Solvable model for distribution networks on random graphs

We propose a simple model that captures the salient properties of distribution networks, and study the possible occurrence of blackouts, i.e., sudden failings of large portions of such networks. The model is defined on a random graph of finite connectivity. The nodes of the graph represent hubs of the network, while the edges of the graph represent the links of the distribution network. Both, the nodes and the edges carry dynamical two state variables representing the functioning or dysfunctional state of the node or link in question. We describe a dynamical process in which the breakdown of a link or node is triggered when the level of maintenance it receives falls below a given threshold. This form of dynamics can lead to situations of catastrophic breakdown, if levels of maintenance are themselves dependent on the functioning of the net, once maintenance levels locally fall below a critical threshold due to fluctuations. We formulate conditions under which such systems can be analyzed in terms of thermodynamic equilibrium techniques, and under these conditions derive a phase diagram characterizing the collective behavior of the system, given its model parameters. The phase diagram is confirmed qualitatively and quantitatively by simulations on explicit realizations of the graph, thus confirming the validity of our approach. © 2007 The American Physical Society.

The characterisation and optimisation of modified herbaceous grasses for identifying pyrolisis-oil quality traits

The primary objective of this work is to relate the biomass fuel quality to fast pyrolysis-oil quality in order to identify key biomass traits which affect pyrolysis-oil stability. During storage the pyrolysis-oil becomes more viscous due to chemical and physical changes, as reactions and volatile losses occur due to aging. The reason for oil instability begins within the pyrolysis reactor during pyrolysis in which the biomass is rapidly heated in the absence of oxygen, producing free radical volatiles which are then quickly condensed to form the oil. The products formed do not reach thermodynamic equilibrium and in tum the products react with each other to try to achieve product stability. The first aim of this research was to develop and validate a rapid screening method for determining biomass lignin content in comparison to traditional, time consuming and hence costly wet chemical methods such as Klason. Lolium and Festuca grasses were selected to validate the screening method, as these grass genotypes exhibit a low range of Klason /Acid Digestible Fibre lignin contents. The screening methodology was based on the relationship between the lignin derived products from pyrolysis and the lignin content as determined by wet chemistry. The second aim of the research was to determine whether metals have an affect on fast pyrolysis products, and if any clear relationships can be deduced to aid research in feedstock selection for fast pyrolysis processing. It was found that alkali metals, particularly Na and K influence the rate and yield of degradation as well the char content. Pre-washing biomass with water can remove 70% of the total metals, and improve the pyrolysis product characteristics by increasing the organic yield, the temperature in which maximum liquid yield occurs and the proportion of higher molecular weight compounds within the pyrolysis-oil. The third aim identified these feedstock traits and relates them to the pyrolysis-oil quality and stability. It was found that the mineral matter was a key determinant on pyrolysis-oil yield compared to the proportion of lignin. However the higher molecular weight compounds present in the pyrolysis-oil are due to the lignin, and can cause instability within the pyrolysis-oil. The final aim was to investigate if energy crops can be enhanced by agronomical practices to produce a biomass quality which is attractive to the biomass conversion community, as well as giving a good yield to the farmers. It was found that the nitrogen/potassium chloride fertiliser treatments enhances Miscanthus qualities, by producing low ash, high volatiles yields with acceptable yields for farmers. The progress of senescence was measured in terms of biomass characteristics and fast pyrolysis product characteristics. The results obtained from this research are in strong agreement with published literature, and provides new information on quality traits for biomass which affects pyrolysis and pyrolysis-oils.

The laminar-turbulent transition in a fibre laser

Studying the transition from a linearly stable coherent laminar state to a highly disordered state of turbulence is conceptually and technically challenging, and of great interest because all pipe and channel flows are of that type. In optics, understanding how a system loses coherence, as spatial size or the strength of excitation increases, is a fundamental problem of practical importance. Here, we report our studies of a fibre laser that operates in both laminar and turbulent regimes. We show that the laminar phase is analogous to a one-dimensional coherent condensate and the onset of turbulence is due to the loss of spatial coherence. Our investigations suggest that the laminar-turbulent transition in the laser is due to condensate destruction by clustering dark and grey solitons. This finding could prove valuable for the design of coherent optical devices as well as systems operating far from thermodynamic equilibrium. © 2013 Macmillan Publishers Limited.

