Uncertainty Relation for a Quantum Open System

We derive the uncertainty relation for a quantum open system comprised of a Brownian particle interacting with a bath of quantum oscillators at finite temperature. We examine how the quantum and thermal fluctuations of the environment contribute to the uncertainty in the canonical variables of the system. We show that upon contact with the bath (assumed ohmic in this paper) the system evolves from a quantum-dominated state to a thermal-dominated state in a time which is the same as the decoherence time in similar models in the discussion of quantum to classical transition. This offers some insight into the physical mechanisms involved in the environment-induced decoherence process. We obtain closed analytic expressions for this generalized uncertainty relation under the conditions of high temperature and weak damping separately. We also consider under these conditions an arbitrarily-squeezed initial state and show how the squeeze parameter enters in the generalized uncertainty relation. Using these results we examine the transition of the system from a quantum pure state to a nonequilibrium quantum statistical state and to an equilibrium quantum statistical state. The three stages are marked by the decoherence time and the relaxation time respectively. With these observations we explicate the physical conditions when the two basic postulates of quantum statistical mechanics become valid. We also comment on the inappropriateness in the usage of the word classicality in many decoherence studies of quantum to classical transition.Comment: 36 pages,Tex,umdpp93-162,(submitted to Phys. Rev. A

Limits of the equivalence of time and ensemble averages in shear flows

In equilibrium systems, time and ensemble averages of physical quantities are equivalent due to ergodic exploration of phase space. In driven systems, it is unknown if a similar equivalence of time and ensemble averages exists. We explore effective limits of such convergence in a sheared bubble raft using averages of the bubble velocities. In independent experiments, averaging over time leads to well converged velocity profiles. However, the time-averages from independent experiments result in distinct velocity averages. Ensemble averages are approximated by randomly selecting bubble velocities from independent experiments. Increasingly better approximations of ensemble averages converge toward a unique velocity profile. Therefore, the experiments establish that in practical realizations of non-equilibrium systems, temporal averaging and ensemble averaging can yield convergent (stationary) but distinct distributions.Comment: accepted to PRL - final figure revision

Aspects of the Hydrocarbon Potential of the Coals and Associated Shales and Mudstones of the Mamu Formation in Anambra Basin, Nigeria

Coals and associated shales and mudstones of the Mamu Formation in Anambra basin were examined for their hydrocarbon potentials by subjecting them to total organic carbon (TOC) and Rock-eval Pyrolysis analyses. The TOC results range from 45.56 to 67.68 wt. %, 0.07 to 5.65 wt. % and 0.12 to 4.46 wt. % for the coals, shales and mudstones respectively, suggesting that the sediments contain appreciably high quantity of organic matter that can generate hydrocarbon. Ranges of Hydrogen Index (HI) and Genetic Potential (GP) for the coals, shales and mudstones are 167 to 327 mg/g and 114.99 to 159.54 mg/g, 50 to 288 mg/g and 2.85 to 15.66 mg/g TOC, 41 to 239 mg/g and 0.54 to 10.96 mg/g respectively. Tmax and Calculated vitrinite reflectance (% Ro) of sediments range from 412 to 432 oC and 0.26 to 0.62 respectively. The Rock-eval data suggested poor to very good source rocks in the sediments, with the shales as good source rocks, the mudstones as poor to good source rocks and the coals as very good source rocks. The predominant organic matter types in the sediments are kerogen type II/III and type III which are oil and gas prone. The coals are dominated by kerogen type II/III while the shales and mudstones are dominated by kerogen type III. Thermal maturity from Rock-eval data indicated that the sediments are immature with respect to hydrocarbon generation and generally at low level conversion. The coals and the associated shales and mudstones of Mamu Formation are therefore capable of generating oil and gas at appropriate maturity. Keywords: Mamu Formation, Coals, Shales, Mudstones, Hydrocarbon generation, Kerogen, Thermal maturit

Bubble kinematics in a sheared foam

We characterize the kinematics of bubbles in a sheared two-dimensional foam using statistical measures. We consider the distributions of both bubble velocities and displacements. The results are discussed in the context of the expected behavior for a thermal system and simulations of the bubble model. There is general agreement between the experiments and the simulation, but notable differences in the velocity distributions point to interesting elements of the sheared foam not captured by prevalent models

An Optimal Linear Time Algorithm for Quasi-Monotonic Segmentation

Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting a sequence in up to K segments. We want segments to be as monotonic as possible and to alternate signs. We propose a quality metric for this problem using the l_inf norm, and we present an optimal linear time algorithm based on novel formalism. Moreover, given a precomputation in time O(n log n) consisting of a labeling of all extrema, we compute any optimal segmentation in constant time. We compare experimentally its performance to two piecewise linear segmentation heuristics (top-down and bottom-up). We show that our algorithm is faster and more accurate. Applications include pattern recognition and qualitative modeling.Comment: This is the extended version of our ICDM'05 paper (arXiv:cs/0702142

Drying of Beulah-Zap Lignite

Lignite dried in a stream of dry nitrogen at moderate temperatures (20-80-degrees-C) loses water in two distinguishable modes. The first mode represents about 80-85% of the loss of moisture. The second represents the other 15-20% lost under these conditions. The rate follows a unimolecular mechanism (like radioactive decay) for each mode. The activation energy for the first mode is close to the heat of vaporization of water. The rate is dependent upon the gas flow around the sample and the weight (or thickness) of the sample. Work at Amoco Oil Company indicated that the oil yield was higher for the dried coal than for raw or partly dried lignite. Work at Southern Illinois University showed that the mechanism was the same when differential scanning calorimetry was used to follow the kinetics of drying. Other work at the University of Southern Mississippi showed that the physical structure of the lignite (measured by X-rav diffraction) is measurably different for the dried and raw materials