Scaling of Star Polymers with one to 80 Arms

We present large statistics simulations of 3-dimensional star polymers with up to $f=80$ arms, and with up to 4000 monomers per arm for small values of $f$. They were done for the Domb-Joyce model on the simple cubic lattice. This is a model with soft core exclusion which allows multiple occupancy of sites but punishes each same-site pair of monomers with a Boltzmann factor $v<1$. We use this to allow all arms to be attached at the central site, and we use the `magic' value $v=0.6$ to minimize corrections to scaling. The simulations are made with a very efficient chain growth algorithm with resampling, PERM, modified to allow simultaneous growth of all arms. This allows us to measure not only the swelling (as observed from the center-to-end distances), but also the partition sum. The latter gives very precise estimates of the critical exponents $\gamma_f$. For completeness we made also extensive simulations of linear (unbranched) polymers which give the best estimates for the exponent $\gamma$.Comment: 7 pages, 7 figure

Maxwell Model of Traffic Flows

We investigate traffic flows using the kinetic Boltzmann equations with a Maxwell collision integral. This approach allows analytical determination of the transient behavior and the size distributions. The relaxation of the car and cluster velocity distributions towards steady state is characterized by a wide range of velocity dependent relaxation scales, $R^{1/2}<\tau(v)<R$, with $R$ the ratio of the passing and the collision rates. Furthermore, these relaxation time scales decrease with the velocity, with the smallest scale corresponding to the decay of the overall density. The steady state cluster size distribution follows an unusual scaling form $P_m \sim ^{-4} \Psi(m/< m>^2)$. This distribution is primarily algebraic, $P_m\sim m^{-3/2}$, for $m\ll ^2$, and is exponential otherwise.Comment: revtex, 10 page

Coefficient of normal restitution of viscous particles and cooling rate of granular gases

We investigate the cooling rate of a gas of inelastically interacting particles. When we assume velocity dependent coefficients of restitution the material cools down slower than with constant restitution. This behavior might have large influence to clustering and structure formation processes.Comment: 3 figures, Phys. Rev. E (in press

A review of Monte Carlo simulations of polymers with PERM

In this review, we describe applications of the pruned-enriched Rosenbluth method (PERM), a sequential Monte Carlo algorithm with resampling, to various problems in polymer physics. PERM produces samples according to any given prescribed weight distribution, by growing configurations step by step with controlled bias, and correcting "bad" configurations by "population control". The latter is implemented, in contrast to other population based algorithms like e.g. genetic algorithms, by depth-first recursion which avoids storing all members of the population at the same time in computer memory. The problems we discuss all concern single polymers (with one exception), but under various conditions: Homopolymers in good solvents and at the $\Theta$ point, semi-stiff polymers, polymers in confining geometries, stretched polymers undergoing a forced globule-linear transition, star polymers, bottle brushes, lattice animals as a model for randomly branched polymers, DNA melting, and finally -- as the only system at low temperatures, lattice heteropolymers as simple models for protein folding. PERM is for some of these problems the method of choice, but it can also fail. We discuss how to recognize when a result is reliable, and we discuss also some types of bias that can be crucial in guiding the growth into the right directions.Comment: 29 pages, 26 figures, to be published in J. Stat. Phys. (2011

A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package

Slug expression is an independent prognostic parameter for poor survival in colorectal carcinoma patients

Slug, a member of the Snail family of transcription factors, plays a crucial role in the regulation of epithelial-mesenchymal transition (EMT) by suppressing several epithelial markers and adhesion molecules including E-cadherin. Recently, several studies have reported Slug to be expressed in breast carcinoma, oesophageal carcinoma accompanied with shorter survival. In this study, we first investigated expression of Slug mRNA in five colorectal carcinoma cell lines by reverse transcription–polymerase chain reaction. Furthermore, we investigated Slug and E-cadherin expression by immunohistochemistry in 138 patients with colorectal carcinoma. Slug mRNA was clearly expressed in four out of five colorectal carcinoma cell lines. Positive expression of Slug and E-cadherin was observed in 37 and 58% of cases, respectively. The positive expression of Slug was significantly associated with Dukes stage and distant metastasis (P=0.0027 and 0.0007), and the positive expression of Slug had a significant impact on patient overall survival (P<0.0001, log-rank test). Moreover, patients with positive expression of Slug and reduced expression of E-cadherin showed the worst prognosis (P<0.0001, log-rank test). Multivariate analysis indicated that Slug expression was an independent prognostic factor. These results suggest that positive Slug expression in colorectal carcinoma patients may become a significant parameter of poor prognosis