Localizing the relativistic electron

A causally well-behaved solution of the localization problem for the free electron is given, with natural space-time transformation properties, in terms of Dirac's position operator x. It is shown that, although x is not an observable in the usual sense, and has no positive-energy (generalized) eigenstates, the four-vector density (rho(x, t), j(x, t)/c) is observable, and can be localized arbitrarily precisely about any point in space, at any instant of time, using only positive energy states. A suitable spin operator can be diagonalized at the same time.

Flow regime, hydrodynamics, floc size distribution and sludge properties in activated sludge bubble column, air-lift and aerated stirred reactors

This paper presents a comparative study how reactor configuration, sludge loading and air flowrate affect flow regimes, hydrodynamics, floc size distribution and sludge solids-liquid separation properties. Three reactor configurations were studied in bench scale activated sludge bubble column reactor (BCR), air-lift reactor (ALR) and aerated stirred reactor (ASR). The ASR demonstrated the highest capacity of gas holdup and resistance, and homogeneity in flow regimes and shearing forces, resulting in producing large numbers of small and compact floes. The fluid dynamics in the ALR created regularly directed recirculation forces to enhance the gas holdup and sludge flocculation. The BCR distributed a high turbulent flow regime and non-homogeneity in gas holdup and mixing, and generated large numbers of larger and looser floes. The sludge size distributions, compressibility and settleability were significantly influenced by the reactor configurations associated with the flow regimes and hydrodynamics.

Hydrodynamics and mass transfer coefficient in activated sludge aerated stirred column reactor: Experimental analysis and modeling

The aerated stirred reactor (ASR) has been widely used in biochemical and wastewater treatment processes. The information describing how the activated sludge properties and operation conditions affect the hydrodynamics and mass transfer coefficient is missing in the literature. The aim of this study was to investigate the influence of flow regime, superficial gas velocity (U-G), power consumption unit (P/V-L), sludge loading, and apparent viscosity (pap) of activated sludge fluid on the mixing time (t(m)), gas hold-up (epsilon), and volumetric mass transfer coefficient (kLa) in an activated sludge aerated stirred column reactor (ASCR). The activated sludge fluid performed a non-Newtonian rheological behavior. The sludge loading significantly affected the fluid hydrodynamics and mass transfer. With an increase in the UG and P/V-L, the epsilon and k(L)a increased, and the t(m), decreased. The E, kLa, and tm,were influenced dramatically as the flow regime changed from homogeneous to heterogeneous patterns. The proposed mathematical models predicted the experimental results well under experimental conditions, indicating that the U-G, P/V-L, and mu(ap) had significant impact on the t(m) epsilon, and k(L)a. These models were able to give the tm, F, and kLa values with an error around +/- 8%, and always less than +/- 10%. (c) 2005 Wiley Periodicals, Inc.

General foundation for the nonlinear ponderomotive four-force in laser-plasma interactions

The interaction of electromagnetic radiation with plasmas is studied in relativistic four-vector formalism. A gauge and Lorentz invariant ponderomotive four-force is derived from the time dependent nonlinear three-force of Hora (1985). This four-force, due to its Lorentz invariance, contains new magnetic field terms. A new gauge and Lorentz invariant model of the response of plasma to electromagnetic radiation is then devised. An expression for the dispersion relation is obtained from this model. It is then proved that the magnetic permeability of plasma is unity for a general reference frame. This is an important result since it has been previously assumed in many plasma models.

Hydrodynamics and mass transfer coefficient in three-phase air-lift reactors containing activated sludge

This study was to investigate the impacts of operating conditions and liquid properties on the hydrodynamics and volumetric mass transfer coefficient in activated sludge air-lift reactors. Experiments were conducted in internal and external air-lift reactors. The activated sludge liquid displayed a non-Newtonian rheological behavior. With an increase in the superficial gas velocity, the liquid circulation velocity, gas holdup and mass transfer coefficient increased, and the gas residence time decreased. The liquid circulation velocity, gas holdup and the mass transfer coefficient decreased as the sludge loading increased. The flow regime in the activated sludge air-lift reactors had significant effect on the liquid circulation velocity and the gas holdup, but appeared to have little impact on the mass transfer coefficient. The experimental results in this study were best described by the empirical models, in which the reactor geometry, superficial gas velocity and/or power consumption unit, and solid and fluid properties were employed. (c) 2006 Elsevier B.V. All rights reserved.

