A holomorphic representation of the Jacobi algebra

A representation of the Jacobi algebra $\mathfrak{h}_1\rtimes \mathfrak{su}(1,1)$ by first order differential operators with polynomial coefficients on the manifold $\mathbb{C}\times \mathcal{D}_1$ is presented. The Hilbert space of holomorphic functions on which the holomorphic first order differential operators with polynomials coefficients act is constructed.Comment: 34 pages, corrected typos in accord with the printed version and the Errata in Rev. Math. Phys. Vol. 24, No. 10 (2012) 1292001 (2 pages) DOI: 10.1142/S0129055X12920018, references update

Force transmission in a packing of pentagonal particles

We perform a detailed analysis of the contact force network in a dense confined packing of pentagonal particles simulated by means of the contact dynamics method. The effect of particle shape is evidenced by comparing the data from pentagon packing and from a packing with identical characteristics except for the circular shape of the particles. A counterintuitive finding of this work is that, under steady shearing, the pentagon packing develops a lower structural anisotropy than the disk packing. We show that this weakness is compensated by a higher force anisotropy, leading to enhanced shear strength of the pentagon packing. We revisit "strong" and "weak" force networks in the pentagon packing, but our simulation data provide also evidence for a large class of "very weak" forces carried mainly by vertex-to-edge contacts. The strong force chains are mostly composed of edge-to-edge contacts with a marked zig-zag aspect and a decreasing exponential probability distribution as in a disk packing

Invariant Differential Operators for Non-Compact Lie Groups: the Sp(n,R) Case

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras sp(n,R), in detail for n=6. Our choice of these algebras is motivated by the fact that they belong to a narrow class of algebras, which we call 'conformal Lie algebras', which have very similar properties to the conformal algebras of Minkowski space-time. We give the main multiplets and the main reduced multiplets of indecomposable elementary representations for n=6, including the necessary data for all relevant invariant differential operators. In fact, this gives by reduction also the cases for n<6, since the main multiplet for fixed n coincides with one reduced case for n+1.Comment: Latex2e, 27 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:0812.2690, arXiv:0812.265

Two-Dimensional Molecular Patterning by Surface-Enhanced Zn-Porphyrin Coordination

In this contribution, we show how zinc-5,10,15,20-meso-tetradodecylporphyrins (Zn-TDPs) self-assemble into stable organized arrays on the surface of graphite, thus positioning their metal center at regular distances from each other, creating a molecular pattern, while retaining the possibility to coordinate additional ligands. We also demonstrate that Zn-TDPs coordinated to 3-nitropyridine display a higher tendency to be adsorbed at the surface of highly oriented pyrolytic graphite (HOPG) than noncoordinated ones. In order to investigate the two-dimensional (2D) self-assembly of coordinated Zn-TDPs, solutions with different relative concentrations of 3-nitropyridine and Zn-TDP were prepared and deposited on the surface of HOPG. STM measurements at the liquid-solid interface reveal that the ratio of coordinated Zn-TDPs over noncoordinated Zn-TDPs is higher at the n-tetradecane/HOPG interface than in n-tetradecane solution. This enhanced binding of the axial ligand at the liquid/solid interface is likely related to the fact that physisorbed Zn-TDPs are better binding sites for nitropyridines.

Memory of the Unjamming Transition during Cyclic Tiltings of a Granular Pile

Discrete numerical simulations are performed to study the evolution of the micro-structure and the response of a granular packing during successive loading-unloading cycles, consisting of quasi-static rotations in the gravity field between opposite inclination angles. We show that internal variables, e.g., stress and fabric of the pile, exhibit hysteresis during these cycles due to the exploration of different metastable configurations. Interestingly, the hysteretic behaviour of the pile strongly depends on the maximal inclination of the cycles, giving evidence of the irreversible modifications of the pile state occurring close to the unjamming transition. More specifically, we show that for cycles with maximal inclination larger than the repose angle, the weak contact network carries the memory of the unjamming transition. These results demonstrate the relevance of a two-phases description -strong and weak contact networks- for a granular system, as soon as it has approached the unjamming transition.Comment: 13 pages, 15 figures, soumis \`{a} Phys. Rev.

Chemical Potential Shift in Nd2−x_{2-x}Cex_{x}CuO4_{4}: Contrasting Behaviors of the Electron- and Hole-Doped Cuprates

We have studied the chemical potential shift in the electron-doped superconductor Nd$_{2-x}$Ce$_{x}$CuO$_{4}$ by precise measurements of core-level photoemission spectra. The result shows that the chemical potential monotonously increases with electron doping, quite differently from La$_{2-x}$Sr$_{x}$CuO$_{4}$, where the shift is suppressed in the underdoped region. If the suppression of the shift in La$_{2-x}$Sr$_{x}$CuO$_{4}$ is attributed to strong stripe fluctuations, the monotonous increase of the chemical potential is consistent with the absence of stripe fluctuations in Nd$_{2-x}$Ce$_{x}$CuO$_{4}$. The chemical potential jump between Nd$_{2}$CuO$_{4}$ and La$_{2}$CuO$_{4}$ is found to be much smaller than the optical band gaps.Comment: 4 pages, 5 figure

THERMODYNAMICS OF A BROWNIAN BRIDGE POLYMER MODEL IN A RANDOM ENVIRONMENT

We consider a directed random walk making either 0 or $+1$ moves and a Brownian bridge, independent of the walk, conditioned to arrive at point $b$ on time $T$. The Hamiltonian is defined as the sum of the square of increments of the bridge between the moments of jump of the random walk and interpreted as an energy function over the bridge connfiguration; the random walk acts as the random environment. This model provides a continuum version of a model with some relevance to protein conformation. The thermodynamic limit of the specific free energy is shown to exist and to be self-averaging, i.e. it is equal to a trivial --- explicitly computed --- random variable. An estimate of the asymptotic behaviour of the ground state energy is also obtained.Comment: 20 pages, uuencoded postscrip

Analysis of donor criteria for the prediction of outcome in clinical liver transplantation.

The results of 219 orthotopic human liver transplants performed during 1985 at the University of Pittsburgh were reviewed to determine whether donor parameters could be used to predict the quality of early graft function. Multivariate discriminant analysis demonstrated that traditional parameters of donor assessment are unreliable predictors of poor graft function. Furthermore, 56% of the donors considered poor by conservative selection criteria produced livers with good early posttransplant function. Survival of recipients of primary allografts from donors rated poor was no different than survival of recipients of allografts from donors rated good

An Integration Formula for the Moment Maps of Circle Actions

The integration of the exponential of the square of the moment map of the circle action is studied by a direct stationary phase computation and by applying the Duistermaat-Heckman formula. Both methods yield two distinct formulas expressing the integral in terms of contributions from the critical set of the square of the moment map. The cohomological pairings on the symplectic quotient, including its volume (which was known to be a piecewise polynomial), are computed explicitly using the asymptotic behavior of the two formulas.Comment: LaTeX file, 17 pages (typos corrected, include non-isolated fixed pts