Phase Transitions in "Small" Systems - A Challenge for Thermodynamics

Traditionally, phase transitions are defined in the thermodynamic limit only. We propose a new formulation of equilibrium thermo-dynamics that is based entirely on mechanics and reflects just the {\em geometry and topology} of the N-body phase-space as function of the conserved quantities, energy, particle number and others. This allows to define thermo-statistics {\em without the use of the thermodynamic limit}, to apply it to ``Small'' systems as well and to define phase transitions unambiguously also there. ``Small'' systems are systems where the linear dimension is of the characteristic range of the interaction between the particles. Also astrophysical systems are ``Small'' in this sense. Boltzmann defines the entropy as the logarithm of the area $W(E,N)=e^{S(E,N)}$ of the surface in the mechanical N-body phase space at total energy E. The topology of S(E,N) or more precisely, of the curvature determinant $D(E,N)=\partial^2S/\partial E^2*\partial^2S/\partial N^2-(\partial^2S/\partial E\partial N)^2$ allows the classification of phase transitions {\em without taking the thermodynamic limit}. The topology gives further a simple and transparent definition of the {\em order parameter.} Attention: Boltzmann's entropy S(E) as defined here is different from the information entropy and can even be non-extensive and convex.Comment: 8 pages, 4 figures, Invited paper for CRIS200

Classical Equilibrium Thermostatistics, "Sancta sanctorum of Statistical Mechanics", From Nuclei to Stars

Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the N-body phase space with the given total energy. Due to Boltzmann-Planck's principle, e^S=tr(\delta(E-H)), its geometrical size is related to the entropy S(E,N,V,...). This definition does not invoke any information theory, no thermodynamic limit, no extensivity, and no homogeneity assumption. Therefore, it describes the equilibrium statistics of extensive as well of non-extensive systems. Due to this fact it is the fundamental definition of any classical equilibrium statistics. It addresses nuclei and astrophysical objects as well. S(E,N,V,...) is multiply differentiable everywhere, even at phase-transitions. All kind of phase transitions can be distinguished harply and uniquely for even small systems. What is even more important, in contrast to the canonical theory, also the region of phase-space which corresponds to phase-separation is accessible, where the most interesting phenomena occur. No deformed q-entropy is needed for equilibrium. Boltzmann-Planck is the only appropriate statistics independent of whether the system is small or large, whether the system is ruled by short or long range forces.Comment: Invited paper for NEXT2003, 10pages, 6 figures Reference 1 correcte

Wireless Backhaul Node Placement for Small Cell Networks

Small cells have been proposed as a vehicle for wireless networks to keep up with surging demand. Small cells come with a significant challenge of providing backhaul to transport data to(from) a gateway node in the core network. Fiber based backhaul offers the high rates needed to meet this requirement, but is costly and time-consuming to deploy, when not readily available. Wireless backhaul is an attractive option for small cells as it provides a less expensive and easy-to-deploy alternative to fiber. However, there are multitude of bands and features (e.g. LOS/NLOS, spatial multiplexing etc.) associated with wireless backhaul that need to be used intelligently for small cells. Candidate bands include: sub-6 GHz band that is useful in non-line-of-sight (NLOS) scenarios, microwave band (6-42 GHz) that is useful in point-to-point line-of-sight (LOS) scenarios, and millimeter wave bands (e.g. 60, 70 and 80 GHz) that are recently being commercially used in LOS scenarios. In many deployment topologies, it is advantageous to use aggregator nodes, located at the roof tops of tall buildings near small cells. These nodes can provide high data rate to multiple small cells in NLOS paths, sustain the same data rate to gateway nodes using LOS paths and take advantage of all available bands. This work performs the joint cost optimal aggregator node placement, power allocation, channel scheduling and routing to optimize the wireless backhaul network. We formulate mixed integer nonlinear programs (MINLP) to capture the different interference and multiplexing patterns at sub-6 GHz and microwave band. We solve the MINLP through linear relaxation and branch-and-bound algorithm and apply our algorithm in an example wireless backhaul network of downtown Manhattan.Comment: Invited paper at Conference on Information Science & Systems (CISS) 201