Explicit derivation of the relativistic mass-energy relation for internal kinetic and potential energies of a composite system

A straightforward derivation of relativistic expressions for the mechanical momentum, kinetic and total energies, and mass-energy equivalence (including potential energy) which does not require any knowledge of the energy-momentum relation for electromagnetic waves or consideration of elastic collisions, but is directly based on Newton's second law and Lorentz's transformations, is presented in this paper. The existence of an invariant force is shown to be important for the validity of the relativistic mechanics.

Geodesics without differential equations: general relativistic calculations for introductory modern physics classes

Introductory courses covering modem physics sometimes introduce some elementary ideas from general relativity, though the idea of a geodesic is generally limited to shortest Euclidean length on a curved surface of two spatial dimensions rather than extremal aging in spacetime. It is shown that Epstein charts provide a simple geometric picture of geodesics in one space and one time dimension and that for a hypothetical uniform gravitational field, geodesics are straight lines on a planar diagram. This means that the properties of geodesics in a uniform field can be calculated with only a knowledge of elementary geometry and trigonometry, thus making the calculation of some basic results of general relativity accessible to students even in an algebra-based survey course on physics.

Two dimensional computational fluid dynamic models for waste stabilisation ponds

Traditional waste stabilisation pond (WSP) models encounter problems predicting pond performance because they cannot account for the influence of pond features, such as inlet structure or pond geometry, on fluid hydrodynamics. In this study, two dimensional (2-D) computational fluid dynamics (CFD) models were compared to experimental residence time distributions (RTD) from literature. In one of the-three geometries simulated, the 2-D CFD model successfully predicted the experimental RTD. However, flow patterns in the other two geometries were not well described due to the difficulty of representing the three dimensional (3-D) experimental inlet in the 2-D CFD model, and the sensitivity of the model results to the assumptions used to characterise the inlet. Neither a velocity similarity nor geometric similarity approach to inlet representation in 2-D gave results correlating with experimental data. However. it was shown that 2-D CFD models were not affected by changes in values of model parameters which are difficult to predict, particularly the turbulent inlet conditions. This work suggests that 2-D CFD models cannot be used a priori to give an adequate description of the hydrodynamic patterns in WSP. (C) 1998 Elsevier Science Ltd. All rights reserved.

A new formation model for M32: a threshed early-type spiral galaxy?

The origin of M32, the closest compact elliptical galaxy (cE), is a long-standing puzzle of galaxy fort-nation in the Local Group. Our N-body/smoothed particle hydrodynamics simulations suggest a new scenario in which the strong tidal field of M31 can transform a spiral galaxy into a compact elliptical galaxy. As a low-luminosity spiral galaxy plunges into the central region of M31, most of the outer stellar and gaseous components of its disk are dramatically stripped as a result of M31's tidal field. The central bulge component, on the other hand, is just weakly influenced by the tidal field, owing to its compact configuration, and retains its morphology. M31's strong tidal field also induces rapid gas transfer to the central region, triggers a nuclear starburst, and consequently forms the central high-density and more metal-rich stellar populations with relatively young ages. Thus, in this scenario, M32 was previously the bulge of a spiral galaxy tidally interacting with M31 several gigayears ago. Furthermore, we suggest that cE's like M32 are rare, the result of both the rather narrow parameter space for tidal interactions that morphologically transform spiral galaxies into cE's and the very short timescale (less than a few times 10(9) yr) for cE's to be swallowed by their giant host galaxies (via dynamical friction) after their formation.

