Integrals of Motion for Critical Dense Polymers and Symplectic Fermions

We consider critical dense polymers ${\cal L}(1,2)$. We obtain for this model the eigenvalues of the local integrals of motion of the underlying Conformal Field Theory by means of Thermodynamic Bethe Ansatz. We give a detailed description of the relation between this model and Symplectic Fermions including the indecomposable structure of the transfer matrix. Integrals of motion are defined directly on the lattice in terms of the Temperley Lieb Algebra and their eigenvalues are obtained and expressed as an infinite sum of the eigenvalues of the continuum integrals of motion. An elegant decomposition of the transfer matrix in terms of a finite number of lattice integrals of motion is obtained thus providing a reason for their introduction.Comment: 53 pages, version accepted for publishing on JSTA

Quasiuniversal connectedness percolation of polydisperse rod systems

The connectedness percolation threshold (eta_c) and critical coordination number (Z_c) of systems of penetrable spherocylinders characterized by a length polydispersity are studied by way of Monte Carlo simulations for several aspect ratio distributions. We find that (i) \eta_c is a nearly universal function of the weight-averaged aspect ratio, with an approximate inverse dependence that extends to aspect ratios that are well below the slender rod limit and (ii) that percolation of impenetrable spherocylinders displays a similar quasiuniversal behavior. For systems with a sufficiently high degree of polydispersity, we find that Z_c can become smaller than unity, in analogy with observations reported for generalized and complex networks.Comment: 5 pages with 3 figures + 2 pages and 4 figures of supplemental materia

Commercial lending distance and historically underserved areas

We study recent changes in the geographic distances between small businesses and their bank lenders, using a large random sample of loans guaranteed by the Small Business Administration. Consistent with extant research, we find that small borrower-lender distances generally increased between 1984 and 2001, with a rapid acceleration in distance beginning in the late-1990s. We also document a new phenomenon: a fundamental reordering of borrower-lender distance by the borrowers' neighborhood income and race characteristics. Historically, borrower-lender distance tended to be shorter than average for historically underserved (for example, low-income and minority) areas, but by 2000 borrowers in these areas tended to be farther away from their lenders on average. This structural change is coincident in time with the adoption of credit scoring models that rely on automated lending processes and quantitative information, and we find indirect evidence consistent with this link. Our findings suggest that there has been increased entry into local markets for small business loans and this should help allay fears that movement toward automated lending processes will reduce small businesses' access to credit in already underserved markets.

Securitization of Small Business Loans

This paper assesses the potential impact of securitization in improving small businesses’ access to credit. It begins by examining the nature of small business lending and the factors that make banks the primary providers of credit to small businesses. The paper then examines the conditions under which the benefits of securitization are fully realized and whether the nature of small business lend­ing satisfies those conditions. We argue that certain characteristics of small firm finance, especially information problems and the need for ongoing monitoring, are likely to mitigate the full benefits of securitization, that is, the substantial funding cost advantages. Specifically, loan buyers will demand substantial levels of loss protection to compensate for their uncertainty over the returns on the underlying credits and to leave intact the seller’s incentive to monitor properly the loans sold. Loss protection, however, will reduce or eliminate any funding cost advantages, including capital cost reductions. In the absence of lower funding costs, banks are unlikely to undertake substantial new lending to small busi­nesses. Securitizations of small business loans could still take place, but they are likely to be undertaken for special purposes rather than as a primary funding mechanism

Speed limit to the Abrikosov lattice in mesoscopic superconductors

We study the instability of the superconducting state in a mesoscopic geometry for the low pinning material Mo$_3$Ge characterized by a large Ginzburg-Landau parameter. We observe that in the current driven switching to the normal state from a nonlinear region of the Abrikosov flux flow, the mean critical vortex velocity reaches a limiting maximum velocity as a function of the applied magnetic field. Based on time dependent Ginzburg-Landau simulations we argue that the observed behavior is due to the high velocity vortex dynamics confined on a mesoscopic scale. We build up a general phase diagram which includes all possible dynamic configurations of Abrikosov lattice in a mesoscopic superconductor.Comment: 7 pages, 6 figure

What is a large-scale dynamo?

We consider kinematic dynamo action in a sheared helical flow at moderate to high values of the magnetic Reynolds number Rm. We find exponentially growing solutions which, for large enough shear, take the form of a coherent part embedded in incoherent fluctuations. We argue that at large Rm large-scale dynamo action should be identified by the presence of structures coherent in time, rather than those at large spatial scales. We further argue that although the growth-rate is determined by small-scale processes, the period of the coherent structures is set by mean-field considerations

Scanning Probe Microscopy on heterogeneous CaCu3Ti4O12 thin films

The conductive atomic force microscopy provided a local characterization of the dielectric heterogeneities in CaCu3Ti4O12 (CCTO) thin films deposited by MOCVD on IrO2 bottom electrode. In particular, both techniques have been employed to clarify the role of the inter- and sub-granular features in terms of conductive and insulating regions. The microstructure and the dielectric properties of CCTO thin films have been studied and the evidence of internal barriers in CCTO thin films has been provided. The role of internal barriers and the possible explanation for the extrinsic origin of the giant dielectric response in CCTO has been evaluated