Free-Field Representation of Group Element for Simple Quantum Group

A representation of the group element (also known as ``universal ${\cal T}$-matrix'') which satisfies $\Delta(g) = g\otimes g$, is given in the form $$g = \left(\prod_{s=1}^{d_B}\phantom.^>\ {\cal E}_{1/q_{i(s)}}(\chi^{(s)}T_{-i(s)})\right) q^{2\vec\phi\vec H} \left(\prod_{s=1}^{d_B}\phantom.^<\ {\cal E}_{q_{i(s)}}(\psi^{(s)} T_{+i(s)})\right)$$ where $d_B = \frac{1}{2}(d_G - r_G)$, $q_i = q^{|| \vec\alpha_i||^2/2}$ and $H_i = 2\vec H\vec\alpha_i/||\vec\alpha_i||^2$ and $T_{\pm i}$ are the generators of quantum group associated respectively with Cartan algebra and the {\it simple} roots. The ``free fields'' $\chi,\ \vec\phi,\ \psi$form a Heisenberg-like algebra:$\psi^{(s)}\psi^{(s')} = q^{-\vec\alpha_{i(s)} \vec\alpha_{i(s')}} \psi^{(s')}\psi^{(s)}, & \chi^{(s)}\chi^{(s')} = q^{-\vec\alpha_{i(s)}\vec\alpha_{i(s')}} \chi^{(s')}\chi^{(s)}& {\rm for} \ s<s', \\ q^{\vec h\vec\phi}\psi^{(s)} = q^{\vec h\vec\alpha_{i(s)}} \psi^{(s)}q^{\vec h\vec\phi}, & q^{\vec h\vec\phi}\chi^{(s)} = q^{\vec h \vec\alpha_{i(s)}}\chi^{(s)}q^{\vec h\vec\phi}, & \\ &\psi^{(s)} \chi^{(s')} = \chi^{(s')}\psi^{(s)} & {\rm for\ any}\ s,s'.$We argue that the$d_G$-parametric ``manifold'' which$g$spans in the operator-valued universal envelopping algebra, can also be invariant under the group multiplication$g \rightarrow g'\cdot g''$. The universal${\cal R}$-matrix with the property that${\cal R} (g\otimes I)(I\otimes g) = (I\otimes g)(g\otimes I){\cal R}$is given by the usual formula$${\cal R} = q^{-\sum_{ij}^{r_G}||\vec\alpha_i||^2|| \vec\alpha_j||^2 (\vec\alpha\vec\alpha)^{-1}_{ij}H_i \otimes H_j}\prod_{ \vec\alpha > 0}^{d_B}{\cal E}_{q_{\vec\alpha}}\left(-(q_{\vec\alpha}- q_{\vec\alpha}^{-1})T_{\vec\alpha}\otimes T_{-\vec\alpha}\right).$$Comment: 68 page

A Super-Integrable Discretization of the Calogero Model

A time-discretization that preserves the super-integrability of the Calogero model is obtained by application of the integrable time-discretization of the harmonic oscillator to the projection method for the Calogero model with continuous time. In particular, the difference equations of motion, which provide an explicit scheme for time-integration, are explicitly presented for the two-body case. Numerical results exhibit that the scheme conserves all the$(=3)$ conserved quantities of the (two-body) Calogero model with a precision of the machine epsilon times the number of iterations.Comment: 22 pages, 5 figures. Added references. Corrected typo

An infinite family of superintegrable Hamiltonians with reflection in the plane

We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly solvable. The angular part of the wave function is expressed in terms of little -1 Jacobi polynomials. The spectra exhibit "accidental" degeneracies. The superintegrability of the model is proved using the recurrence relation approach. The (higher-order) constants of motion are constructed and the structure equations of the symmetry algebra obtained.Comment: 19 page

PHASE SPACE DYNAMICS OF HEAVY ION NUCLEAR COLLISIONS IN THE FERMI ENERGY DOMAIN

No abstract availabl

The Dynamics of Sustained Reentry in a Loop Model with Discrete Gap Junction Resistance

