Interaccion among systems of finite size in predictive relativistic mechanics -II. Electromagnetic and gravitational interactions

We explicitly construct a closed system of differential equations describing the electromagnetic and gravitational interactions among bodies to first order in the coupling constants, retaining terms up to order c-2. The Breit and Barker and O'Connell Hamiltonians are recovered by means of a coordinate transformation. The method used throws light on the meaning of these coordinates.

Interactions among systems of finite size en predictive relativistic mechanics III. Short-range interaction and second-order terms

We compute up to and including all the c-2 terms in the dynamical equations for extended bodies interacting through electromagnetic, gravitational, or short-range fields. We show that these equations can be reduced to those of point particles with intrinsic angular momentum assuming spherical symmetry.

Classical cross sections for relativistic spinning particles

We propose a definition of classical differential cross sections for particles with essentially nonplanar orbits, such as spinning ones. We give also a method for its computation. The calculations are carried out explicitly for electromagnetic, gravitational, and short-range scalar interactions up to the linear terms in the slow-motion approximation. The contribution of the spin-spin terms is found to be at best 10-6 times the post-Newtonian ones for the gravitational interaction.

Discretized integral hydrodynamics

Using an interpolant form for the gradient of a function of position, we write an integral version of the conservation equations for a fluid. In the appropriate limit, these become the usual conservation laws of mass, momentum, and energy. We also discuss the special cases of the Navier-Stokes equations for viscous flow and the Fourier law for thermal conduction in the presence of hydrodynamic fluctuations. By means of a discretization procedure, we show how the integral equations can give rise to the so-called particle dynamics of smoothed particle hydrodynamics and dissipative particle dynamics.

Modelling hydrodynamics in the Rio Parana, Argentina : an evaluation and inter-comparison of reduced-complexity and physics based models applied to a large sand-bed river

Depth-averaged velocities and unit discharges within a 30 km reach of one of the world's largest rivers, the Rio Parana, Argentina, were simulated using three hydrodynamic models with different process representations: a reduced complexity (RC) model that neglects most of the physics governing fluid flow, a two-dimensional model based on the shallow water equations, and a three-dimensional model based on the Reynolds-averaged Navier-Stokes equations. Row characteristics simulated using all three models were compared with data obtained by acoustic Doppler current profiler surveys at four cross sections within the study reach. This analysis demonstrates that, surprisingly, the performance of the RC model is generally equal to, and in some instances better than, that of the physics based models in terms of the statistical agreement between simulated and measured flow properties. In addition, in contrast to previous applications of RC models, the present study demonstrates that the RC model can successfully predict measured flow velocities. The strong performance of the RC model reflects, in part, the simplicity of the depth-averaged mean flow patterns within the study reach and the dominant role of channel-scale topographic features in controlling the flow dynamics. Moreover, the very low water surface slopes that typify large sand-bed rivers enable flow depths to be estimated reliably in the RC model using a simple fixed-lid planar water surface approximation. This approach overcomes a major problem encountered in the application of RC models in environments characterised by shallow flows and steep bed gradients. The RC model is four orders of magnitude faster than the physics based models when performing steady-state hydrodynamic calculations. However, the iterative nature of the RC model calculations implies a reduction in computational efficiency relative to some other RC models. A further implication of this is that, if used to simulate channel morphodynamics, the present RC model may offer only a marginal advantage in terms of computational efficiency over approaches based on the shallow water equations. These observations illustrate the trade off between model realism and efficiency that is a key consideration in RC modelling. Moreover, this outcome highlights a need to rethink the use of RC morphodynamic models in fluvial geomorphology and to move away from existing grid-based approaches, such as the popular cellular automata (CA) models, that remain essentially reductionist in nature. In the case of the world's largest sand-bed rivers, this might be achieved by implementing the RC model outlined here as one element within a hierarchical modelling framework that would enable computationally efficient simulation of the morphodynamics of large rivers over millennial time scales. (C) 2012 Elsevier B.V. All rights reserved.

Dynamical sectors of a relativistic two particle model

We reconsider a model of two relativistic particles interacting via a multiplicative potential, as an example of a simple dynamical system with sectors, or branches, with different dynamics and degrees of freedom. The presence or absence of sectors depends on the values of rest masses. Some aspects of the canonical quantization are described. The model could be interpreted as a bigravity model in one dimension.

Nuclear surface properties in relativistic effective field theory

We perform Hartree calculations of symmetric and asymmetric semi-infinite nuclear matter in the framework of relativistic models based on effective hadronic field theories as recently proposed in the literature. In addition to the conventional cubic and quartic scalar self-interactions, the extended models incorporate a quartic vector self-interaction, scalar-vector non-linearities and tensor couplings of the vector mesons. We investigate the implications of these terms on nuclear surface properties such as the surface energy coefficient, surface thickness, surface stiffness coefficient, neutron skin thickness and the spin-orbit force.

