Collision of Polymers in a Vacuum

In a number of experimental situations, single polymer molecules can be suspended in a vacuum. Here collisions between such molecules are considered. The limit of high collision velocity is investigated numerically for a variety of conditions. The distribution of contact times, scattering angles, and final velocities are analyzed. In this limit, self avoiding chains are found to become highly stretched as they collide with each other, and have a distribution of scattering times that depends on the scattering angle. The velocity of the molecules after the collisions is similar to predictions of a model assuming thermal equilibration of molecules during the collision. The most important difference is a significant subset of molecules that inelastically scatter but do not substantially change direction.Comment: 7 pages, 6 figure

Phase diagram for the asymmetric nuclear matter in the multifragmentation model

We assume that, in equilibrium, nuclear matter at reduced density and moderate finite temperature, breaks up into many fragments. A strong support to this assumption is provided by date accumulated from intermediate energy heavy ion collisions. The break-up of hot and expanded nuclear matter according to rules of equilibrium statistical mechanics is the multifragmentation model. The model gives a first order phase transition. This is studied in detail here. Phase-equilibrium lines for different degrees of asymmetry are computed.Comment: 22 pages, 10 figure

A Model for Phase Transition based on Statistical Disassembly of Nuclei at Intermediate Energies

Consider a model of particles (nucleons) which has a two-body interaction which leads to bound composites with saturation properties. These properties are : all composites have the same density and the ground state energies of composites with k nucleons are given by -kW+\sigma k^{2/3} where W and \sigma are positive constants. W represents a volume term and \sigma a surface tension term. These values are taken from nuclear physics. We show that in the large N limit where N is the number of particles such an assembly in a large enclosure at finite temperature shows properties of liquid-gas phase transition. We do not use the two-body interaction but the gross properties of the composites only. We show that (a) the p-\rho isotherms show a region where pressure does not change as $\rho$ changes just as in Maxwell construction of a Van der Waals gas, (b) in this region the chemical potential does not change and (c) the model obeys the celebrated Clausius-Clapeyron relations. A scaling law for the yields of composites emerges. For a finite number of particles N (upto some thousands) the problem can be easily solved on a computer. This allows us to study finite particle number effects which modify phase transition effects. The model is calculationally simple. Monte-Carlo simulations are not needed.Comment: RevTex file, 21 pages, 5 figure

Semantic Web technologies in software engineering

Over the years, the software engineering community has developed various tools to support the specification, development, and maintainance of software. Many of these tools use proprietary data formats to store artifacts which hamper interoperability. However, the Semantic Web provides a common framework that allows data to be shared and reused across application, enterprise, and community boundaries. Ontologies are used define the concepts in the domain of discourse and their relationships and as such provide the formal vocabulary applications use to exchange data. Beside the Web, the technologies developed for the Semantic Web have proven to be useful also in other domains, especially when data is exchanged between applications from different parties. Software engineering is one of these domains in which recent research shows that Semantic Web technologies are able to reduce the barriers of proprietary data formats and enable interoperability. In this tutorial, we present Semantic Web technologies and their application in software engineering. We discuss the current status of ontologies for software entities, bug reports, or change requests, as well as semantic representations for software and its documentation. This way, architecture, design, code, or test models can be shared across application boundaries enabling a seamless integration of engineering results

Negative Interactions in Irreversible Self-Assembly

This paper explores the use of negative (i.e., repulsive) interaction the abstract Tile Assembly Model defined by Winfree. Winfree postulated negative interactions to be physically plausible in his Ph.D. thesis, and Reif, Sahu, and Yin explored their power in the context of reversible attachment operations. We explore the power of negative interactions with irreversible attachments, and we achieve two main results. Our first result is an impossibility theorem: after t steps of assembly, Omega(t) tiles will be forever bound to an assembly, unable to detach. Thus negative glue strengths do not afford unlimited power to reuse tiles. Our second result is a positive one: we construct a set of tiles that can simulate a Turing machine with space bound s and time bound t, while ensuring that no intermediate assembly grows larger than O(s), rather than O(s * t) as required by the standard Turing machine simulation with tiles

