Computing optimal scalings by parametric network algorithms

Asymmetric scaling of a square matrixA 0 is a matrix of the formXAX ^–1 whereX is a nonnegative, nonsingular, diagonal matrix having the same dimension ofA. Anasymmetric scaling of a rectangular matrixB 0 is a matrix of the formXBY ^–1 whereX andY are nonnegative, nonsingular, diagonal matrices having appropriate dimensions. We consider two objectives in selecting a symmetric scaling of a given matrix. The first is to select a scalingA of a given matrixA such that the maximal absolute value of the elements ofA is lesser or equal that of any other corresponding scaling ofA. The second is to select a scalingB of a given matrixB such that the maximal absolute value of ratios of nonzero elements ofB is lesser or equal that of any other corresponding scaling ofB. We also consider the problem of finding an optimal asymmetric scaling under the maximal ratio criterion (the maximal element criterion is, of course, trivial in this case). We show that these problems can be converted to parametric network problems which can be solved by corresponding algorithms.This research was supported by NSF Grant ECS-83-10213.     

Network theory of the nonlinear behaviour of polymer melts. Simple shear flow

Summary The network model developed in a previous paper is applied to the simple shear flow of polymer melts. The constitutive equation obtained consists of two terms. One of them describes the stress due to the network strands which exist at the onset of the deformation, dissociate during the deformation and result in a single integral constitutive equation with a strain dependent damping function. The formulation of the damping function in invariant form seems to be almost impossible.The second normal stress differenceN ₂ of the model is not zero,but has negative values. According to our model this is a consequence of the deformation dependence of the disentanglement process. The theory is compared with experimental data for a LDPE melt. It is found that the model explains the main features of the shear flow behaviour of the LDPE melt investigated preciously.

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Zusammenfassung Das Netzwerk-Modell, das in einer vorangegangenen Arbeit entwickelt wurde, wird für die einfache Scherströmung von Polymerschelzen angewendet. Die abgeleitete rheologische Zustandsgleichung besteht aus zwei Gliedern. Das erste beschreibt die Spannung-Dehnung-Beziehung der Kettensegmente, die zu Beginn der Deformation existieren und während der Deformation aufgelöst werden. Es hat die Form der einfachen Integralbeziehung mit einer Gedächtnisfunktion. Es ist kaum möglich, die dabei erhaltene Gedächtnisfunktion als Funktion der Invarianten der der Tensoren darzustellen. Die zweite Normal-SpannungsdifferenzN ₂ des Modells ist nicht Null und hat einen negativen Wert. Dies ist nach unserem Modell eine Folge der Deformationsabhängigkeit des Entschlaufungsprozesses. Die Theorie wird mit dem experimentellen Daten für eine LDPE-Schmelze verglichen, wobei sich zeigt, daß das Modell die wesentlichen Merkmale des Scherverhaltens der LDPE-Schmelze gut erklärt.

     

Entrapment and release of sodium polystyrene sulfonate (SPS) from calcium alginate gel beads

The release of sodium polystyrene sulfonate (SPS) from calcium alginate hydrogel beads has been studied. It has been shown that the structure of the cross-linked calcium alginate network is of primary importance in the retention and/or release of the SPS. This has been evidenced by studying the influence of Ca²⁺ concentration, molar masses (M_n) and the ratio of mannuronic acid/guluronic acid components. A minimum in the SPS release is observed in relation with the organization of the network structure. Conditions inducing the organization of a strong gel (e.g. high Ca²⁺ concentration for example) are not always related to a low release. A good control of release is found when a compromise between a well-structured hydrogel and sterical consideration of SPS is reached.     

Cost operator algorithms for the transportation problem

A primal transportation algorithm is devised via post-optimization on the costs of a modified problem. The procedure involves altering the costs corresponding to the basic cells of the initial (primal feasible) solution so that it is dual feasible as well. The altered costs are then successively restored to their true values with appropriate changes in the optimal solution by the application of cell or area cost operators discussed elsewhere. The cell cost operator algorithm converges to optimum within (2T – 1) steps for primal nondegenerate transportation problems and [(2T + 1) min (m, n)] – 1 steps for primal degenerate transportation problems, whereT is the sum of the (integer) warehouse availabilities (also the sum of the (integer) market requirements) andm andn denote the number of warehouses and markets respectively. For the area cost operator algorithm the corresponding bounds on the number of steps areT and (T + 1) min (m, n) respectively.This report was prepared as part of the activities of the Management Sciences Research Group, Carnegie—Mellon University, under Contract N00014-67-A-0314-0007 NR 047-048 with the U.S. Office of Naval Research.     

