Mathematical modelling of the catalyst layer of a polymer-electrolyte fuel cell

In this paper we derive a mathematical model for the cathode catalyst layer of a polymer electrolyte fuel cell. The model explicitly incorporates the restriction placed on oxygen in reaching the reaction sites, capturing the experimentally observed fall in the current density to a limiting value at low cell voltages. Temperature variations and interfacial transfer of O2 between the dissolved and gas phases are also included. Bounds on the solutions are derived, from which we provide a rigorous proof that the model admits a solution. Of particular interest are the maximum and minimum attainable values. We perform an asymptotic analysis in several limits inherent in the problem by identifying important groupings of parameters. This analysis reveals a number of key relationships between the solutions, including the current density, and the composition of the layer. A comparison of numerically computed and asymptotic solutions shows very good agreement. Implications of the results are discussed and future work is outlined

Baryonic Response of Dense Holographic QCD

The response function of a homogeneous and dense hadronic system to a time-dependent (baryon) vector potential is discussed for holographic dense QCD (D4/D8 embedding) both in the confined and deconfined phases. Confined holographic QCD is an uncompressible and static baryonic insulator at large N_c and large \lambda, with a gapped vector spectrum and a massless pion. Deconfined holographic QCD is a diffusive conductor with restored chiral symmetry and a gapped transverse baryonic current. Similarly, dense D3/D7 is diffusive for any non-zero temperature at large N_c and large \lambda. At zero temperature dense D3/D7 exhibits a baryonic longitudinal visco-elastic mode with a first sound speed \lambda/\sqrt{3} and a small width due to a shear viscosity to baryon ratio \eta/n_B=\hbar/4. This mode is turned diffusive by arbitrarily small temperatures, a hallmark of holography.Comment: V2: 47 pages, 7 figures, references added, typos correcte

A prohibition of equilibrium spin currents in multi-terminal ballistic devices

We show that in the multi-terminal ballistic devices with intrinsic spin-orbit interaction connected to normal metal contacts there are no equilibrium spin currents present at any given electron energy. Obviously, this statement holds also after the integration over all occupied states. Based on the proof of this fact, a number of scenarios involving nonequilibrium spin currents is identified and further analyzed. In particular, it is shown that an arbitrary two-terminal device cannot polarize transient current. The same is true for the output terminal of an N-terminal device when all N-1 inputs are connected in parallel.Comment: 3 pages, 1 figure; presented at the DARPA SPinS review (#Th-19), San Francisco, CA, October 25-28, 200

Containerless preparation of advanced optical glasses: Experiment 77F095

Containerless processing of optical glasses was studied in preparation for space shuttle MEA flight experiments. Ground based investigation, experiment/hardware coordination activities and development of flight experiment and sample characterization plans were investigated. In the ground based investigation over 100 candidate glass materials for space processing were screened and promising compositions were identified. The system of Nb2O5-TiO2-CaO was found to be very rich with containerless glass compositions and as extensive number of the oxides combinations were tried resulting in a glass formation ternary phase diagram. The frequent occurrence of glass formation by containerless processing among the compositions for which no glass formations were previously reported indicated the possibility and an advantage of containerless processing in a terrestrial environment

Exploring the feasibility of international collaboration and relationship building through a virtual partnership scheme

International collaboration is an under-studied component of the Scholarship of Teaching and Learning (SoTL). This study sheds light on the process of international collaboration by illustrating an exploratory approach to the process of forming and maintaining collaborative partnerships. Participants in this study were put into pairs (each one comprised of one individual from the University of Glasgow and another from the University of Wisconsin System) and asked to participate in email correspondence over the course of one year. The text of participants’ emails was pooled and analyzed through a general inductive approach using NVivo software. The study, though small in nature, helps to illustrate and further understand international collaborative relationships. We offer suggestions for future international collaborations and discuss the implications of emphasizing such partnerships within SoTL

Distances of qubit density matrices on Bloch sphere

We recall the Einstein velocity addition on the open unit ball \B of $\R^{3}$ and its algebraic structure, called the Einstein gyrogroup. We establish an isomorphism between the Einstein gyrogroup on \B and the set of all qubit density matrices representing mixed states endowed with an appropriate addition. Our main result establishes a relation between the trace metric for the qubit density matrices and the rapidity metric on the Einstein gyrogroup \B.Comment: I thank to my supervisor, Jimmie Lawson. This was accepted in Journal of Mathematical Physics at September 26, 201

Multivariate p-dic L-function

We construct multivariate p-adic L-function in the p-adic number fild by using Washington method.Comment: 9 page

Quantum network architecture of tight-binding models with substitution sequences

We study a two-spin quantum Turing architecture, in which discrete local rotations \alpha_m of the Turing head spin alternate with quantum controlled NOT-operations. Substitution sequences are known to underlie aperiodic structures. We show that parameter inputs \alpha_m described by such sequences can lead here to a quantum dynamics, intermediate between the regular and the chaotic variant. Exponential parameter sensitivity characterizing chaotic quantum Turing machines turns out to be an adequate criterion for induced quantum chaos in a quantum network.Comment: Accepted for publication in J. mod. Optics [Proc. Workshop "Entanglement and Decoherence", Gargnano (Italy), Sept 1999], 3 figure