In “Is the Frobenius Matrix Norm Induced?”, the authors ask whether the Frobenius and the norms are induced. There, they claimed that the Frobenius norm is not induced and, consequently, conjectured that the norm may not be induced. In this note, it is shown that the Frobenius norm is induced on particular matrix spaces. It is then shown that the norm is in fact induced on a particular matrix-v...

We present an algorithm to evaluate large deviation functions associated to historydependent observables. Instead of relying on a time discretisation procedure to approximate the dynamics, we provide a direct continuous-time algorithm valuable for systems with multiple time scales, thus extending the work of Giardinà, Kurchan and Peliti [1]. The procedure is supplemented with a thermodynamic-in...

As part of an ongoing investigation into environmentally acceptable alternatives to the CFC refrigerants a series of tests have been completed comparing the thermodynamic performance of Rl34a with Rl2. The tests were carried out under controlled conditions in a well instrumented water/water heat pump test facility, using an open-drive reciprocating compressor and counter flow heat e%changers. B...

Hong Qian Department of Applied Mathematics, University of Washington, Box 352420, Seattle, WA 98195, USA Abstract The consistency across scales of a recently developed mathematical thermodynamic structure, between a continuous stochastic nonlinear dynamical system (diffusion process with Langevin or Fokker-Planck equations) and its emergent discrete, inter-attractoral Markov jump process, is i...

Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local vacuum counterterms. For this the theory has to be renormalizable in the usual sense and the self-consistent scheme must follow Baym's Φ-derivable concept. Our BPHZ-renormalization scheme leads to renormalized self-consistent equations of motio...

The mean ionic activity coefficients of aqueous NaCl solutions of varying concentrations at 298.15 K and 1 bar have been obtained from molecular dynamics simulations by gradually turning on the interactions of an ion pair inserted into the solution. Several common non-polarizable water and ion models have been used in the simulations. Gibbs-Duhem equation calculations of the thermodynamic activ...

A computer program, GeoSteamNet, for the numerical simulation of steam transport in geothermal pipeline networks is written in Visual Studio .NET. The program considers (a) internally consistent thermodynamic properties of water, and (b) a numerical algorithm based on the principles of conservation of mass, linear momentum (Newton’s second law), and energy (the first and second laws of thermody...