The lowest crossing in 2D critical percolation

We study the following problem for critical site percolation on the triangular lattice. Let A and B be sites on a horizontal line e separated by distance n. Consider, in the half-plane above e, the lowest occupied crossing R from the half-line left of A to the half-line right of B. We show that the probability that R has a site at distance smaller than m from AB is of order (log (n/m))^{-1}, uniformly in 1 <= m < n/2. Much of our analysis can be carried out for other two-dimensional lattices as well.Comment: 16 pages, Latex, 2 eps figures, special macros: percmac.tex. Submitted to Annals of Probabilit

Optimization problems involving the first Dirichlet eigenvalue and the torsional rigidity

We present some open problems and obtain some partial results for spectral optimization problems involving measure, torsional rigidity and first Dirichlet eigenvalue.Comment: 18 pages, 4 figure

Non-Extensive Bose-Einstein Condensation Model

The imperfect Boson gas supplemented with a gentle repulsive interaction is completely solved. In particular it is proved that it has non-extensive Bose-Einstein condensation, i.e., there is condensation without macroscopic occupation of the ground state (k=0) level

Eradication-resolution dynamics with stochastic flare-ups

In infectious disease as well as in cancer, the ultimate outcome of the curative response, mediated by the body itself or through drug treatment, is either successful eradication or a resurgence of the disease (“flare-up” or “relapse”), depending on random fluctuations that dominate the dynamics of the system when the number of diseased cells has become very low. The presence of a low-numbers bottle-neck in the dynamics, which is unavoidable if eradication is to take place at all, renders at least one phase of the dynamics essentially stochastic. However, the eradicating agents (e.g. immune cells, drug molecules) generally remain at high numbers during the critical bottle-neck phase, sufficiently so to warrant a deterministic treatment. This leads us to consider a hybrid stochastic-deterministic approach where the infected cells are treated stochastically whereas the eradicating agents are treated deterministically. Exploiting the fact that the number of eradicating agents typically decreases monotonically during the resolution phase of the response, we derive a set of coupled first-order differential equations that describe the probability of ultimate eradication as a function of the system's state, and we consider a number of biomedical applications

Change Impact Analysis based on Formalization of Trace Relations for Requirements

Evolving customer needs is one of the driving factors in software development. There is a need to analyze the impact of requirement changes in order to determine possible conflicts and design alternatives influenced by these changes. The analysis of the impact of requirement changes on related requirements can be based on requirements traceability. In this paper, we propose a requirements metamodel with well defined types of requirements relations. This metamodel represents the common concepts extracted from some prevalent requirements engineering approaches. The requirements relations in the metamodel are used to trace related requirements for change impact analysis. We formalize the relations. Based on this formalization, we define change impact rules for requirements. As a case study, we apply these rules to changes in the requirements specification for Course Management System

µTransparent insulating channels as components for miniaturized chemical separation Devices

Currently, miniaturized devices that apply electro osmotic pumping or electrophoretic separations are mostly constructed by etching small insulating channels for supply and separation on glass substrates. In principle, silicon is a superior construction material in terms of inertness and design flexibility. However, because of its semiconducting properties, the use in high voltage applications like the ones mentioned above is quite limited. In this paper, the use of μTransparent Insulating Channel (μTIC) technology is demonstrated as a standard procedure to manufacture miniaturized analytical separation devices. This technique, μchannels having extremely thin, transparent and insulating walls can be fabricated. An overview of the impact of this technology is given, showing the advantages of a fabrication technology that is as flexible as silicon technology for the fabrication of μTAS or “lab on a chip” devices. The following basic technology and control parameters will be highlighted. 1. Up to 100 μm wide rectangular channels 2. Bosses and leak-free connections to external μ fluidics. 3. Web-like structures for inlets/outlets>100 μm. 4. Implementation of conductivity electrodes 5. Good thermal dissipation properties of the thin walls 6. Control of the electro osmotic flow by a radial voltage

A novel approach to low-power hot-surface devices with decoupled electrical and thermal resistances

This work employs the idea of maintaining a hot surface by means of dissipating power at a nano-scale conductive link. The link is created between two polysilicon electrodes separated by a dielectric (a capacitor-like structure). From modelling, a link of 10 nm in diameter should be possible to maintain the surface temperature ranging between 750 and 1150 K within the surface diameter of 2 μm by absorbing a 3.3 mW of electric power. The devices can also be designed in such a way that the hot surface area is reduced to a sub-μm-size hotspot. The main advantage of the proposed idea is decoupling the electrical resistance and thermal resistance of the device. In this paper, two device structures based on antifuse technology are described. Both the thermo-electrical properties and feasibility to perform as a Pellistor-type gas sensor are discussed

Transport in nanofluidic systems: a review of theory and applications

In this paper transport through nanochannels is assessed, both of liquids and of dissolved molecules or ions. First, we review principles of transport at the nanoscale, which will involve the identification of important length scales where transitions in behavior occur. We also present several important consequences that a high surface-to-volume ratio has for transport. We review liquid slip, chemical equilibria between solution and wall molecules, molecular adsorption to the channel walls and wall surface roughness. We also identify recent developments and trends in the field of nanofluidics, mention key differences with microfluidic transport and review applications. Novel opportunities are emphasized, made possible by the unique behavior of liquids at the nanoscale

Deep drawing simulations of Tailored Blanks and experimental verification

Tailored Blanks are increasingly used in the automotive industry.\ud A combination of different materials, thickness, and coatings can be welded\ud together to form a blank for stamping car body panels. The main advantage\ud of using Tailored Blanks is to have specific characteristics at particular parts\ud of the blank in order to reduce the material weight and costs.\ud To investigate the behaviour of Tailored Blanks during deep drawing, the\ud finite element code DiekA is used. In this paper, simulations of the deep\ud drawing of two products using Tailored Blanks are discussed. For\ud verification, the two products are stamped to gain experimental information.\ud The correlation between the experimental results and the simulation results\ud appears to be satisfactory