Notes on higher-dimensional partitions

We show the existence of a series of transforms that capture several structures that underlie higher-dimensional partitions. These transforms lead to a sequence of triangles whose entries are given combinatorial interpretations as the number of particular types of skew Ferrers diagrams. The end result of our analysis is the existence of a triangle, that we denote by F, which implies that the data needed to compute the number of partitions of a given positive integer is reduced by a factor of half. The number of spanning rooted forests appears intriguingly in a family of entries in the triangle F. Using modifications of an algorithm due to Bratley-McKay, we are able to directly enumerate entries in some of the triangles. As a result, we have been able to compute numbers of partitions of positive integers <= 25 in any dimension.Comment: 36 pages; Mathematica file attached; See http://www.physics.iitm.ac.in/~suresh/partitions.html to generate numbers of partition

Multicomponent transport in nanoporous networks: theory and simulation

We present a new theory to estimate fluxes and effective transport conductances of binary mixtures through a membrane comprising a nonuniform porous medium with both pore size and pore length distributions, using the Onsager formulation at the single pore level. The theory defines a conductance of each species that is dependent on the concentration gradients of the various species, and on using effective medium theory determines the fluxes and concentration profiles self-consistently in the porous medium. The transport of CH/H mixtures in a silica membrane having a known pore size distribution is examined using this theory, and the results compared with those from rigorous simulations, showing good agreement. It is found that an optimal network coordination number exists at which species fluxes are a maximum, due to the opposing effects of increasing porosity and mean pore length with increase in coordination number. Further, network fluxes decrease with increase in pore dispersion, indicating that uniform pore size is optimal. A species and pressure-dependent optimal temperature is also predicted, due to the competing effects of increase in diffusivity and decrease in adsorption on increasing temperature. It is seen that the CH selectivity is very sensitive to temperature, and undergoes a cross-over, with the membrane being more selective to CH at low temperature and to H at high temperature. In general, the selectivity is very sensitive to the distribution of pore volume, and for bimodal pore networks, undergoes a sharp transition at the percolation threshold, when the smaller pore size is impermeable to the larger species, CH. The approach offers a convenient adaption of effective medium theory to multicomponent systems with nonlinear isotherms, overcoming drawbacks of existing theory

Modeling mixture transport at the nanoscale: Departure from existing paradigms

We present a novel theory of mixture transport in nanopores, which represents wall effects via a species-specific friction coefficient determined by its low density diffusion coefficient. Onsager coefficients from the theory are in good agreement with those from molecular dynamics simulation, when the nonuniformity of the density distribution is included. It is found that the commonly used assumption of a uniform density in the momentum balance is in serious error, as is also the traditional use of a mixture center of mass based frame of reference

Appropriate location for remanufacturing plant towards sustainable supply chain

© 2019 The Author(s). Confronted with the scarcity of natural resources, increase in product returns and government regulations on protection of environment, firms are implementing remanufacturing operations to achieve growth which is more sustainable and contribute to the millennium sustainable development goals. The challenge before the managers is to decide the appropriate location to establish the remanufacturing facilities in the reverse supply chain. Several conflicting criteria need to be considered before establishing a remanufacturing facility. In this paper, a framework is proposed to evaluate an ideal location for opening a remanufacturing plant, with the aid of ideal solution based multi criteria decision making (MCDM) tools, specifically TOPSIS, GRA and VIKOR. The suitable candidate location is then selected using the veto rule, which helps to overcome the limitation of using a single MCDM tool. An illustrative application in the Indian automotive sector is demonstrated to show the applicability of proposed framework. The approach is useful when there is a lack of quantitative data or the information is incomplete. The developed framework will help industries and economies to impact the use of eco-efficient and socio-economic systems and suggest pathways of transitioning to a more sustainable future

Atomistic Investigation of Mixed-Gas Separation in a Fluorinated Polyimide Membrane