Enhancing Mobile Learning Delivery through Exploration of the Learner Experience

This paper was presented as a short paper at the conference, on Wednesday, March 26th. There were several questions posed after the presentation. One person wondered if the small number of responders represented only a small group of people who would be using mobile devices anyway. Another person was interested in the IMD LD methodology used. A third person stated he would be interested in further research of this type that broke the responders down into demographics such as age and rural/urban locations. Attendees from the Ulyanovsk State Technical University in Russia expressed an interest in future collaboration based on the mobile technology in the presentation. Finally, two attendees from Massey University in New Zealand asked me submit a paper to present further results from the research at the DEANZ Conference in New Zealand Aug/08 and invited me to present to staff at Massey University in the same visit as well.M-Learning research at the School of Computing and Information Systems (SCIS) at Athabasca University has been directed at improving mobile device access to distance learning materials through improved device detection, use of mobile device style sheets, and alternate files and graphics that are tailored to smaller screens. However, there is a greater significance placed in determining how learners perceive these enhancements to online learning. During this study, students were directed to access their regular online course materials using their mobile devices, then asked to complete a survey regarding their perception of this experience. This paper discusses the results from this study.Office of the VP, Academic & Academic & Professional Development Fund (A&PDF

Recent developments in the characterization of superconducting films by microwaves

We describe and analyze selected surface impedance data recently obtained by different groups on cuprate, ruthenate and diboride superconducting films on metallic and dielectric substrates for fundamental studies and microwave applications. The discussion includes a first review of microwave data on MgB2, the weak-link behaviour of RABiTS-type YBa2Cu3O7-d tapes, and the observation of a strong anomalous power-dependence of the microwave losses in MgO at low temperatures. We demonstrate how microwave measurements can be used to investigate electronic, magnetic, and dielectric dissipation and relaxation in the films and substrates. The impact of such studies reaches from the extraction of microscopic information to the engineering of materials and further on to applications in power systems and communication technology.Comment: Invited contribution to EUCAS2001, accepted for publication in Physica C in its present for

Making Progress in Forecasting

Twenty-five years ago, the International Institute of Forecasters was established “to bridge the gap between theory and practice.” Its primary vehicle was the Journal of Forecasting and is now the International Journal of Forecasting. The Institute emphasizes empirical comparisons of reasonable forecasting approaches. Such studies can be used to identify the best forecasting procedures to use under given conditions, a process we call evidence-based forecasting. Unfortunately, evidence-based forecasting meets resistance from academics and practitioners when the findings differ from currently accepted beliefs. As a consequence, although much progress has been made in developing improved forecasting methods, the diffusion of useful forecasting methods has been disappointing. To bridge the gap between theory and practice, we recommend a stronger emphasis on the method of multiple hypotheses and on invited replications of important research. It is then necessary to translate the findings into principles that are easy to understand and apply. The Internet and software provide important opportunities for making the latest findings available to researchers and practitioners. Because researchers and practitioners believe that their areas are unique, we should organize findings so that they are relevant to each area and make them easily available when people search for information about forecasting in their area. Organisational barriers to change still remain to be overcome. Research into the specific issues faced when forecasting remains a priority

Decoherence in Quantum Systems

We discuss various definitions of decoherence and how it can be measured. We compare and contrast decoherence in quantum systems with an infinite number of eigenstates (such as the free particle and the oscillator) and spin systems. In the former case, we point out the essential difference between assuming "entanglement at all times" and entanglement with the reservoir occuring at some initial time. We also discuss optimum calculational techniques in both arenas.Comment: To be published in Proceedings of the 2004 IEEE NTC Quantum Device Technology Workshop, IEEE Transactions on Nanotechnology, 4, 77, 200