how parents become concerned. The level of concern, and parents’ knowledge and perceived access to resources seemed to influence their decision whether or not to consult health care professionals. Parents provided many suggestions to improve services to promote child development and support families. Discussion: Results highlight the importance of supporting parents in recognizing if their child is at risk of delay, and increasing awareness of available resources. It appears particularly important to ensure health care professionals and community-based support services are accessible to provide parents with the support they need, especially when they have concerns

Front Stability in Mean Field Models of Diffusion Limited Growth

We present calculations of the stability of planar fronts in two mean field models of diffusion limited growth. The steady state solution for the front can exist for a continuous family of velocities, we show that the selected velocity is given by marginal stability theory. We find that naive mean field theory has no instability to transverse perturbations, while a threshold mean field theory has such a Mullins-Sekerka instability. These results place on firm theoretical ground the observed lack of the dendritic morphology in naive mean field theory and its presence in threshold models. The existence of a Mullins-Sekerka instability is related to the behavior of the mean field theories in the zero-undercooling limit.Comment: 26 pp. revtex, 7 uuencoded ps figures. submitted to PR

The Speed of Fronts of the Reaction Diffusion Equation

We study the speed of propagation of fronts for the scalar reaction-diffusion equation $u_t = u_{xx} + f(u)$\, with $f(0) = f(1) = 0$. We give a new integral variational principle for the speed of the fronts joining the state $u=1$ to $u=0$. No assumptions are made on the reaction term $f(u)$ other than those needed to guarantee the existence of the front. Therefore our results apply to the classical case $f > 0$ in $(0,1)$, to the bistable case and to cases in which $f$ has more than one internal zero in $(0,1)$.Comment: 7 pages Revtex, 1 figure not include

Structural Stability and Renormalization Group for Propagating Fronts

A solution to a given equation is structurally stable if it suffers only an infinitesimal change when the equation (not the solution) is perturbed infinitesimally. We have found that structural stability can be used as a velocity selection principle for propagating fronts. We give examples, using numerical and renormalization group methods.Comment: 14 pages, uiucmac.tex, no figure

Generalized empty-interval method applied to a class of one-dimensional stochastic models

In this work we study, on a finite and periodic lattice, a class of one-dimensional (bimolecular and single-species) reaction-diffusion models which cannot be mapped onto free-fermion models. We extend the conventional empty-interval method, also called {\it interparticle distribution function} (IPDF) method, by introducing a string function, which is simply related to relevant physical quantities. As an illustration, we specifically consider a model which cannot be solved directly by the conventional IPDF method and which can be viewed as a generalization of the {\it voter} model and/or as an {\it epidemic} model. We also consider the {\it reversible} diffusion-coagulation model with input of particles and determine other reaction-diffusion models which can be mapped onto the latter via suitable {\it similarity transformations}. Finally we study the problem of the propagation of a wave-front from an inhomogeneous initial configuration and note that the mean-field scenario predicted by Fisher's equation is not valid for the one-dimensional (microscopic) models under consideration.Comment: 19 pages, no figure. To appear in Physical Review E (November 2001

Renormalization Group Theory And Variational Calculations For Propagating Fronts

We study the propagation of uniformly translating fronts into a linearly unstable state, both analytically and numerically. We introduce a perturbative renormalization group (RG) approach to compute the change in the propagation speed when the fronts are perturbed by structural modification of their governing equations. This approach is successful when the fronts are structurally stable, and allows us to select uniquely the (numerical) experimentally observable propagation speed. For convenience and completeness, the structural stability argument is also briefly described. We point out that the solvability condition widely used in studying dynamics of nonequilibrium systems is equivalent to the assumption of physical renormalizability. We also implement a variational principle, due to Hadeler and Rothe, which provides a very good upper bound and, in some cases, even exact results on the propagation speeds, and which identifies the transition from ` linear'- to ` nonlinear-marginal-stability' as parameters in the governing equation are varied.Comment: 34 pages, plain tex with uiucmac.tex. Also available by anonymous ftp to gijoe.mrl.uiuc.edu (128.174.119.153), file /pub/front_RG.tex (or .ps.Z

Functional limit theorems for random regular graphs

Consider d uniformly random permutation matrices on n labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree 2d on n vertices. We consider limit theorems for various combinatorial and analytical properties of this graph (or the matrix) as n grows to infinity, either when d is kept fixed or grows slowly with n. In a suitable weak convergence framework, we prove that the (finite but growing in length) sequences of the number of short cycles and of cyclically non-backtracking walks converge to distributional limits. We estimate the total variation distance from the limit using Stein's method. As an application of these results we derive limits of linear functionals of the eigenvalues of the adjacency matrix. A key step in this latter derivation is an extension of the Kahn-Szemer\'edi argument for estimating the second largest eigenvalue for all values of d and n.Comment: Added Remark 27. 39 pages. To appear in Probability Theory and Related Field

Demonstration of Universal Parametric Entangling Gates on a Multi-Qubit Lattice

We show that parametric coupling techniques can be used to generate selective entangling interactions for multi-qubit processors. By inducing coherent population exchange between adjacent qubits under frequency modulation, we implement a universal gateset for a linear array of four superconducting qubits. An average process fidelity of $\mathcal{F}=93\%$ is estimated for three two-qubit gates via quantum process tomography. We establish the suitability of these techniques for computation by preparing a four-qubit maximally entangled state and comparing the estimated state fidelity against the expected performance of the individual entangling gates. In addition, we prepare an eight-qubit register in all possible bitstring permutations and monitor the fidelity of a two-qubit gate across one pair of these qubits. Across all such permutations, an average fidelity of $\mathcal{F}=91.6\pm2.6\%$ is observed. These results thus offer a path to a scalable architecture with high selectivity and low crosstalk

A comparison of attachment representations to father and mother using the MCAST

The aim of the current study was to examine the factorial structure of the Manchester Child Attachment Story Task (MCAST), using a father doll to address the child's attachment representation to father. While the MCAST, a doll story completion task measuring attachment representations in early childhood, has been validated for use with a mother doll, its use for assessing attachment to father is relatively unexplored. Thus, an additional aim was to compare the factorial structure of the child's attachment representation to father and mother, respectively. We analyzed data from 118 first-grade children who underwent counterbalanced administration of the MCAST with a mother and father doll, respectively, within a period of three months. Exploratory factorial analysis revealed similar, three-factor solutions for attachment to father and mother, with a first factor capturing the child's (scripted) knowledge of secure base/safe haven and a second factor reflecting intrusive and conflict behavior. The third factor was different in the father and mother representations, capturing self-care and role-reversal in attachment to father and disorganization in attachment to mother. Findings support the potential usefulness of the MCAST for exploring the father-child relationship and highlight a need for further research on early attachment representations to father