We have used equilibrium molecular dynamics (EMD) simulations to investigate the temperature dependence of Maxwell–Stefan (MS) diffusivities of a pure component as well as an equimolar mixture of CO2 and CH4 in a fluorinated polyimide polymer membrane. The morphology of the polymer membrane is characterized, and gas adsorption isotherms of the pure as well as an equimolar mixture of CO2 and CH4 are extracted considering the polymer swelling upon gas adsorption, using a combination of EMD in the constant pressure ensemble and grand canonical Monte Carlo simulation. Significant swelling of the polymer in the presence of CO2 is found, as a result of which, the predictions of traditional models, such as ideal adsorption solution theory and dual mode sorption for mixed gases in mixed-gas conditions, are inaccurate, particularly for CH4. Our results show that plasticization behavior of the polymer leads to increase in CO2 permeability with increase in pressure. The Onsager coefficients indicate that, in mixed-gas conditions, finite correlations exist between the diffusing species in the polymer membrane. Further, the swollen membrane is kinetically selective for CH4 at high pressures in mixtures due to availability of large pores, in contrast to pure gas conditions where the membrane is kinetically selective for CO2 over CH4 at all pressures. Analysis of membrane behavior under practical conditions using EMD-based transport coefficients shows that, while the CO2/CH4 perm-selectivity increases with an increase in pressure based on pure component data, the trend is opposite for mixture data. Thus, the commonly used approach of screening membrane materials based on pure component data can be misleading, as it overlooks the correlation effects arising from the presence of other species in the mixture

A Comparative Analysis of the Metabolomic Response of Electron Beam Inactivated E. coli O26:H11 and Salmonella Typhimurium ATCC 13311

Ionizing radiation such as Electron beam (EB) and gamma irradiation inactivate microbial cells preventing their multiplication. These cells, however, are structurally intact and appear to have residual metabolic activity. We were interested in understanding the metabolic pathways that were still functional in EB-inactivated cells. Therefore, the primary objective of this study was to compare the metabolites accumulating in EB-inactivated pathogens E. coli 026:H11 and S. Typhimurium immediately after EB inactivation and 24 h post inactivation. Defined aliquots (109 CFU/mL) of E. coli O26-H11 (TW 1597) and S. Typhimurium (ATCC 13311) suspended in phosphate-buffered saline were exposed to lethal EB doses of 3 kGy and 2 kGy, respectively. Complete inactivation (inability of cells to multiply) was confirmed by traditional plating methods. An untargeted analysis of the primary metabolites accumulating in un-irradiated (control) cells, EB-inactivated cells immediately after irradiation, and EB-inactivated cells that were incubated at room temperature for 24 h post EB inactivation was performed using gas chromatography/mass spectrometry. A total of 349 different metabolites were detected in the EB-inactivated S. Typhimurium and E. coli O26:H11 cells, out of which, only 50% were identifiable. In S. Typhimurium, 98 metabolites were expressed at statistically different concentrations (P &lt; 0.05) between the three treatment groups. In E. coli O26:H11, 63 metabolites were expressed at statistically different concentrations (P &lt; 0.05) between the three treatment groups. In both these pathogens, the β-alanine, alanine, aspartate, and glutamate metabolic pathways were significantly impacted (P &lt; 0.01). Furthermore, the metabolomic changes in EB-inactivated cells were amplified significantly after 24 h storage at room temperature in phosphate-buffered saline. These results suggest that EB-inactivated cells are very metabolically active and, therefore, the term Metabolically Active yet Non-culturable is an apt term describing EB-inactivated bacterial cells

Tractable molecular theory of transport of Lennard-Jones fluids in nanopores

We present here a tractable theory of transport of simple fluids in cylindrical nanopores, which is applicable over a wide range of densities and pore sizes. In the Henry law low-density region the theory considers the trajectories of molecules oscillating between diffuse wall collisions, while at higher densities beyond this region the contribution from viscous flow becomes significant and is included through our recent approach utilizing a local average density model. The model is validated by means of equilibrium as well nonequilibrium molecular dynamics simulations of supercritical methane transport in cylindrical silica pores over a wide range of temperature, density, and pore size. The model for the Henry law region is exact and found to yield an excellent match with simulations at all conditions, including the single-file region of very small pore size where it is shown to provide the density-independent collective transport coefficient. It is also shown that in the absence of dispersive interactions the model reduces to the classical Knudsen result, but in the presence of such interactions the latter model drastically overpredicts the transport coefficient. For larger micropores beyond the single-file region the transport coefficient is reduced at high density because of intermolecular interactions and hindrance to particle crossings leading to a large decrease in surface slip that is not well represented by the model. However, for mesopores the transport coefficient increases monotonically with density, over the range studied, and is very well predicted by the theory, though at very high density the contribution from surface slip is slightly overpredicted. It is also seen that the concept of activated diffusion, commonly associated with diffusion in small pores, is fundamentally invalid for smooth pores, and the apparent activation energy is not simply related to the minimum pore potential or the adsorption energy as generally assumed. (C) 2004 American Institute of Physics

