Exact clesed form of the return probability on the Bethe lattice

An exact closed form solution for the return probability of a random walk on the Bethe lattice is given. The long-time asymptotic form confirms a previously known expression. It is however shown that this exact result reduces to the proper expression when the Bethe lattice degenerates on a line, unlike the asymptotic result which is singular. This is shown to be an artefact of the asymptotic expansion. The density of states is also calculated.Comment: 7 pages, RevTex 3.0, 2 figures available upon request from [email protected], to be published in J.Phys.A Let

Flory theory for Polymers

We review various simple analytical theories for homopolymers within a unified framework. The common guideline of our approach is the Flory theory, and its various avatars, with the attempt of being reasonably self-contained. We expect this review to be useful as an introduction to the topic at the graduate students level.Comment: Topical review appeared J. Phys.: Condens. Matter, 46 pages, 8 Figures. Sec. VIF added. Typos fixed. Few references adde

Colour analysis of degraded parchment

Multispectral imaging was employed to collect data on the degradation of an 18th century parchment by a series of physical and chemical treatments. Each sample was photographed before and after treatment by a monochrome digital camera with 21 narrow-band filters. A template-matching technique was used to detect the circular holes in each sample and a four-point projective transform to register the 21 images. Colour accuracy was verified by comparison of reconstructed spectra with measurements by spectrophotometer

A pseudo-spectral approach to inverse problems in interface dynamics

An improved scheme for computing coupling parameters of the Kardar-Parisi-Zhang equation from a collection of successive interface profiles, is presented. The approach hinges on a spectral representation of this equation. An appropriate discretization based on a Fourier representation, is discussed as a by-product of the above scheme. Our method is first tested on profiles generated by a one-dimensional Kardar-Parisi-Zhang equation where it is shown to reproduce the input parameters very accurately. When applied to microscopic models of growth, it provides the values of the coupling parameters associated with the corresponding continuum equations. This technique favorably compares with previous methods based on real space schemes.Comment: 12 pages, 9 figures, revtex 3.0 with epsf style, to appear in Phys. Rev.

Diffusion and Trapping on a one-dimensional lattice

The properties of a particle diffusing on a one-dimensional lattice where at each site a random barrier and a random trap act simultaneously on the particle are investigated by numerical and analytical techniques. The combined effect of disorder and traps yields a decreasing survival probability with broad distribution (log-normal). Exact enumerations, effective-medium approximation and spectral analysis are employed. This one-dimensional model shows rather rich behaviours which were previously believed to exist only in higher dimensionality. The possibility of a trapping-dominated super universal class is suggested.Comment: 20 pages, Revtex 3.0, 13 figures in compressed format using uufiles command, to appear in Phys. Rev. E, for an hard copy or problems e-mail to: [email protected]

Diffusion with critically correlated traps and the slow relaxation of the longest wavelength mode

We study diffusion on a substrate with permanent traps distributed with critical positional correlation, modeled by their placement on the perimeters of a critical percolation cluster. We perform a numerical analysis of the vibrational density of states and the largest eigenvalue of the equivalent scalar elasticity problem using the method of Arnoldi and Saad. We show that the critical trap correlation increases the exponent appearing in the stretched exponential behavior of the low frequency density of states by approximately a factor of two as compared to the case of no correlations. A finite size scaling hypothesis of the largest eigenvalue is proposed and its relation to the density of states is given. The numerical analysis of this scaling postulate leads to the estimation of the stretch exponent in good agreement with the density of states result.Comment: 15 pages, LaTeX (RevTeX

Yang-Lee Edge Singularity on a Class of Treelike Lattices

The density of zeros of the partition function of the Ising model on a class of treelike lattices is studied. An exact closed-form expression for the pertinent critical exponents is derived by using a couple of recursion relations which have a singular behavior near the Yang-Lee edge.Comment: 9 pages AmsTex, 2 eps figures, to appear in J.Phys.

Phase diagram of the penetrable square well-model

We study a system formed by soft colloidal spheres attracting each other via a square-well potential, using extensive Monte Carlo simulations of various nature. The softness is implemented through a reduction of the infinite part of the repulsive potential to a finite one. For sufficiently low values of the penetrability parameter we find the system to be Ruelle stable with square-well like behavior. For high values of the penetrability the system is thermodynamically unstable and collapses into an isolated blob formed by a few clusters each containing many overlapping particles. For intermediate values of the penetrability the system has a rich phase diagram with a partial lack of thermodynamic consistency.Comment: 6 pages and 5 figure

Correlation of vulnerability and damage between artistic assets and structural elements: The DataBAES archive for the conservation planning of CH masonry buildings in seismic areas

Historical buildings in seismic hazard-prone regions need specific measures in safety protection, largely due to the presence of artistic assets and/or decorations, both movable (e.g., statues, pinnacles, etc.) and unmovable (e.g., frescoes, valuable plasters or wall paintings, mosaics, and stuccoes). A correlation of damage between structural systems and artworks is fundamental for defining limit states, which can identify the proper conditions for interventions. Nevertheless, several vulnerability aspects can be identified before a seismic event occurs, the study of which can provide the basic dataset for setting up preventive measures in conservation programs. In this paper, the vulnerability and damage conditions related to structural elements (SE) and unmovable artistic assets (AA) belonging to historical masonry buildings are analysed. Optimized survey forms for the onsite detection of either intrinsic (e.g., compositional) defects or deterioration phenomena for both materials and structure are proposed, and results are provided in a web data system (called DataBAES). This enables us to compare the current levels of vulnerability and damage of AA and SE on a scale of five increasing grades. This procedure has been validated on a series of buildings struck by earthquakes in Italy and can be used for correlations of the seismic behaviour of SE and AA in predictive analyses