On entanglement and Lorentz transformations

We study the transformation of maximally entangled states under the action of Lorentz transformations in a fully relativistic setting. By explicit calculation of the Wigner rotation, we describe the relativistic analog of the Bell states as viewed from two inertial frames moving with constant velocity with respect to each other. Though the finite dimensional matrices describing the Lorentz transformations are non-unitary, each single particle state of the entangled pair undergoes an effective, momentum dependent, local unitary rotation, thereby preserving the entanglement fidelity of the bipartite state. The details of how these unitary transformations are manifested are explicitly worked out for the Bell states comprised of massive spin 1/2 particles and massless photon polarizations. The relevance of this work to non-inertial frames is briefly discussed.

Surface foam film waves studied with high-speed linescan camera

Dynamic foam films have been investigated using an improved experimental set-up with a CCD high-speed linescan camera in conjunction with the Scheludko micro-interferometric cell for studying the drainage and rupture of liquid foam films. The improved experimental set-up increased the sensibility of detection of the local thickness heterogeneities and domains during the film evolution. The evolution of the foam films up to the formation of black spots was recorded in the time intervals of 50ms. The wavelengths of the propagating surface waves and their frequencies were determined experimentally. The experimental results show that the current quasi-static hydrodynamic theory does not properly describe the wave dynamics with inter-domain channels. However, the thermodynamic condition for formation of black spots in the foam films was met by the experimental results. (c) 2005 Elsevier B.V. All rights reserved.

Tidal influence on behaviour of a coastal aquifer adjacent to a low-relief estuary

The tidal influence on groundwater hydrodynamics, salt-water intrusion and submarine groundwater discharge from coastal/estuarine aquifers is poorly quantified for systems with a mildly sloping beach, in contrast to the case where a vertical beach face is assumed. We investigated the effect of beach slope for a coastal aquifer adjacent to a low-relief estuary, where industrial waste was emplaced over the aquifer. The waste was suspected to discharge leachate towards the estuary. Field observations at various locations showed that tidally induced groundwater head fluctuations were skewed temporally. Frequency analysis suggested that the fluctuation amplitudes decreased exponentially and the phase-tags increased Linearly for the primary tidal signals as they propagated inland. Salinisation zones were observed in the bottom part of the estuary and near the beach surface. Flow and transport processes in a cross-section perpendicular to the estuary were simulated using SEAWAT-2000, which is capable of depicting density-dependent flow and multi-species transport. The simulations showed that the modelled water table fluctuations were in good agreement with the monitored data. Further simulations were conducted to gain insight into the effects of beach slope. In particular the limiting case of a vertical beach face was considered. The simulations showed that density difference and tidal forcing drive a more complex hydrodynamic pattern for the mildly sloping beach than the vertical beach, as well as a profound asymmetry in tidally induced water table fluctuations and enhanced salt-water intrusion. The simulation results also indicated that contaminant transport from the aquifer to the estuary was affected by the tide, where for the mildly sloping beach, the tide tended to intensify the vertical mass exchange in the vicinity of the shorelines, (c) 2005 Elsevier B.V. All rights reserved.

Causal and localizable quantum operations

We examine constraints on quantum operations imposed by relativistic causality. A bipartite superoperator is said to be localizable if it can be implemented by two parties (Alice and Bob) who share entanglement but do not communicate, it is causal if the superoperator does not convey information from Alice to Bob or from Bob to Alice. We characterize the general structure of causal complete-measurement superoperators, and exhibit examples that are causal but not localizable. We construct another class of causal bipartite superoperators that are not localizable by invoking bounds on the strength of correlations among the parts of a quantum system. A bipartite superoperator is said to be semilocalizable if it can be implemented with one-way quantum communication from Alice to Bob, and it is semicausal if it conveys no information from Bob to Alice. We show that all semicausal complete-measurement superoperators are semi localizable, and we establish a general criterion for semicausality. In the multipartite case, we observe that a measurement superoperator that projects onto the eigenspaces of a stabilizer code is localizable.