Characterization of design and economic sensitivity of vapor phase carbon adsorption systems to environmental uncertainties

Vapor phase carbon adsorption systems are used to remove aromatics, aliphatics, and halogenated hydrocarbons. The adsorption capacity of granular activated carbon is reduced when environmental parameters (temperature, pressure, and humidity) interfere with homogeneous surface diffusion and pore distribution dynamics. The purpose of this study was to investigate the effects of parametric uncertainties in adsorption efficiency. ^ Modified versions of the Langmuir isotherm in conjunction with thermodynamic equations described gaseous adsorption of single component influent onto microporous media. Experimental test results derived from Wang et al. (1999) simulated adsorption kinetics while the Myer and monsoon Langmuir constant accounted for isothermal gas compression and energetic heterogeneity under thermodynamic equilibrium conditions. Responsiveness of adsorption capacity to environmental uncertainties was analyzed by statistical sensitivity and modeled by breakthrough curves. Results indicated that extensive fluctuations in adsorption capacity significantly reduced carbon consumption while isothermal variations had a pronounced effect on saturation capacity. ^

Dynamics of spatial heterogeneity in a landfill with interacting phase densities:a stochastic analysis

A landfill represents a complex and dynamically evolving structure that can be stochastically perturbed by exogenous factors. Both thermodynamic (equilibrium) and time varying (non-steady state) properties of a landfill are affected by spatially heterogenous and nonlinear subprocesses that combine with constraining initial and boundary conditions arising from the associated surroundings. While multiple approaches have been made to model landfill statistics by incorporating spatially dependent parameters on the one hand (data based approach) and continuum dynamical mass-balance equations on the other (equation based modelling), practically no attempt has been made to amalgamate these two approaches while also incorporating inherent stochastically induced fluctuations affecting the process overall. In this article, we will implement a minimalist scheme of modelling the time evolution of a realistic three dimensional landfill through a reaction-diffusion based approach, focusing on the coupled interactions of four key variables - solid mass density, hydrolysed mass density, acetogenic mass density and methanogenic mass density, that themselves are stochastically affected by fluctuations, coupled with diffusive relaxation of the individual densities, in ambient surroundings. Our results indicate that close to the linearly stable limit, the large time steady state properties, arising out of a series of complex coupled interactions between the stochastically driven variables, are scarcely affected by the biochemical growth-decay statistics. Our results clearly show that an equilibrium landfill structure is primarily determined by the solid and hydrolysed mass densities only rendering the other variables as statistically "irrelevant" in this (large time) asymptotic limit. The other major implication of incorporation of stochasticity in the landfill evolution dynamics is in the hugely reduced production times of the plants that are now approximately 20-30 years instead of the previous deterministic model predictions of 50 years and above. The predictions from this stochastic model are in conformity with available experimental observations.

Combined Conduction-Convection-Radiation Heat Transfer of Slip Flow inside a Micro-channel Filled with a Cellular Porous Material

Combined conduction–convection–radiation heat transfer is investigated numerically in a micro-channel filled with a saturated cellular porous medium, with the channel walls held at a constant heat flux. Invoking the velocity slip and temperature jump, the thermal behaviour of the porous–fluid system are studied by considering hydrodynamically fully developed flow and applying the Darcy–Brinkman flow model. One energy equation model based on the local thermal equilibrium condition is adopted to evaluate the temperature field within the porous medium. Combined conduction and radiation heat transfer is treated as an effective conduction process with a temperature-dependent effective thermal conductivity. Results are reported in terms of the average Nusselt number and dimensionless temperature distribution, as a function of velocity slip coefficient, temperature jump coefficient, porous medium shape parameter and radiation parameters. Results show that increasing the radiation parameter (Tr)(Tr) and the temperature jump coefficient flattens the dimensionless temperature profile. The Nusselt numbers are more sensitive to the variation in the temperature jump coefficient rather than to the velocity slip coefficient. Such that for high porous medium shape parameter, the Nusselt number is found to be independent of velocity slip. Furthermore, it is found that as the temperature jump coefficient increases, the Nusselt number decrease. In addition, for high temperature jump coefficients, the Nusselt number is found to be insensitive to the radiation parameters and porous medium shape parameter. It is also concluded that compared with the conventional macro-channels, wherein using a porous material enhances the rate of heat transfer (up to about 40 % compared to the clear channel), insertion of a porous material inside a micro-channel in slip regime does not effectively enhance the rate of heat transfer that is about 2 %.

