Theory of Gas Hydrates: Effect of the Approximation of Rigid Water Lattice

One of the assumptions of the van der Waals and Platteeuw theory for gas hydrates is that the host water lattice is rigid and not distorted by the presence of guest molecules. In this work, we study the effect of this approximation on the triple-point lines of the gas hydrates. We calculate the triple-point lines of methane and ethane hydrates via Monte Carlo molecular simulations and compare the simulation results with the predictions of van der Waals and Platteeuw theory. Our study shows that even if the exact intermolecular potential between the guest molecules and water is known, the dissociation temperatures predicted by the theory are significantly higher. This has serious implications to the modeling of gas hydrate thermodynamics, and in spite of the several impressive efforts made toward obtaining an accurate description of intermolecular interactions in gas hydrates, the theory will suffer from the problem of robustness if the issue of movement of water molecules is not adequately addressed.

Self-organization of multiple components in a steroidal hydrogel matrix: design, construction and studies on novel tunable luminescent gels and xerogels

The present work combines two rapidly growing research areas-functional supramolecular gels and lanthanide based hybrid materials. Facile hydrogel formation from several lanthanide(III) cholates has been demonstrated. The morphological and mechanical properties of these cholate gels were investigated by TEM and rheology. The hydrogel matrix was subsequently utilized for the sensitization of Tb(III) by doping a non-coordinating chromophore, 2,3-dihydroxynaphthalene (DHN), at micromolar concentrations. In the mixed gels of Tb(III)-Eu(III), an energy transfer pathway was found to operate from Tb(III) to Eu(III) and by utilizing this energy transfer, tunable multiple-color luminescent hydrogels were obtained. The emissive properties of the hydrogels were also retained in the xerogels and their suspensions in n-hexane were used for making luminescent coating on glass surface.

Fast edge splitting and Edmonds' arborescence construction for unweighted graphs

Given an unweighted undirected or directed graph with n vertices, m edges and edge connectivity c, we present a new deterministic algorithm for edge splitting. Our algorithm splits-off any specified subset S of vertices satisfying standard conditions (even degree for the undirected case and in-degree ≥ out-degree for the directed case) while maintaining connectivity c for vertices outside S in Õ(m+nc2) time for an undirected graph and Õ(mc) time for a directed graph. This improves the current best deterministic time bounds due to Gabow [8], who splits-off a single vertex in Õ(nc2+m) time for an undirected graph and Õ(mc) time for a directed graph. Further, for appropriate ranges of n, c, |S| it improves the current best randomized bounds due to Benczúr and Karger [2], who split-off a single vertex in an undirected graph in Õ(n2) Monte Carlo time. We give two applications of our edge splitting algorithms. Our first application is a sub-quadratic (in n) algorithm to construct Edmonds' arborescences. A classical result of Edmonds [5] shows that an unweighted directed graph with c edge-disjoint paths from any particular vertex r to every other vertex has exactly c edge-disjoint arborescences rooted at r. For a c edge connected unweighted undirected graph, the same theorem holds on the digraph obtained by replacing each undirected edge by two directed edges, one in each direction. The current fastest construction of these arborescences by Gabow [7] takes Õ(n2c2) time. Our algorithm takes Õ(nc3+m) time for the undirected case and Õ(nc4+mc) time for the directed case. The second application of our splitting algorithm is a new Steiner edge connectivity algorithm for undirected graphs which matches the best known bound of Õ(nc2 + m) time due to Bhalgat et al [3]. Finally, our algorithm can also be viewed as an alternative proof for existential edge splitting theorems due to Lovász [9] and Mader [11].

Modified lattice model for mode-I fracture analysis of notched plain concrete beam using probabilistic approach

A modified lattice model using finite element method has been developed to study the mode-I fracture analysis of heterogeneous materials like concrete. In this model, the truss members always join at points where aggregates are located which are modeled as plane stress triangular elements. The truss members are given the properties of cement mortar matrix randomly, so as to represent the randomness of strength in concrete. It is widely accepted that the fracture of concrete structures should not be based on strength criterion alone, but should be coupled with energy criterion. Here, by incorporating the strain softening through a parameter ‘α’, the energy concept is introduced. The softening branch of load-displacement curves was successfully obtained. From the sensitivity study, it was observed that the maximum load of a beam is most sensitive to the tensile strength of mortar. It is seen that by varying the values of properties of mortar according to a normal random distribution, better results can be obtained for load-displacement diagram.

Intruder detection over sensor placement in a hexagonal lattice

The problem of intrusion detection and location identification in the presence of clutter is considered for a hexagonal sensor-node geometry. It is noted that in any practical application,for a given fixed intruder or clutter location, only a small number of neighboring sensor nodes will register a significant reading. Thus sensing may be regarded as a local phenomenon and performance is strongly dependent on the local geometry of the sensor nodes. We focus on the case when the sensor nodes form a hexagonal lattice. The optimality of the hexagonal lattice with respect to density of packing and covering and largeness of the kissing number suggest that this is the best possible arrangement from a sensor network viewpoint. The results presented here are clearly relevant when the particular sensing application permits a deterministic placement of sensors. The results also serve as a performance benchmark for the case of a random deployment of sensors. A novel feature of our analysis of the hexagonal sensor grid is a signal-space viewpoint which sheds light on achievable performance.Under this viewpoint, the problem of intruder detection is reduced to one of determining in a distributed manner, the optimal decision boundary that separates the signal spaces SI and SC associated to intruder and clutter respectively. Given the difficulty of implementing the optimal detector, we present a low-complexity distributive algorithm under which the surfaces SI and SC are separated by a wellchosen hyperplane. The algorithm is designed to be efficient in terms of communication cost by minimizing the expected number of bits transmitted by a sensor.

