Percolation of randomly distributed growing clusters

We investigate the problem of growing clusters, which is modeled by two dimensional disks and three dimensional droplets. In this model we place a number of seeds on random locations on a lattice with an initial occupation probability, $p$. The seeds simultaneously grow with a constant velocity to form clusters. When two or more clusters eventually touch each other they immediately stop their growth. The probability that such a system will result in a percolating cluster depends on the density of the initially distributed seeds and the dimensionality of the system. For very low initial values of $p$ we find a power law behavior for several properties that we investigate, namely for the size of the largest and second largest cluster, for the probability for a site to belong to the finally formed spanning cluster, and for the mean radius of the finally formed droplets. We report the values of the corresponding scaling exponents. Finally, we show that for very low initial concentration of seeds the final coverage takes a constant value which depends on the system dimensionality.Comment: 5 pages, 7 figure

A Comprehensive Review of Critical Issues on Transitioning to a Vehicle Miles Traveled Fee System

Due to increased vehicle fuel efficiency, electric vehicles, inflation, and the fuel tax not being raised in the past 20 years, the Highway Trust Fund has been unable to cover the costs associated with expanding and maintaining the transportation system. Despite improved construction methods, better planning and superior materials, municipalities cannot keep up with wear and tear on roadways, let alone keep up with future expansion. There is simply not enough revenue to support the roadway system. This shortfall has led experts to look for alternative solutions to the current major method of funding the Highway Trust Fund: the fuel tax. The most attractive solution to emerge is the Vehicle Miles Traveled (VMT) fee.A VMT fee is an answer to many of the current problems facing fuel taxes such as increased fuel efficiency in vehicles, the rise in hybrids and electric vehicles, and responding to inflation. The VMT fee has been recommended by a number of professionals and experts as a complete replacement for the current fuel tax for these reasons. However, there are many obstacles to this attractive alternative including perception, administration, and implementation. The purpose of this study is to provide a thorough literature review of several states' approaches to the VMT fee, address prominent issues and concerns associated with the VMT fee, and provide several transition schemes which would minimize the concerns of the public, motorists, and decision-makers. It was found that allowing the motorist to choose the VMT fee collection system eases privacy concerns and thus has less resistance when passing the fee through legislation. It was found that allowing for a longer transition phase will be most desirable, because the user will have the option of paying the VMT fee or the fuel tax

Percolation of randomly distributed growing clusters: Finite Size Scaling and Critical Exponents

We study the percolation properties of the growing clusters model. In this model, a number of seeds placed on random locations on a lattice are allowed to grow with a constant velocity to form clusters. When two or more clusters eventually touch each other they immediately stop their growth. The model exhibits a discontinuous transition for very low values of the seed concentration $p$ and a second, non-trivial continuous phase transition for intermediate $p$ values. Here we study in detail this continuous transition that separates a phase of finite clusters from a phase characterized by the presence of a giant component. Using finite size scaling and large scale Monte Carlo simulations we determine the value of the percolation threshold where the giant component first appears, and the critical exponents that characterize the transition. We find that the transition belongs to a different universality class from the standard percolation transition.Comment: 5 two-column pages, 6 figure

Two-photon ionization of Helium studied with the multiconfigurational time-dependent Hartree-Fock method

The multiconfigurational time-dependent Hartree-Fock method (MCTDHF) is applied for simulations of the two-photon ionization of Helium. We present results for the single- and double ionization from the groundstate for photon energies in the non-sequential regime, and compare them to direct solutions of the Schr\"odinger equation using the time-dependent (full) Configuration Interaction method (TDCI). We find that the single-ionization is accurately reproduced by MCTDHF, whereas the double ionization results correctly capture the main trends of TDCI

Multiscale model of electronic behavior and localization in stretched dry DNA

When the DNA double helix is subjected to external forces it can stretch elastically to elongations reaching 100% of its natural length. These distortions, imposed at the mesoscopic or macroscopic scales, have a dramatic effect on electronic properties at the atomic scale and on electrical transport along DNA. Accordingly, a multiscale approach is necessary to capture the electronic behavior of the stretched DNA helix. To construct such a model, we begin with accurate density-functional-theory calculations for electronic states in DNA bases and base pairs in various relative configurations encountered in the equilibrium and stretched forms. These results are complemented by semi-empirical quantum mechanical calculations for the states of a small size [18 base pair poly(CG)–poly(CG)] dry, neutral DNA sequence, using previously published models for stretched DNA. The calculated electronic states are then used to parametrize an effective tight-binding model that can describe electron hopping in the presence of environmental effects, such as the presence of stray water molecules on the backbone or structural features of the substrate. These effects introduce disorder in the model hamiltonian which leads to electron localization. The localization length is smaller by several orders of magnitude in stretched DNA relative to that in the unstretched structure

Time-dependent calculation of ionization in Potassium at mid-infrared wavelengths

We study the dynamics of the Potassium atom in the mid-infrared, high intensity, short laser pulse regime. We ascertain numerical convergence by comparing the results obtained by the direct expansion of the time-dependent Schroedinger equation onto B-Splines, to those obtained by the eigenbasis expansion method. We present ionization curves in the 12-, 13-, and 14-photon ionization range for Potassium. The ionization curve of a scaled system, namely Hydrogen starting from the 2s, is compared to the 12-photon results. In the 13-photon regime, a dynamic resonance is found and analyzed in some detail. The results for all wavelengths and intensities, including Hydrogen, display a clear plateau in the peak-heights of the low energy part of the Above Threshold Ionization (ATI) spectrum, which scales with the ponderomotive energy Up, and extends to 2.8 +- 0.5 Up.Comment: 15 two-column pages with 15 figures, 3 tables. Accepted for publication in Phys. Rev A. Improved figures, language and punctuation, and made minor corrections. We also added a comparison to the ADK theor

Variational finite-difference representation of the kinetic energy operator

A potential disadvantage of real-space-grid electronic structure methods is the lack of a variational principle and the concomitant increase of total energy with grid refinement. We show that the origin of this feature is the systematic underestimation of the kinetic energy by the finite difference representation of the Laplacian operator. We present an alternative representation that provides a rigorous upper bound estimate of the true kinetic energy and we illustrate its properties with a harmonic oscillator potential. For a more realistic application, we study the convergence of the total energy of bulk silicon using a real-space-grid density-functional code and employing both the conventional and the alternative representations of the kinetic energy operator.Comment: 3 pages, 3 figures, 1 table. To appear in Phys. Rev. B. Contribution for the 10th anniversary of the eprint serve

Posterior probability and fluctuation theorem in stochastic processes

A generalization of fluctuation theorems in stochastic processes is proposed. The new theorem is written in terms of posterior probabilities, which are introduced via the Bayes theorem. In usual fluctuation theorems, a forward path and its time reversal play an important role, so that a microscopically reversible condition is essential. In contrast, the microscopically reversible condition is not necessary in the new theorem. It is shown that the new theorem adequately recovers various theorems and relations previously known, such as the Gallavotti-Cohen-type fluctuation theorem, the Jarzynski equality, and the Hatano-Sasa relation, when adequate assumptions are employed.Comment: 4 page