Similarity solutions describing the melting of a mushy layer

A model of the melting of a mushy region in the absence of fluid flow is presented. Similarity solutions are obtained which are used to describe melting from a hot plate with and without the generation of a completely molten region. These solutions are extended to describe the melting of a mushy region in contact with a hot liquid. A significant feature of melting mushy regions is that the phase change occurs internally by dissolution. Our solutions for melting of a mushy region are used to investigate this internal phase change and are compared with the classical Neumann solutions for melting of a pure substance.

Morphosyntactic processing in advanced second language (L2) learners: An event-related potential investigation of the effects of L1-L2 similarity and structural distance

Different theoretical accounts of second language (L2) acquisition differ with respect to whether or not advanced learners are predicted to show native like processing for features not instantiated in the native language (L1). We examined how native speakers of English, a language with number but not gender agreement, process number and gender agreement in Spanish. We compare agreement within a determiner phrase (órgano muy complejo “[DP organ-MASC-SG very complex-MASC-SG]”) and across a verb phrase (cuadro es auténtico “painting-MASC-SG [VP is authentic-MASC-SG]”) in order to investigate whether native like processing is limited to local domains (e.g. within the phrase), in line with Clahsen and Felser (2006). We also examine whether morphological differences in how the L1 and L2 realize a shared feature impact processing by comparing number agreement between nouns and adjectives, where only Spanish instantiates agreement, and between demonstratives and nouns, where English also instantiates agreement. Similar to Spanish natives, advanced learners showed a P600 for both number and gender violations overall, in line with the Full Transfer/Full Access Hypothesis (Schwartz and Sprouse, 1996), which predicts that learners can show native-like processing for novel features. Results also show that learners can establish syntactic dependencies outside of local domains, as suggested by the presence of a P600 for both within and across phrase violations. Moreover, similar to native speakers, learners were impacted by the structural distance (number of intervening phrases) between the agreeing elements, as suggested by the more positive waveforms for within than across-phrase agreement overall. These results are consistent with the proposal that learners are sensitive to hierarchical structure.

Kraichnan–Leith–Batchelor similarity theory and two-dimensional inverse cascades

We study the scaling properties and Kraichnan–Leith–Batchelor (KLB) theory of forced inverse cascades in generalized two-dimensional (2D) fluids (α-turbulence models) simulated at resolution 8192x8192. We consider α=1 (surface quasigeostrophic flow), α=2 (2D Euler flow) and α=3. The forcing scale is well resolved, a direct cascade is present and there is no large-scale dissipation. Coherent vortices spanning a range of sizes, most larger than the forcing scale, are present for both α=1 and α=2. The active scalar field for α=3 contains comparatively few and small vortices. The energy spectral slopes in the inverse cascade are steeper than the KLB prediction −(7−α)/3 in all three systems. Since we stop the simulations well before the cascades have reached the domain scale, vortex formation and spectral steepening are not due to condensation effects; nor are they caused by large-scale dissipation, which is absent. One- and two-point p.d.f.s, hyperflatness factors and structure functions indicate that the inverse cascades are intermittent and non-Gaussian over much of the inertial range for α=1 and α=2, while the α=3 inverse cascade is much closer to Gaussian and non-intermittent. For α=3 the steep spectrum is close to that associated with enstrophy equipartition. Continuous wavelet analysis shows approximate KLB scaling ℰ(k)∝k−2 (α=1) and ℰ(k)∝k−5/3 (α=2) in the interstitial regions between the coherent vortices. Our results demonstrate that coherent vortex formation (α=1 and α=2) and non-realizability (α=3) cause 2D inverse cascades to deviate from the KLB predictions, but that the flow between the vortices exhibits KLB scaling and non-intermittent statistics for α=1 and α=2.

The relationship between L3 transfer and structural similarity across L3 development: raising across an experience in Brazilian Portuguese

The present study examines three competing models of morphosyntactic transfer in third language (L3) acquisition, examining the particular domain of the feature configuration of embedded T in L3 Brazilian Portuguese (BP) at the initial stages and then through development. The methodology alternates Spanish and English as the L1 and L2 to tease apart the source of transfer to L3 BP. Results from a scalar grammaticality acceptability task show unequivocal transfer of Spanish irrespective of Spanish’s status as an L1 or L2. The data thus support the Typological Primacy Model (Rothman 2010, 2011, 2013a, 2013b), which proposes that multilingual transfer is selected by factors related to comparative structural similarity. Given that Spanish transfer at the L3 initial stages creates the need for feature reconfiguration to converge on the target BP grammar, the second part of this chapter examines the developmental consequences of what the TPM models in cases of non-facilitative initial transfer, that is, the developmental path of feature reconfiguration of embedded T in L3 BP by English/Spanish bilinguals. Given what these data reveal, we address the role of regressive transfer as a correlate of L3 proficiency gains.