An O(mn) Gomory-Hu Tree Construction Algorithm for Unweighted Graphs

We present a fast algorithm for computing a Gomory-Hu tree or cut tree for an unweighted undirected graph G = (V,E). The expected running time of our algorithm is Õ(mc) where |E| = m and c is the maximum u-vedge connectivity, where u,v ∈ V. When the input graph is also simple (i.e., it has no parallel edges), then the u-v edge connectivity for each pair of vertices u and v is at most n-1; so the expected running time of our algorithm for simple unweighted graphs is Õ(mn).All the algorithms currently known for constructing a Gomory-Hu tree [8,9] use n-1 minimum s-t cut (i.e., max flow) subroutines. This in conjunction with the current fastest Õ(n20/9) max flow algorithm due to Karger and Levine [11] yields the current best running time of Õ(n20/9n) for Gomory-Hu tree construction on simpleunweighted graphs with m edges and n vertices. Thus we present the first Õ(mn) algorithm for constructing a Gomory-Hu tree for simple unweighted graphs.We do not use a max flow subroutine here; we present an efficient tree packing algorithm for computing Steiner edge connectivity and use this algorithm as our main subroutine. The advantage in using a tree packing algorithm for constructing a Gomory-Hu tree is that the work done in computing a minimum Steiner cut for a Steiner set S ⊆ V can be reused for computing a minimum Steiner cut for certain Steiner sets S' ⊆ S.

Optimal Exact-Regenerating Codes for Distributed Storage at the MSR and MBR Points via a Product-Matrix Construction

Regenerating codes are a class of distributed storage codes that allow for efficient repair of failed nodes, as compared to traditional erasure codes. An [n, k, d] regenerating code permits the data to be recovered by connecting to any k of the n nodes in the network, while requiring that a failed node be repaired by connecting to any d nodes. The amount of data downloaded for repair is typically much smaller than the size of the source data. Previous constructions of exact-regenerating codes have been confined to the case n = d + 1. In this paper, we present optimal, explicit constructions of (a) Minimum Bandwidth Regenerating (MBR) codes for all values of [n, k, d] and (b) Minimum Storage Regenerating (MSR) codes for all [n, k, d >= 2k - 2], using a new product-matrix framework. The product-matrix framework is also shown to significantly simplify system operation. To the best of our knowledge, these are the first constructions of exact-regenerating codes that allow the number n of nodes in the network, to be chosen independent of the other parameters. The paper also contains a simpler description, in the product-matrix framework, of a previously constructed MSR code with [n = d + 1, k, d >= 2k - 1].

Electrocatalysis and redox behavior of Pt(2+) ion in CeO(2) and Ce(0.85)Ti(0.15)O(2): XPS evidence of participation of lattice oxygen for high activity

Electronic states of CeO(2), Ce(1 -aEuro parts per thousand x) Pt (x) O(2 -aEuro parts per thousand delta) , and Ce(1 -aEuro parts per thousand x -aEuro parts per thousand y) Ti (y) Pt (x) O(2 -aEuro parts per thousand delta) electrodes have been investigated by X-ray photoelectron spectroscopy as a function of applied potential for oxygen evolution and formic acid and methanol oxidation. Ionically dispersed platinum in Ce(1 -aEuro parts per thousand x) Pt (x) O(2 -aEuro parts per thousand delta) and Ce(1 -aEuro parts per thousand x -aEuro parts per thousand y) Ti (y) Pt (x) O(2 -aEuro parts per thousand delta) is active toward these reactions compared with CeO(2) alone. Higher electrocatalytic activity of Pt(2+) ions in CeO(2) and Ce(1 -aEuro parts per thousand x) Ti (x) O(2) compared with the same amount of Pt(0) in Pt/C is attributed to Pt(2+) ion interaction with CeO(2) and Ce(1 -aEuro parts per thousand x) Ti (x) O(2) to activate the lattice oxygen of the support oxide. Utilization of this activated lattice oxygen has been demonstrated in terms of high oxygen evolution in acid medium with these catalysts. Further, ionic platinum in CeO(2) and Ce(1 -aEuro parts per thousand x) Ti (x) O(2) does not suffer from CO poisoning effect unlike Pt(0) in Pt/C due to participation of activated lattice oxygen which oxidizes the intermediate CO to CO(2). Hence, higher activity is observed toward formic acid and methanol oxidation compared with same amount of Pt metal in Pt/C.

Output-Sensitive Construction of Reeb Graphs

The Reeb graph of a scalar function represents the evolution of the topology of its level sets. This paper describes a near-optimal output-sensitive algorithm for computing the Reeb graph of scalar functions defined over manifolds or non-manifolds in any dimension. Key to the simplicity and efficiency of the algorithm is an alternate definition of the Reeb graph that considers equivalence classes of level sets instead of individual level sets. The algorithm works in two steps. The first step locates all critical points of the function in the domain. Critical points correspond to nodes in the Reeb graph. Arcs connecting the nodes are computed in the second step by a simple search procedure that works on a small subset of the domain that corresponds to a pair of critical points. The paper also describes a scheme for controlled simplification of the Reeb graph and two different graph layout schemes that help in the effective presentation of Reeb graphs for visual analysis of scalar fields. Finally, the Reeb graph is employed in four different applications-surface segmentation, spatially-aware transfer function design, visualization of interval volumes, and interactive exploration of time-varying data.