Influence of boundaries on pattern selection in through-flow

The problem of pattern selection in absolutely unstable open flow systems is investigated by considering the example of Rayleigh-B\'{e}nard convection. The spatiotemporal structure of convection rolls propagating downstream in an externally imposed flow is determined for six different inlet/outlet boundary conditions. Results are obtained by numerical simulations of the Navier-Stokes equations and by comparison with the corresponding Ginzburg-Landau amplitude equation. A unique selection process is observed being a function of the control parameters and the boundary conditions but independent of the history and the system length. The problem can be formulated in terms of a nonlinear eigen/boundary value problem where the frequency of the propagating pattern is the eigenvalue. PACS: 47.54.+r, 47.20.Bp, 47.27.Te, 47.20.KyComment: 8 pages, 5 Postscript figures, Physica D 97, 253-263 (1996

Noise sensitivity of sub- and supercritically bifurcating patterns with group velocities close to the convective-absolute instability

The influence of small additive noise on structure formation near a forwards and near an inverted bifurcation as described by a cubic and quintic Ginzburg Landau amplitude equation, respectively, is studied numerically for group velocities in the vicinity of the convective-absolute instability where the deterministic front dynamics would empty the system.Comment: 16 pages, 7 Postscript figure

Pattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow

A unique pattern selection in the absolutely unstable regime of a driven, nonlinear, open-flow system is analyzed: The spatiotemporal structures of rotationally symmetric vortices that propagate downstream in the annulus of the rotating Taylor-Couette system due to an externally imposed axial through-flow are investigated for two different axial boundary conditions at the in- and outlet. Unlike the stationary patterns in systems without through-flow the spatiotemporal structures of propagating vortices are independent of parameter history, initial conditions, and system's length. They do, however, depend on the axial boundary conditions, the driving rate of the inner cylinder and the through-flow rate. Our analysis of the amplitude equation shows that the pattern selection can be described by a nonlinear eigenvalue problem with the frequency being the eigenvalue. Approaching the border between absolute and convective instability the eigenvalue problem becomes effectively linear and the selection mechanism approaches that one of linear front propagation. PACS:47.54.+r,47.20.Ky,47.32.-y,47.20.FtComment: 15 pages (LateX-file), 8 figures (Postscript

Pattern selection as a nonlinear eigenvalue problem

A unique pattern selection in the absolutely unstable regime of driven, nonlinear, open-flow systems is reviewed. It has recently been found in numerical simulations of propagating vortex structures occuring in Taylor-Couette and Rayleigh-Benard systems subject to an externally imposed through-flow. Unlike the stationary patterns in systems without through-flow the spatiotemporal structures of propagating vortices are independent of parameter history, initial conditions, and system length. They do, however, depend on the boundary conditions in addition to the driving rate and the through-flow rate. Our analysis of the Ginzburg-Landau amplitude equation elucidates how the pattern selection can be described by a nonlinear eigenvalue problem with the frequency being the eigenvalue. Approaching the border between absolute and convective instability the eigenvalue problem becomes effectively linear and the selection mechanism approaches that of linear front propagation. PACS: 47.54.+r,47.20.Ky,47.32.-y,47.20.FtComment: 18 pages in Postsript format including 5 figures, to appear in: Lecture Notes in Physics, "Nonlinear Physics of Complex Sytems -- Current Status and Future Trends", Eds. J. Parisi, S. C. Mueller, and W. Zimmermann (Springer, Berlin, 1996

Psychometric Properties of the Make My Day Tool to Assess Perceived Performance of Children’s Daily Activities

Background: No instrument with strong psychometric qualities exists to measure occupational performance in young children through child-reporting. We investigated the reliability and validity of the Make My Day (MMD) tool for children aged 4 to 7 years and their parents. Method: We administered a demographic questionnaire, the MMD, and two other tools having similar objectives to a sample of 75 typically-developing Jewish-Israeli children aged 4 to 7 years and their parents. For internal consistency, we pooled the data with those from our earlier study involving 62 typically-developing Arab-Israeli children. Results: The MMD exhibited acceptable to good internal consistency for the pooled children’s (α = .65 – .89) and parental (α = .68 – .84) data. Paired student’s t-testing revealed significantly higher children’s self-ratings than parental ratings for performance quality, independence, and performance satisfaction in some activity areas. Factor loadings were of adequate strength, significant, and consistent with the theoretical underpinnings of the tool. The parental version of the MMD exhibits good concurrent validity and good discriminant validity. Conclusion: The MMD has good reliability and validity and, although some aspects remain to be investigated, the MMD is the first self-report tool for children in this age group for which any such data have been reported

Association between Sensory Processing by Children with High Functioning Autism Spectrum Disorder and their Daily Routines

Background: Children diagnosed with autism spectrum disorder exhibit persistent deficits in social communication and social interaction accompanied by restricted, repetitive patterns of behavior, interests, or activities. Those with normal intelligence are considered to have high functioning autism spectrum disorder (HFASD). Method: The study participants were 20 children with HFASD aged 5 to 7 years old attending mainstream educational programs and their parents (study group) and 30 typically-developing age-matched children from the same socio-economic background and their parents (control group). Parents from both groups completed the Short Sensory Profile to investigate their children’s sensory processing and the presence of Sensory Processing Disorder. Children and parents from both groups were administered the Make My Day (MMD) to obtain information regarding the children’s participation and performance in daily activities. Results: The study group had significantly more sensory difficulties, which correlated with restricted daily routines, compared with the control group. SPD significantly predicted the quality and independence of the performance of daily activities by children with HFASD as measured by the MMD. Conclusions: SPD may be a worthwhile therapeutic target for therapists seeking to improve participation in and performance of daily activities, as identified by the MMD, among children with HFASD

Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts

Fronts that start from a local perturbation and propagate into a linearly unstable state come in two classes: pulled and pushed. ``Pulled'' fronts are ``pulled along'' by the spreading of linear perturbations about the unstable state, so their asymptotic speed $v^*$ equals the spreading speed of linear perturbations of the unstable state. The central result of this paper is that the velocity of pulled fronts converges universally for time $t\to\infty$ like $v(t)=v^*-3/(2\lambda^*t) + (3\sqrt{\pi}/2) D\lambda^*/(D{\lambda^*}^2t)^{3/2}+O(1/t^2)$. The parameters $v^*$, $\lambda^*$, and $D$ are determined through a saddle point analysis from the equation of motion linearized about the unstable invaded state. The interior of the front is essentially slaved to the leading edge, and we derive a simple, explicit and universal expression for its relaxation towards $\phi(x,t)=\Phi^*(x-v^*t)$. Our result, which can be viewed as a general center manifold result for pulled front propagation, is derived in detail for the well known nonlinear F-KPP diffusion equation, and extended to much more general (sets of) equations (p.d.e.'s, difference equations, integro-differential equations etc.). Our universal result for pulled fronts thus implies independence (i) of the level curve which is used to track the front position, (ii) of the precise nonlinearities, (iii) of the precise form of the linear operators, and (iv) of the precise initial conditions. Our simulations confirm all our analytical predictions in every detail. A consequence of the slow algebraic relaxation is the breakdown of various perturbative schemes due to the absence of adiabatic decoupling.Comment: 76 pages Latex, 15 figures, submitted to Physica D on March 31, 1999 -- revised version from February 25, 200