Influence of in-plane Stone-Thrower-Wales defects and edge functionalisation on the adsorption of CO2 and H2O on graphene

There is now increasing recognition of the potential of graphene membranes for gas separation, with the application to CO2 capture being one of specific interest; however, the co-adsorption of H2O which saturates flue-gas remains a major impediment. Towards enhancing hydrophobic characteristics of graphene while increasing specificity to CO2, we investigate here the adsorption characteristics of CO2 and H2O on four different kinds of graphene sheet - namely, hydrogen-terminated and fluorine-terminated pristine sheets, and the corresponding Stone-Thrower-Wales (STW) defect-incorporated sheets using density functional theory methods. Our results reveal that fluorine termination enhances hydrophobicity and favours the adsorption of CO2, while reducing that of H2O, in comparison to hydrogen termination. On the other hand, H2O adsorption affinity is increased on introducing the Stone-Thrower-Wales defect in both H-terminated and F-terminated sheets, while for CO2 the affinity change is more marginal, evidenced from the change in height of the adsorbed molecule above the surface, and of the adsorption energy. The Henry law constant for H2O is reduced by 54% on F-termination, for both pristine and defective H-terminated graphene sheets, while for CO2 it is increased by 12% and reduced by 18% respectively, on F-termination of the two sheets; indicating the pristine F-terminated sheet as the preferred option. From the density of states analysis, the Fermi level shows a 0.7 eV shift towards the valence band for fluorine termination in both pristine and STW sheets, but is not influenced by CO2 and H2O adsorption. Fluorine termination is shown to have a significant effect on the valence band, and offers a convenient route for tuning the electronic structure of graphene

Comparison of hollow fiber and flat mixed-matrix membranes: theory and simulation

We extend effective medium theory (EMT) to composite hollow fiber mixed matrix membranes, considering the asymmetric filler volume fraction profile arising from finite system size. This volume fraction profile leads to strong variation of the driving force (i.e. pseudo-bulk concentration gradient) in the regions adjacent to the composite ends, and to sensitivity of the effective permeability of the composite to the geometrical configuration. The new theory is validated against rigorous simulations of the transport in mixed-matrix membranes (MMMs) using both concentration-independent and concentration-dependent diffusivities in the MMM constituent phases. Both theory and simulations show that flat mixed-matrix membranes (F-MMMs) have higher effective overall permeability than hollow fiber mixed-matrix membranes (HF-MMMs), upon comparison of systems having identical operating conditions, filler phase loading and particle size. Furthermore, we show here that the sensitivity to the geometry vanishes with increase of inner radius of the hollow fiber membrane at fixed thickness, and the effective permeability of a HF-MMM is found to asymptotically approach that of a F-MMM

Exceptionally high performance of charged carbon nanotube arrays for CO2 separation from flue gas

We use grand canonical Monte Carlo simulation to investigate the adsorption of a CO/N mixture in neutral and charged (7, 7) carbon nanotube (CNT) arrays. It is found that both the adsorption of CO, and the CO/N selectivity are either enhanced or reduced when the charges are positive or negative. The CO/N selectivity in a CNT bundle carrying +0.05e charge with intertube distance of 0.335 nm exceeds 1000 for pressures up to 15 bar, which is remarkably high. It is seen that strong electrostatic interactions from neighbouring CNTs enhance the adsorption of CO over N, and while the adsorption of CO has complex dependence on intertube distance, the CO/N selectivity decreases with intertube spacing. We propose a quantitative performance coefficient as an aid to assessing the efficiency of CNT bundles to separate CO from flue gas, and show that a +0.05e charged bundle with intertube distance of 0.335 nm provides the best performance. Further, it is found that water vapor in flue gas imposes negligible effect on the adsorption of CO and its selectivity over N in the neutral and positively charged (7, 7) CNT bundles, but dramatically reduces the adsorption of CO and N in negatively charged bundles