A Paradox of State-Dependent Diffusion and How to Resolve It

Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal proportions of time in the two regions in the long term? Statistical mechanics would suggest yes, since the number of accessible states in each region is presumably the same. However, another line of reasoning suggests that the particle should spend less time in the region with faster diffusion, since it will exit that region more quickly. We demonstrate with a simple microscopic model system that both predictions are consistent with the information given. Thus, specifying the diffusion rate as a function of position is not enough to characterize the behaviour of a system, even assuming the absence of external forces. We propose an alternative framework for modelling diffusive dynamics in which both the diffusion rate and equilibrium probability density for the position of the particle are specified by the modeller. We introduce a numerical method for simulating dynamics in our framework that samples from the equilibrium probability density exactly and is suitable for discontinuous diffusion coefficients.Comment: 21 pages, 6 figures. Second round of revisions. This is the version that will appear in Proc Roy So

Quasi-Particle Degrees of Freedom versus the Perfect Fluid as Descriptors of the Quark-Gluon Plasma

The hot nuclear matter created at the Relativistic Heavy Ion Collider (RHIC) has been characterized by near-perfect fluid behavior. We demonstrate that this stands in contradiction to the identification of QCD quasi-particles with the thermodynamic degrees of freedom in the early (fluid) stage of heavy ion collisions. The empirical observation of constituent quark ``$n_q$'' scaling of elliptic flow is juxtaposed with the lack of such scaling behavior in hydrodynamic fluid calculations followed by Cooper-Frye freeze-out to hadrons. A ``quasi-particle transport'' time stage after viscous effects break down the hydrodynamic fluid stage, but prior to hadronization, is proposed to reconcile these apparent contradictions. However, without a detailed understanding of the transitions between these stages, the ``$n_q$'' scaling is not a necessary consequence of this prescription. Also, if the duration of this stage is too short, it may not support well defined quasi-particles. By comparing and contrasting the coalescence of quarks into hadrons with the similar process of producing light nuclei from nucleons, it is shown that the observation of ``$n_{q}$'' scaling in the final state does not necessarily imply that the constituent degrees of freedom were the relevant ones in the initial state.Comment: 9 pages, 7 figures, Updated text and figure

New Geometric Algorithms for Fully Connected Staged Self-Assembly

We consider staged self-assembly systems, in which square-shaped tiles can be added to bins in several stages. Within these bins, the tiles may connect to each other, depending on the glue types of their edges. Previous work by Demaine et al. showed that a relatively small number of tile types suffices to produce arbitrary shapes in this model. However, these constructions were only based on a spanning tree of the geometric shape, so they did not produce full connectivity of the underlying grid graph in the case of shapes with holes; designing fully connected assemblies with a polylogarithmic number of stages was left as a major open problem. We resolve this challenge by presenting new systems for staged assembly that produce fully connected polyominoes in O(log^2 n) stages, for various scale factors and temperature {\tau} = 2 as well as {\tau} = 1. Our constructions work even for shapes with holes and uses only a constant number of glues and tiles. Moreover, the underlying approach is more geometric in nature, implying that it promised to be more feasible for shapes with compact geometric description.Comment: 21 pages, 14 figures; full version of conference paper in DNA2

Sub-milliKelvin spatial thermometry of a single Doppler cooled ion in a Paul trap

We report on observations of thermal motion of a single, Doppler-cooled ion along the axis of a linear radio-frequency quadrupole trap. We show that for a harmonic potential the thermal occupation of energy levels leads to Gaussian distribution of the ion's axial position. The dependence of the spatial thermal spread on the trap potential is used for precise calibration of our imaging system's point spread function and sub-milliKelvin thermometry. We employ this technique to investigate the laser detuning dependence of the Doppler temperature.Comment: 5 pages, 4 figure