Methane Clathrates in the Solar System

We review the reservoirs of methane clathrates that may exist in the different bodies of the Solar System. Methane was formed in the interstellar medium prior to having been embedded in the protosolar nebula gas phase. This molecule was subsequently trapped in clathrates that formed from crystalline water ice during the cooling of the disk and incorporated in this form into the building blocks of comets, icy bodies, and giant planets. Methane clathrates may play an important role in the evolution of planetary atmospheres. On Earth, the production of methane in clathrates is essentially biological, and these compounds are mostly found in permafrost regions or in the sediments of continental shelves. On Mars, methane would more likely derive from hydrothermal reactions with olivine-rich material. If they do exist, martian methane clathrates would be stable only at depth in the cryosphere and sporadically release some methane into the atmosphere via mechanisms that remain to be determined. In the case of Titan, most of its methane probably originates from the protosolar nebula, where it would have been trapped in the clathrates agglomerated by the satellite's building blocks. Methane clathrates are still believed to play an important role in the present state of Titan. Their presence is invoked in the satellite's subsurface as a means of replenishing its atmosphere with methane via outgassing episodes. The internal oceans of Enceladus and Europa also provide appropriate thermodynamic conditions that allow formation of methane clathrates. In turn, these clathrates might influence the composition of these liquid reservoirs. Finally, comets and Kuiper Belt Objects might have formed from the agglomeration of clathrates and pure ices in the nebula. The methane observed in comets would then result from the destabilization of clathrate layers in the nuclei concurrent with their approach to perihelion. Thermodynamic equilibrium calculations show that methane-rich clathrate layers may exist on Pluto as well. Key Words: Methane clathrate-Protosolar nebula-Terrestrial planets-Outer Solar System.

Local equilibrium of the Gibbs interface in two-phase systems

We analyze the local equilibrium assumption for interfaces from the perspective of gauge transformations, which are the small displacements of Gibbs' dividing surface. The gauge invariance of thermodynamic properties turns out to be equivalent to conditions for jumps of bulk densities across the interface. This insight strengthens the foundations of the local equilibrium assumption for interfaces and can be used to characterize nonequilibrium interfaces in a compact and consistent way, with a clear focus on gauge-invariant properties. Using the principle of gauge invariance, we show that the validity of Clapeyron equations can be extended to nonequilibrium interfaces, and an additional jump condition for the momentum density is recognized to be of the Clapeyron type. © 2012 Europhysics Letters Association.

Thermodynamic study of Fe2O3 Fe2(SO4)3 equilibrium using an oxyanionic electrolyte (Na2SO4 I)

The emf of the cell, Pt, Ar + O2 + SO2 + SO3/Na2SO4-I/Fe2O2 + Fe2(SO4)3, Pt, has been measured in the temperature range 800 to 1000 K, using a gas mixture of known input composition as the reference electrode. The equilibrium composition of the reference gas at the measuring temperatures was computed using the thermodynamic data on the gaseous species reported in the literature. A mixture of ferric oxide and sulfate was kept in a closed system to ensure establishment of equilibrium partial pressure at the electrode. The cell was designed to avoid physical contact between Fe2(SO4)3 and Na2SO4 electrolyte. Uncertainties arising from the formation of sulfate solid solution were thus eliminated. The Gibbs’ energy of formation of ferric sulfate calculated from the emf is discussed in comparison with data reported in the literature. There is no evidence for the formation of oxysulfates in the Fe-S-0 system. Based on the results obtained in the present study for Fe2(SO4)3 and literature data for other phases, chemical potential diagrams have been constructed for the Fe-S-O system at 900 and 1100 K.

Reactive interdiffusion: deviation from local equilibrium in the Fe-NiTiO3 couple

Deviation from local equilibrium between Fe–Ni alloy and (Fe,Ni)TiO3 solid solution in the reaction–diffusion zone of the Fe–NiTiO3 couple at 1273 K is evaluated by comparing the measured compositions in the zone with experimentally determined equilibrium tie-lines. The deviation is quantified by computing the Gibbs energy change for the reaction, Fe + NiTiO3 → FeTiO3 + Ni, from measured compositions in the zone and activity data available in the literature. Except near the extremities of the zone, the computed Gibbs energy change is constant, 8.2 kJ mol−1 higher than the standard Gibbs energy change for the reaction.

Phosphorus Adsorption onto an Industrial Acidified Laterite By‒Product: Equilibrium and Thermodynamic Investigation

The present research investigates the uptake of phosphate ions from aqueous solutions using acidified laterite (ALS), a by-product from the production of ferric aluminium sulfate using laterite. Phosphate adsorption experiments were performed in batch systems to determine the amount of phosphate adsorbed as a function of solution pH, adsorbent dosage and thermodynamic parameters per fixed P concentration. Kinetic studies were also carried out to study the effect of adsorbent particle sizes. The maximum removal capacity of ALS observed at pH 5 was 3.68 mg P g^-1. It was found that as the adsorbent dosage increases, the equilibrium pH decreases, so an adsorbent dosage of 1.0 g L^-1 of ALS was selected. Adsorption capacity (q_m) calculated from the Langmuir isotherm was found to be 2.73 mg g^-1. Kinetic experimental data were mathematically well described using the pseudo first-order model over the full range of the adsorbent particle size. The adsorption reactions were endothermic, and the process of adsorption was favoured at high temperature; the ΔG and ΔH values implied that the main adsorption mechanism of P onto ALS is physisorption. The desorption studies indicated the need to consider a NaOH 0.1M solution as an optimal solution for practical regeneration applications.