Critical O(d)O(d)-equivariant biharmonic maps

We study $O(d)$-equivariant biharmonic maps in the critical dimension. A major consequence of our study concerns the corresponding heat flow. More precisely, we prove that blowup occurs in the biharmonic map heat flow from $B^4(0, 1)$ into $S^4$. To our knowledge, this was the first example of blowup for the biharmonic map heat flow. Such results have been hard to prove, due to the inapplicability of the maximum principle in the biharmonic case. Furthermore, we classify the possible $O(4)$-equivariant biharmonic maps from $\mathbf{R}^4$ into $S^4$, and we show that there exists, in contrast to the harmonic map analogue, equivariant biharmonic maps from $B^4(0,1)$ into $S^4$ that wind around $S^4$ as many times as we wish. We believe that the ideas developed herein could be useful in the study of other higher-order parabolic equations.Comment: 24 pages, 1 figure. Published online in Calculus of Variations and Partial Differential Equations, 201

Oral motor deficits in speech-impaired children with autism

Absence of communicative speech in autism has been presumed to reflect a fundamental deficit in the use of language, but at least in a subpopulation may instead stem from motor and oral motor issues. Clinical reports of disparity between receptive vs. expressive speech/language abilities reinforce this hypothesis. Our early-intervention clinic develops skills prerequisite to learning and communication, including sitting, attending, and pointing or reference, in children below 6 years of age. In a cohort of 31 children, gross and fine motor skills and activities of daily living as well as receptive and expressive speech were assessed at intake and after 6 and 10 months of intervention. Oral motor skills were evaluated separately within the first 5 months of the child's enrolment in the intervention programme and again at 10 months of intervention. Assessment used a clinician-rated structured report, normed against samples of 360 (for motor and speech skills) and 90 (for oral motor skills) typically developing children matched for age, cultural environment and socio-economic status

The magnitude of viscous dissipation in strongly stratified two-dimensional convection

Convection in astrophysical systems must be maintained against dissipation. Although the effects of dissipation are often assumed to be negligible, theory suggests that in strongly stratified convecting fluids, the dissipative heating rate can exceed the luminosity carried by convection. Here we explore this possibility using a series of numerical simulations. We consider two-dimensional numerical models of hydrodynamic convection in a Cartesian layer under the anelastic approximation and demonstrate that the dissipative heating rate can indeed exceed the imposed luminosity. We establish a theoretical expression for the ratio of the dissipative heating rate to the luminosity emerging at the upper boundary, in terms only of the depth of the layer and the thermal scale height. In particular, we show that this ratio is independent of the diffusivities and confirm this with a series of numerical simulations. Our results suggest that dissipative heating may significantly alter the internal dynamics of stars and planets.Comment: 8 pages, 5 figures, accepted for publication in ApJ Letter

Guest editorial: special issue on bone tissue engineering

No abstract availabl

The Separate or Concurrent Effects of Methylphenidate and Alcohol on Acquisition and Retention of the Morris Water Maze in Adolescent Rats

Alcohol’s (A) capacity to impair learning and memory has been well documented in the Morris Water Maze (MWM) but few studies have examined methylphenidate’s (MPH) impact on MWM performance (Haidun et al., 2010; Zeise et al., 2007). Even fewer studies have evaluated concurrent administration of these two drugs in adolescent rats (see Markwiese, et al., 1998). This project used a rat model of adolescent drug use to examine individual effects of MPH and A, as well as polypharmacy interactions between MPH and A, on MWM spatial acquisition and retention. Thirty-two adolescent (P30) male Long-Evans hooded rats were used. Subjects were assigned to one of 4 conditions based on drug administered prior to 6 consecutive acquisition sessions. Animals received 2 i.p. injections prior to each session. The methylphenidate group (MPH+S) received 2 mg/kg MPH and 1 ml/kg saline solution (S), the alcohol group (A+S) received 2 g/kg ethanol and S, the methylphenidate and alcohol group (MPH+A) received both MPH and A, and the saline control group (S+S) received S injections. MPH was administered 50 mins prior to each session and A administered 20 mins prior to each session. Each session consisted of 4 trials and rats swam from one of four start locations (N,E,S,W) to a submerged platform in the NE quadrant. Trial duration was 60 seconds and rats remained on the platform for 10 secs. Performances were video recorded, and latency and swim accuracy scored. Whishaw Corridors established a direct swim path from start location to platform and an error was recorded when swim paths exited the corridor. On day 7, the submerged platform was removed and a single, 60 sec retention test was conducted with no drug administered prior to test. Amount of time spent swimming in the NE quadrant was analyzed to assess retention. Acquisition: Both dependent measures, latency and swim accuracy, yielded similar outcomes. Factorial ANOVAs and post hoc tests showed improvement across training sessions for all groups. Importantly, the MPH+A group was impaired relative to all other conditions, and the S+S group performed better than the A group. No significant differences were observed between S+S and MPH+S groups. Retention: A one-way ANOVA of swim time in the NE quadrant revealed longer swim times for the S+S group compared to the A+S group, and longer swim times for the MPH+S group compared to the A+S group. No other significant differences were observed. While all groups improved performance during acquisition, methylphenidate + alcohol compromised spatial learning, and alcohol alone impaired learning relative to controls. Interestingly, measures of retention indicated only alcohol diminished spatial memory in adolescent rats

Numerical studies of various Neel-VBS transitions in SU(N) anti-ferromagnets

In this manuscript we review recent developments in the numerical simulations of bipartite SU(N) spin models by quantum Monte Carlo (QMC) methods. We provide an account of a large family of newly discovered sign-problem free spin models which can be simulated in their ground states on large lattices, containing O(10^5) spins, using the stochastic series expansion method with efficient loop algorithms. One of the most important applications so far of these Hamiltonians are to unbiased studies of quantum criticality between Neel and valence bond phases in two dimensions -- a summary of this body of work is provided. The article concludes with an overview of the current status of and outlook for future studies of the "designer" Hamiltonians.Comment: Mini-review article for the proceedings of CCP 2014 (Boston