Giant monopole energies from a constrained relativistic mean-field approach

Background:Average energies of nuclear collective modes may be efficiently and accurately computed using a nonrelativistic constrained approach without reliance on a random phase approximation (RPA). Purpose: To extend the constrained approach to the relativistic domain and to establish its impact on the calibration of energy density functionals. Methods: Relativistic RPA calculations of the giant monopole resonance (GMR) are compared against the predictions of the corresponding constrained approach using two accurately calibrated energy density functionals. Results: We find excellent agreement at the 2% level or better between the predictions of the relativistic RPA and the corresponding constrained approach for magic (or semimagic) nuclei ranging from 16 O to 208 Pb. Conclusions: An efficient and accurate method is proposed for incorporating nuclear collective excitations into the calibration of future energy density functionals.

Hydrodynamics and Heat Transfer in an Airlift Reactor

Työn teoriaosassa esitetään kirjallisuudessa esiintyviä teoreettisia ja kokeellisia yhtälöitä nesteen nopeuden, kaasun tilavuusosuuden, painehäviön ja lämmönsiirron laskemiseksi. Lisäksi käsitellään airlift-reaktoreiden toimintaa, rakennetta ja teollisia sovelluksia, sekä sekoitusta ja geometrian vaikutusta airlift-reaktoreiden hydrodynaamisiin ominaisuuksiin. Kokeellisessa osassa kuvataan käytetty koelaitteisto ja mittausmenetelmät sekä esitetään saadut koetulokset. Koelaitteisto on viidellä nousuputkella varustettu ulkoisen kierron airlift-reaktori. Kokeellisessa osassa pyritään ratkaisemaan tällaisessa reaktorissa mahdollisesti esiintyviä ongelmia, kuten "slug flown" muodostuminen nousuputkissa sekä fluidien epätasainen jakautuminen nousuputkiin. Lisäksi tutkitaan erilaisten muuttujien, kuten kaasun tilavuusvirran, nesteen viskositeetin, suutinkoon ja nesteen jakoputken rakenteen, vaikutusta kaasun tilavuusosuuteen ja nesteen nopeuteen nousuputkissa. Nesteen nopeudet mitataan merkkiainemenetelmällä ja kaasun tilavuusosuudet manometrimenetelmällä. Lämmönsiirtoa tutkitaan mittaamalla lämpötilaeroja nousuputkissa NiCr-Ni –termoelementeillä. Mittaustulosten perusteella muokataan korrelaatiot kaasun tilavuusosuudelle ja nesteen tyhjäputkinopeudelle. Korrelaatioista lasketut tulokset sopivat kohtuullisen hyvin yhteen mitattujen tulosten kanssa. "Slug flown" ei todettu muodostuvan ongelmaksi 2.5 mPa s pienemmillä viskositeetin arvoilla 2 metriä pitkissä ja 19 mm halkaisijaltaan olevissa putkissa. Lisäksi todettiin, että kaasu- ja nestefaasien jakautumisongelmat voidaan ratkaista rakenteellisesti.

Current Sheet Regulation of Solar Near-relativistic Electron Injection Histories

We present a sample of three large near-relativistic (>50 keV) electron events observed in 2001 by both the ACE and the Ulysses spacecraft, when Ulysses was at high-northern latitudes (>60◦) and close to 2 AU. Despite the large latitudinal distance between the two spacecraft, electrons injected near the Sun reached both heliospheric locations. All three events were associated with large solar flares, strong decametric type II radio bursts and accompanied by wide (>212◦) and fast (>1400 km s−1) coronal mass ejections (CMEs). We use advanced interplanetary transport simulations and make use of the directional intensities observed in situ by the spacecraft to infer the electron injection profile close to the Sun and the interplanetary transport conditions at both low and high latitudes. For the three selected events, we find similar interplanetary transport conditions at different heliolatitudes for a given event, with values of the mean free path ranging from 0.04 AU to 0.27 AU. We find differences in the injection profiles inferred for each spacecraft. We investigate the role that sector boundaries of the heliospheric current sheet (HCS) have on determining the characteristics of the electron injection profiles. Extended injection profiles, associated with coronal shocks, are found if the magnetic footpoints of the spacecraft lay in the same magnetic sector as the associated flare, while intermittent sparse injection episodes appear when the spacecraft footpoints are in the opposite sector or a wrap in the HCS bounded the CME structure.

Current Sheet Regulation of Solar Near-Relativistic Electron Injection Histories

We present a sample of three large near-relativistic (>50 keV) electron events observed in 2001 by both the ACE and the Ulysses spacecraft, when Ulysses was at high-northern latitudes (>60°) and close to 2 AU. Despite the large latitudinal distance between the two spacecraft, electrons injected near the Sun reached both heliospheric locations. All three events were associated with large solar flares, strong decametric type II radio bursts and accompanied by wide (>212°) and fast (>1400 km s-1) coronal mass ejections (CMEs). We use advanced interplanetary transport simulations and make use of the directional intensities observed in situ by the spacecraft to infer the electron injection profile close to the Sun and the interplanetary transport conditions at both low and high latitudes. For the three selected events, we find similar interplanetary transport conditions at different heliolatitudes for a given event, with values of the mean free path ranging from 0.04 AU to 0.27 AU. We find differences in the injection profiles inferred for each spacecraft. We investigate the role that sector boundaries of the heliospheric current sheet (HCS) have on determining the characteristics of the electron injection profiles. Extended injection profiles, associated with coronal shocks, are found if the magnetic footpoints of the spacecraft lay in the same magnetic sector as the associated flare, while intermittent sparse injection episodes appear when the spacecraft footpoints are in the opposite sector or a wrap in the HCS bounded the CME structure.