Influence of silica fillers during the electron irradiation of DGEBA/TETA epoxy resins, part II: Study of the thermomechanical properties

This work describes the influence of silica fillers on the thermomechanical properties of diglycidyl ether of bisphenol A/triethylenetetramine (DGEBA/TETA) epoxy resins during ageing under electron beam irradiation. Whatever be the silica filler (pure micrometric ground and spherical silicas, nanometric silicas and coupling agent treated silicas), the glass transition temperature of the epoxy resins decreases with increasing irradiation dose, meaning that the main effect of the irradiation is chain scission. No influence of the silica fillers has been detected from the changes in the glass transition temperature with the increase in the irradiation dose. The disappearance of the cooperativity of the γ relaxation, the decrease of the α relaxation and the decrease of the elastic modulus at the rubbery plateau observed by dynamic mechanical analyses involve a decrease in the crosslink density of the epoxy resins. The occurrence of chemical reactions between the epoxy resin and the silica surface at high irradiation doses has been shown. Moreover, we show evidence that chemical reactions between the epoxy resin and the silica surface occur at high irradiation dose.     

New double negative and positive temperature coefficients of conductive EPDM rubber TiC ceramic composites

In this paper, we have successfully prepared ethylene-propylene-diene monomer (EPDM)/TiC composites as thermistors, with new double negative and positive temperature coefficients of conductivity (NTCC/PTCC). EPDM composites loaded with 50 phr HAF carbon black and different concentrations of TiC were prepared. This study focuses on the effect of TiC content on the vulcanization process, the network structure and the electrical and thermal properties of EPDM/TiC composites. The effect of TiC on the network structure was evaluated e.g. the curing process, the characteristic time constant during vulcanization, the volume fraction of rubber, gel fraction, interparticle distance between conductive particles, the extent of TiC reinforcement in the rubber matrix and molecular weight between cross-linking through experimental and affine-phantom models. The effects of TiC content on the percolation theory, electrical conductivity, conducting mechanism of conductivity, conducting hysteresis and I-V characteristics were also studied, as well as its TiC on the (NTCC/PTCC), thermoelectric power, dielectric constant and thermal conductivity. Stability and reproducibility of the thermal cycles for heating element applications was tested. Specific heat and the amount of heat transfer by radiation and convection as a function of TiC content was calculated using both the calorimetric technique and a theoretical model. It was proved that TiC improves the network structure, electrical and thermal properties of EPDM composites for practical applications.     

Synthesis and Crystal Structure of Blue Luminescent Cadmium(II) Coordination Networks with 4,4′-Bis(imidazol-1-ylmethyl)biphenyl from Different Solvent Systems

Two supramolecular complexes, [Cd(bimb)²Cl²] (1) and [Cd(bimb)(DMF)Cl²]·DMF (2) [bimb=4,4′-bis(imidazol-1-ylmethyl)biphenyl], were synthesized by reactions of CdCl²·2.5H²O with bimb ligand in ethanol and N,N′-dimethylformamide (DMF), respectively, and their structures were determined by X-ray crystallography. Complex 1 is an infinite 2D grid network bridged by bimb ligands, and the 2D sheets were further linked by C–H ?Cl hydrogen bonds to form a polycatenated 3D framework. Complex 2 has dicadmium(II) di-μ-chloride units which are connected by bimb bridging ligands to form an infinite non-interpenetrating 2D network. The results provide a nice example of the solvent system exerting a great effect on the construction of supramolecular frameworks.     

Adaptive multimedia streaming using a simulation test bed

The major purpose of this paper is to transmit an existing video above a complete simulated video streaming architecture based on Network Simulator (NS2). Thanks to our architecture, the visual quality evaluation of the distributed streaming platform under various conditions is simplified. Indeed, the received video can be easily visualized using a classic video client or be compared using the Peak Signal-Noise Ratio (PSNR) value and the Structural SIMilarity (SSIM) value. In the case study, we compare adaptive video congestion strategies using a transcoder, Datagram Congestion Control Protocol (DCCP) and TCP-Friendly Rate Control (TFRC).     

The cut condition for robust network design

We consider the Robust Network Design problem, i.e. the problem of dimensioning the capacities on the edges of a graph to serve point-to-point traffic demands subject to uncertainty. The scope of the paper is to investigate when the cut condition is sufficient to guarantee the feasibility for such problem.     

Vulnerability analysis of interdependent infrastructure systems: A methodological framework

Infrastructure systems such as power and water supplies make up the cornerstone of modern society which is essential for the functioning of a society and its economy. They become more and more interconnected and interdependent with the development of scientific technology and social economy. Risk and vulnerability analysis of interdependent infrastructures for security considerations has become an important subject, and some achievements have been made in this area. Since different infrastructure systems have different structural and functional properties, there is no universal all-encompassing ‘silver bullet solution’ to the problem of analyzing the vulnerability associated with interdependent infrastructure systems. So a framework of analysis is required. This paper takes the power and water systems of a major city in China as an example and develops a framework for the analysis of the vulnerability of interdependent infrastructure systems. Four interface design strategies based on distance, betweenness, degree, and clustering coefficient are constructed. Then two types of vulnerability (long-term vulnerability and focused vulnerability) are illustrated and analyzed. Finally, a method for ranking critical components in interdependent infrastructures is given for protection purposes. It is concluded that the framework proposed here is useful for vulnerability analysis of interdependent systems and it will be helpful for the system owners to make better decisions on infrastructure design and protection.