Dynamics of reentry are studied in a one dimensional loop of model cardiac cells with discrete intercellular gap junction resistance ($R$). Each cell is represented by a continuous cable with ionic current given by a modified Beeler-Reuter formulation. For $R$ below a limiting value, propagation is found to change from period-1 to quasi-periodic ($QP$) at a critical loop length ($L_{crit}$) that decreases with $R$. Quasi-periodic reentry exists from $L_{crit}$ to a minimum length ($L_{min}$) that is also shortening with $R$. The decrease of $L_{crit}(R)$ is not a simple scaling, but the bifurcation can still be predicted from the slope of the restitution curve giving the duration of the action potential as a function of the diastolic interval. However, the shape of the restitution curve changes with $R$.Comment: 6 pages, 7 figure

SOLUTIONS OF THE LANDAU-VLASOV EQUATION IN NUCLEAR PHYSICS

The properties of Vlasov equation solutions obtained by projection on coherent state basis are discussed. Such solutions satisfy stationarity conditions and satisfactorily describe the average diffusivity of nuclear phase space and reproduce the bulk properties of nuclei. Sampling methods and their effects on dynamics are discussed for the study of heavy ion reactions at intermediate energies. The non-local Gogny force is easily computable on this basis which allows to use it for dynamical nuclear studies

Sur l'origine de l'augmentation apparente des inondations en région méditerranéenne

En septembre 2002, les régions méditerranéennes françaises et notamment le département du Gard ont été affectées par des précipitations d'une extrême intensité. On estime que 80% de ce département a été inondé, on dénombre 23 victimes et les dégâts ont été évalués à 1.2 milliards d'euros. Cette catastrophe hydrologique soulève à nouveau les problèmes de la fréquence de ces événements et de l'augmentation des forts cumuls de pluie ces dernières années. L'objet de cet article est d'apporter quelques éléments de réponse, notamment à travers l'analyse régionale des pluies extrêmes journalières ayant affecté la région Languedoc-Roussillon de 1958 à 2002.La fréquence régionale des pluies extrêmes est estimée en prenant en compte la superficie couverte par ces événements en fonction des hauteurs pluviométriques. A l'échelle régionale la période de retour de l'événement varie entre 80 ans pour la superficie touchée par au moins 200 mm à 140 ans pour celle couverte par 300 mm.La stationnarité des fréquences des pluies extrêmes est analysée à partir des chroniques du nombre annuel d'événements pluvieux dépassant 200 mm, 250 mm et 300 mm en 24h maximum, entre 1958 et 2002 sur la région. Les tests de stationnarité ne révèlent pas de tendance significative à l'augmentation de ces fréquences. Les données historiques aboutissent aux mêmes conclusions. L'augmentation réelle des inondations est en fait principalement liée à l'augmentation de la vulnérabilité des bassins.In September 2002, the Gard department in the South of France was affected by heavy precipitation that covered a broad geographical area. It was estimated that 80% of the department was flooded; there were 23 victims and the damage was evaluated to be 1.2 billion euros. This hydrological catastrophe raised questions about a possible increase in the frequency of these events during recent years, since several other severe flooding events have been observed in the region over the last 15 years. The aim of this article is to explore these questions through a regional analysis of the extreme daily rainfall that affected the Languedoc-Roussillon region between 1958 and 2002. The daily rain data were used because they are the most available type of information over the observation period. Usually, the rainfall hazard description is based on statistical analysis of the maximum rainfall depth observed at a given rain gauge. However, because the spatial variability of rainfall in the Mediterranean region, such results are only representative of local rainfall conditions. Moreover, this type of analysis does not take into account the spatial coverage of the precipitation, which is another factor influencing the resulting floods. Thus, the regional frequency of extreme rainfall was estimated by taking into account the area covered according to a given rainfall depth. For each rainfall event, a rain field was built using a kriging interpolation (NEPPEL et al., 1997). The isohyet area defined a rainfall threshold from 10 to 300 mm with a step of 10 mm calculated for each rainfall event. For each rainfall depth from 10 to 300 mm with a step of 10 mm, the probability distribution of the isohyet area was estimated. The regional rainfall hazards were described with the Depth-Area-Frequency curves (DAF) for 24-h periods. It was shown that at on regional scale, the return period of the last event varied between 80 years for the surface affected by at least 200 mm and 140 years for the surface covered by 300 mm. Compared with other major events that have occurred in the region, it appears that the September 2002 event one was characterized by :1. the spatial extension of the heavy rainfall, for example more than 1800 km² were affected by at least 400 mm in less than 24 h;2. the spatial localisation of the heaviest rainfall depths, which were measured over the highest relief (1000 m to 1500 m) as usual in the 'cévenols' meteorological situation, but rather in the plain where the altitude lies between 200 m and 300 m.The stationnarity analysis of the extreme rainfall frequency was based on the annual number of events exceeding 200 mm, 250 mm and 300 mm over a 24 h maximum duration, between 1958 and 2002. The hypothesis of random events against the hypothesis of a trend or a sudden break in the mean was examined through several statistical tests. The procedures used were the rank correlation test, PETTITT's test, BUISHAND's test, HUBERT's segmentation procedure, a linear regression procedure, and the turning points procedure. Detailed descriptions of these tests can be found in KENDALL and STUART (1977), LUBES-NIEL et al. (1998) and WMO (2000). Except for the rank correlation test, all the procedures led to the conclusion that the three series are randomly distributed at the level of significance 1%, 5% and 10% respectively. Thus no significant increase in extreme rainfall frequency seems to appear. Although the study period was short, 45 years, compared with climatological variability, LUBES-NIEL et al. (1998) show that the procedures used were adapted in detecting trends in 50-yr time series. In considering historical rainfall data before 1958 in the same region, at least two extreme rainfall events could be compared with the event on 8-9 September 2002: in October 1940, 840 mm of rainfall were measured during 24 h in the Pyrénées-Orientales district and in September 1900, 940 mm were observed over 24 h in Valleraugue, upstream in the Herault catchment. Furthermore, if the evolution of the rain gauge network density is taken into account, one can argue that such an event could have occurred more frequently. Indeed, the number of rain gauges has varied from 162 gauges in 1900 to 330 today. It has been shown that the number of observed rainfall events varied according to the area of the events and the network density (NEPPEL et al., 1998b). For example, an event of 150 km2 (corresponding to the area covered by more than 600 mm in September 2002) had a probability of 70% to be observed by the network between 1958 and 1993. If one considers the period 1920-1939, this probability decreases to 30%.In addition, the basin vulnerability has increased. The regional population has grown from 1,460,000 inhabitants in 1949 to 2,300,000 in 2000. At the same time, urbanization has expanded widely. Moreover, this new population came from other districts, and they are not familiar with the Mediterranean rainfall regime and the resulting flash floods. Buildings have often been constructed near rivers, which are attractive building sites, and sometimes even in the river's main channel, increasing the flooding risk and the flood damages. Thus, rather than climate change, for which the effect on extreme rainfalls cannot be proved, the development of basin urbanisation and vulnerability could explain the apparent increase in floods. As the regional population is expected to reach more than 3,000,000 by 2030, it is necessary to take into account the flood risk in future urban planning