Hints for a fast precessing relativistic radio jet in LS I + 61° 303

Here we discuss two consecutive MERLIN observations of the X-ray binary LS I +61° 303 . The first observation shows a double-sided jet extending up to about 200 AU on both sides of a central source. The jet shows a bent S-shaped structure similar to the one displayed by the well-known precessing jet of SS 433 . The precession suggested in the first MERLIN image becomes evident in the second one, showing a one-sided bent jet significantly rotated with respect to the jet of the day before. We conclude that the derived precession of the relativistic (beta=0.6) jet explains puzzling previous VLBI results. Moreover, the fact that the precession is fast could be the explanation of the never understood short term (days) variability of the associated gamma-ray source 2CG 135+01 / 3EG J0241+6103

Effect of hydrodynamics on modelling, monitoring and control of crystallization

Crystallization is a purification method used to obtain crystalline product of a certain crystal size. It is one of the oldest industrial unit processes and commonly used in modern industry due to its good purification capability from rather impure solutions with reasonably low energy consumption. However, the process is extremely challenging to model and control because it involves inhomogeneous mixing and many simultaneous phenomena such as nucleation, crystal growth and agglomeration. All these phenomena are dependent on supersaturation, i.e. the difference between actual liquid phase concentration and solubility. Homogeneous mass and heat transfer in the crystallizer would greatly simplify modelling and control of crystallization processes, such conditions are, however, not the reality, especially in industrial scale processes. Consequently, the hydrodynamics of crystallizers, i.e. the combination of mixing, feed and product removal flows, and recycling of the suspension, needs to be thoroughly investigated. Understanding of hydrodynamics is important in crystallization, especially inlargerscale equipment where uniform flow conditions are difficult to attain. It is also important to understand different size scales of mixing; micro-, meso- and macromixing. Fast processes, like nucleation and chemical reactions, are typically highly dependent on micro- and mesomixing but macromixing, which equalizes the concentrations of all the species within the entire crystallizer, cannot be disregarded. This study investigates the influence of hydrodynamics on crystallization processes. Modelling of crystallizers with the mixed suspension mixed product removal (MSMPR) theory (ideal mixing), computational fluid dynamics (CFD), and a compartmental multiblock model is compared. The importance of proper verification of CFD and multiblock models is demonstrated. In addition, the influence of different hydrodynamic conditions on reactive crystallization process control is studied. Finally, the effect of extreme local supersaturation is studied using power ultrasound to initiate nucleation. The present work shows that mixing and chemical feeding conditions clearly affect induction time and cluster formation, nucleation, growth kinetics, and agglomeration. Consequently, the properties of crystalline end products, e.g. crystal size and crystal habit, can be influenced by management of mixing and feeding conditions. Impurities may have varying impacts on crystallization processes. As an example, manganese ions were shown to replace magnesium ions in the crystal lattice of magnesium sulphate heptahydrate, increasing the crystal growth rate significantly, whereas sodium ions showed no interaction at all. Modelling of continuous crystallization based on MSMPR theory showed that the model is feasible in a small laboratoryscale crystallizer, whereas in larger pilot- and industrial-scale crystallizers hydrodynamic effects should be taken into account. For that reason, CFD and multiblock modelling are shown to be effective tools for modelling crystallization with inhomogeneous mixing. The present work shows also that selection of the measurement point, or points in the case of multiprobe systems, is crucial when process analytical technology (PAT) is used to control larger scale crystallization. The thesis concludes by describing how control of local supersaturation by highly localized ultrasound was successfully applied to induce nucleation and to control polymorphism in reactive crystallization of L-glutamic acid.

Hydrodynamics Characteristics and Gas-Liquid Mass Transfer in a Three Phase Fluidized Bed Reactor

This paper presents the experimental characterization of hydrodynamics and gas-liquid mass transfer in a three-phase fluidized bed containing polystyrene and nylon particles. The influence of gas and liquid velocities on phase holdups and volumetric gas-liquid mass transfer coefficient was investigated for flow conditions similar to those applied in biotechnological process. The phase holdups were obtained by the pressure profile technique. The volumetric gas-liquid mass transfer coefficient was obtained adjusting the experimental concentration profiles of dissolved oxygen in the liquid phase with the predictions of the axial dispersion model. According to experimental results the liquid holdup increases with the gas velocity, whereas the solid holdup decreases. The gas holdup increases significantly with the increase in gas velocity, and it shows for the three-phase fluidized bed comparable values or larger than those of bubble column. The volumetric gas-liquid mass transfer coefficient increases significantly with an increase in the air velocity for both bubble column and fluidized beds. In addition, in the operational condition of high liquid velocity, the presence of low-density particles in the bed increased the gas-liquid mass transfer, and thus the volumetric mass transfer coefficient values obtained in the fluidized bed were comparable or larger than those of bubble column.