One-dimensional quantum magnetism in the S= 1/2 Mo(V) system KMoOP2O7

We present a comprehensive experimental and ab initio study of the S=1/2Mo5+ system, KMoOP2O7, and show that it realizes the S=12 Heisenberg chain antiferromagnet model. Powder neutron diffraction reveals that KMoOP2O7 forms a magnetic network comprised of pairs of Mo5+ chains within its monoclinic P21/n structure. Antiferromagnetic interactions within the Mo5+ chains are identified through magnetometry measurements and confirmed by analysis of the magnetic specific heat. The latter reveals a broad feature centered on TN=0.54 K, which we ascribe to the onset of long-range antiferromagnetic order. No magnetic Bragg scattering is observed in powder neutron-diffraction data collected at 0.05 K, however, which is consistent with a strongly suppressed ordered moment with an upper limit μord<0.15μB. The one-dimensional character of the magnetic correlations in KMoOP2O7 is verified through analysis of inelastic neutron-scattering data, resulting in a model with J2≈34 K and J1≈-2 K for the intrachain and interchain exchange interactions, respectively. The origin of these experimental findings are addressed through density-functional theory calculations

About control of electricity market

We consider auction problem for network of inter-connected energy markets. The conditions of optimality for this problem are derived. The numerical method based on these conditions for running auction is constructed. It is shown how running auction can be achieved by using automated control system. © 2009 Pleiades Publishing, Ltd

Thermodynamic constraints on temperature distribution in a stationary system with heat engine or refrigerator

In this paper we consider a stationary thermodynamic system that includes a transformer of mechanical energy into heat energy or heat into mechanical energy. We derive conditions that determine temperature distribution (temperature field) inside such a system permitted by thermodynamics. We obtain conditions that divide feasible temperature fields into two classes - one where mechanical energy has to be spent and another where it is extracted. Closed-form expressions for the minimal supplied/maximal extracted power are derived. It is shown that for a linear heat transfer law and heat engine operating at maximal power the ratio of engine working body's temperatures during contact with reservoirs is equal to the square root of the ratio of reservoirs' temperatures irrespective of the system's structure and whether the engine is internally irreversible or not. Therefore, an engine's efficiency at maximal power does not depend on its internal structure. The problem of maintaining given temperatures in a subset of inter-connected chambers is considered. The conditions that determine optimal temperatures in the chambers where temperatures are not fixed which minimize energy are derived. © 2006 IOP Publishing Ltd