LOW AND INTERMEDIATE ENERGY HEAVY ION COLLISIONS IN THE SEMI-CLASSICAL MICROSCOPIC DESCRIPTION

It is shown how peripheral and central heavy-ion collisions can be described by Landau-Vlasov dynamics. For peripheral collisions at intermediate energies, mass-mass correlations, ejectile mean energies and angular distributions are obtained and compared with fragmentation data. For central collisions, one shows that the collision term destroys the TDHF property of transparency at low impact parameters for collisions close from the Coulomb barrier. Above 20 MeV/u incomplete fusion is described with associated linear momentum transfer and nuclear deformations. One exhibits how coupling to the continuum is obtained in Vlasov and Landau-Vlasov dynamics. Coulomb interaction being taken into account, we present also results concerning the isospin transfer and the excitation of the isovector dipole mode near and well above the Coulomb barrier. Some perspectives to further studies of physical observables are finally drawn

Reconfigurable quadruple quantum dots in a silicon nanowire transistor

We present a novel reconfigurable metal-oxide-semiconductor multi-gate transistor that can host a quadruple quantum dot in silicon. The device consist of an industrial quadruple-gate silicon nanowire field-effect transistor. Exploiting the corner effect, we study the versatility of the structure in the single quantum dot and the serial double quantum dot regimes and extract the relevant capacitance parameters. We address the fabrication variability of the quadruple-gate approach which, paired with improved silicon fabrication techniques, makes the corner state quantum dot approach a promising candidate for a scalable quantum information architecture