Effective medium approach for heterogeneous reaction-diffusion media

An effective medium theory that can be used to calculate effective diffusion and reaction rate coefficients in random heterogeneous reaction-diffusion systems is described. The predictions of the theory are compared with simulations of spatially distributed media with different types of heterogeneity. The magnitude of the front velocity in bistable media is used to gauge the accuracy of the theoretical predictions. Quantitative agreement is found if the diffusion length in the heterogeneities is large compared to the characteristic width of the front. However, for small diffusion lengths the agreement depends on the type of heterogeneity. The effective medium predictions are also compared with simulations on systems with regular or temporal disorder.Peer ReviewedPostprint (published version

The solvation and dissociation of 4-benzylaniline hydrochloride in chlorobenzene

A reaction scheme is proposed to account for the liberation of 4-benzylaniline from 4-benzylaniline hydrochloride, using chlorobenzene as a solvent at a temperature of 373 K. Two operational regimes are explored: “closed” reaction conditions correspond to the retention of evolved hydrogen chloride gas within the reaction medium, whereas an “open” system permits gaseous hydrogen chloride to be released from the reaction medium. The solution phase chemistry is analyzed by 1H NMR spectroscopy. Complete liberation of solvated 4-benzylaniline from solid 4-benzylaniline hydrochloride is possible under “open” conditions, with the entropically favored conversion of solvated hydrogen chloride to the gaseous phase thought to be the thermodynamic driver that effectively controls a series of interconnecting equilibria. A kinetic model is proposed to account for the observations of the open system

From R_AA via correlations to jets - the long road to tomography

The main motivation to investigate hard probes in heavy ion collisions is to do tomography, i.e. to infer medium properties from the in-medium modification of hard processes. Yet while the suppression of high P_T hadrons has been measured for some time, solid tomographic information is slow to emerge. This can be traced back to theoretical uncertainties and ambiguities in modelling both medium evolution and parton-medium interaction. Ways to overcome these difficulties are to constrain models better and to focus on more differential observables. Correlations of high P_T hadrons offer non-trivial information beyond what can be deduced from single hadron suppression. They reflect not only the hard reaction being modified by the medium, but also the back reaction of the medium to the hard probe. Models for hard back-to-back correlations are now very well constrained by a wealth of data and allow insights into the nature of the parton-medium interaction as well as first true tomographic results. Models of full in-medium jet evolution are being actively developed, but have yet to make substantial contact with data. Progress is slower in the understanding of low P_T correlations, the ridge and the cone, although a qualitative understanding of the nature of the physics behind these correlations starts to emerge.Comment: 8 pages, 3 figures- To appear in the conference proceedings for Quark Matter 2009, March 30 - April 4, Knoxville, Tennesse

In-medium enhancement of the modified Urca neutrino reaction rates

We calculate modified Urca neutrino emission rates in the dense nuclear matter in neutron star cores. We find that these rates are strongly enhanced in the beta-stable matter in regions of the core close to the direct Urca process threshold. This enhancement can be tracked to the use of the in-medium nucleon spectrum in the virtual nucleon propagator. We describe the in-medium nucleon scattering in the non-relativistic Bruckner-Hartree-Fock framework taking into account two-body as well as the effective three-body forces, although the proposed enhancement does not rely on a particular way of the nucleon interaction treatment. Finally we suggest a simple approximate expression for the emissivity of the n-branch of the modified Urca process that can be used in the neutron stars cooling simulations with any nucleon equation of state of dense matter.Comment: 8 pages, 3 figures; accepted for publication in PLB. In v.2 misprint in eq.(9) corrected and discussion of cooling curves expande

Complex wave patterns in an effective reaction–diffusion model for chemical reactions in microemulsions

An effective medium theory is employed to derive a simple qualitative model of a pattern forming chemical reaction in a microemulsion. This spatially heterogeneous system is composed of water nanodroplets randomly distributed in oil. While some steps of the reaction are performed only inside the droplets, the transport through the extended medium occurs by diffusion of intermediate chemical reactants as well as by collisions of the droplets. We start to model the system with heterogeneous reaction–diffusion equations and then derive an equivalent effective spatially homogeneous reaction–diffusion model by using earlier results on homogenization in heterogeneous reaction–diffusion systems [ S. Alonso, M. Bär, and R. Kapral, J. Chem. Phys. 134, 214102 (2009)]. We study the linear stability of the spatially homogeneous state in the resulting effective model and obtain a phase diagram of pattern formation, that is qualitatively similar to earlier experimental results for the Belousov–Zhabotinsky reaction in an aerosol OT (AOT)-water-in-oil microemulsion [ V. K. Vanag and I. R. Epstein, Phys. Rev. Lett. 87, 228301 (2001)]. Moreover, we reproduce many patterns that have been observed in experiments with the Belousov–Zhabotinsky reaction in an AOT oil-in-water microemulsion by direct numerical simulations.Peer ReviewedPostprint (published version