A review of giant correlation-length effects via proximity and weak-links coupling in a critical system: 4He near the superfluid transition.

We review measurements of 4He near the superfluid transition in arrangements whereby an array of weak links couple relatively larger, more bulk-like 4He regions. In contrast to experiments which focus on the dependence of the superflow on the chemical potential difference across the links, these studies focus on the specific heat of both the weak links and that of the larger coupled regions, as well as the behavior of the superfluid fraction within the weak links. The data show unexpected results which reflect a very long range coupling as well as modification of the weak link itself due to the proximity to bulk-like helium. One finds that while the three-dimensional correlation length [Formula: see text], where [Formula: see text], is involved in these long-range effects, the distance over which these can be seen is of the order of 100 to 1000 times [Formula: see text]. These results call into question our understanding of the meaning of the correlation length at a critical point as the 'range' over which information can propagate. These studies are the first to measure the thermodynamic properties of weak links for a critical system where fluctuations are important. They differ in essential ways with expectations from mean-field considerations. We compare results with other 4He measurements, with superconductors and the theoretical calculations of the Ising model.

[A clinical study of the number processing system: decimal size effects on reading numbers in patients with left parieto-occipital gliomas]. / Effet de la grandeur décimale sur la lecture de chiffres dans les gliomes du carrefour gauche.

An increasing number of studies are focusing on the anatomo-functional organisation of number processing and some cognitive models have been recently developed. Nevertheless, relationships between areas implicated in number processing, and language areas and circuits remain unclear. Recently, Dehaene and Cohen, in their "triple-code model of number processing", (Dehaene and Cohen, 1995) distinguished two alternative number representation and processing systems: one depending on verbal processes, the other representing a quantity manipulation. According to this model, the retrieval of "arithmetical facts" (AF), learned by rote at school and memorised in a verbal form (such as the multiplication table or simple addition problems) can be considered as a verbal automatism; conversely, subtraction problems, which require mental manipulation of the quantities, represent an abstract, semantic elaboration: "Actual Calculation" (AC). The anatomical correlate of the retrieval of AF (depending on automatic verbal associations) seems to correspond to the left-hemispheric perisylvian areas, while impairment of the actual calculation (AC) depends on the intraparietal region, particularly in the left dominant hemisphere. The present study describes the neuropsychological assessment of three patients, tested after surgery for left parieto-occipital tumors. Two of them were affected by an anaplasic glioma, the third by a low-grade glioma. The cognitive evaluation included: words of Rey, numeral (directed and reversed) span, reading of "simple" numbers (from 1 to 10) and of "complex" numbers (many decimals), writing (dictation) and reading a standard text, finger denomination and right-left distinction. All patients showed language disturbances, dysgraphia and severe dyslexia. In reading numbers, we identified two types of errors: lexical and syntactic. "Lexical errors" consisted in a wrong choice among words in the number's lexicon. For instance, all patients made errors in reading "complex" numbers composed by many decimals, switching single numbers but respecting the decimal size and the structure of the whole number (such as 69107 instead of 68107). On the other hand, only one patient committed syntactic errors, misunderstanding the decimal size and the structure of the number. We considered lexical errors as verbal errors, and syntactic errors as semantic errors, affecting the notion of quantity. We tried to explain verbal disturbances as well as lexical errors as a consequence of lesion of the left-hemispheric perisylvian areas, while syntactic errors as a consequence of impairment of the intraparietal region.

Three-dimensional critical behavior with 2D, 1D, and 0D dimensionality crossover: surface and edge specific heats.

The critical behavior at a second order phase transition is characterized by the divergence of the correlation length xi. We have studied the superfluid transition of 4He in a series of experimental cells in which this divergence of xi is modified due to finite-size confinement. In particular, the design of these cells is such that the smallest dimension is kept the same, 1 microm, but the geometry is such that one obtains crossover to dimensionality of 2, 1, and 0. This corresponds to films, channels, and boxes filled with helium. We measure the specific heat and compare these results with theoretical expectations. We identify surface and line specific heat contributions by analyzing the deviation of the specific heat from its behavior in the thermodynamic limit. The design of these cells is made possible by a combination of silicon lithography and direct wafer bonding.

Superfluid fraction of (3)He-(4)He mixtures confined at 0.0483 microm between silicon wafers.

We report measurements of the superfluid fraction rho(s)/rho of films of (3)He-(4)He mixtures confined between silicon wafers at 0.0483 microm separation. The data obtained using adiabatic fountain resonance (AFR) can be used to test for the first time expectations of correlation-length scaling in the case of planar mixtures. For the mixtures, the data for rho(s)/rho collapse well on a universal function. The dissipation associated with AFR can also be scaled, and indicates two-dimensional crossover. These results are in contrast to pure (4)He, where over a wider range of confinements, the data for rho(s)/rho are found not to scale.