Thermodynamic derivative properties and densities for hyperbaric gas condensates: SRK equation of state predictions versus Monte Carlo data

The ability of Soave–Redlich–Kwong cubic equation of state (SRK EoS) to predict densities and thermodynamic derivative properties such as thermal expansivity, isothermal compressibility, calorific capacity, and Joule–Thompson coefficients, for two gas condensates over a wide range of pressures (up to 110 MPa) was studied. The predictions of the EoS were compared to Monte Carlo simulation data obtained by Lagache et al. [M.H. Lagache, P. Ungerer, A. Boutin, Fluid Phase Equilibr. 220 (2004) 221]. Two completely different alpha functions for the SRK EoS attractive term were used and their respective effects on the predictions of such properties were analyzed. Also, two different forms of the crossed terms of the attractive parameter, a_ij, and three expressions of the crossed terms of the repulsive parameter, b_ij, were combined in different ways, and predictions were carried out. Little sensitivity of the properties on the chosen alpha function, except for the calorific capacities, was found in the systems studied. The most commonly used combination rules to model phase behavior of reservoir fluids, i.e. geometric and arithmetic forms of a_ij and b_ij, respectively, predicted very deficient results for these fluids at extreme conditions, specially for density calculations.     

Naturally occurring polyamines: interaction with macromolecules

The naturally occurring polyamines, spermine [NH2(CH2)3NH(CH2)4NH(CH2)3NH2] and spermidine [NH2(CH2)3NH(CH2)4NH2], as well as the diamine putrescine [NH2(CH2)4NH2], are widely spread in nature. They occur in plants, micro-organisms and animal tissues and fulfil many important physiological functions. Due to their cationic nature they interact with negatively charged macromolecules such nucleic acids, phospholipids and proteins. This ionic interaction, which is reversible, leads to the stabilization of DNA, tRNA, membranes and some proteins. Early studies demonstrated that polyamines stimulate the growth of pro- and eukaryotic cells and that they play an important role in carcinogenesis and in malignant transformation processes. As a result of these studies various inhibitors of polyamine biosynthesis have been synthesized and are used to combat cancer and parasitic diseases (e.g., African sleeping sickness).     

Optimal partitions having disjoint convex and conic hulls

LetA ¹,,A ⁿ be distinctk-dimensional vectors. We consider the problem of partitioning these vectors intom sets so as to maximize an objective which is a quasi-convex function of the sum of vectors in each set. We show that there exists an optimal partition whose sets have (pairwise) disjoint conic hulls. We also show that if the number of vectors in each of the sets is constrained, then a weaker conclusion holds, namely, there exists an optimal partition whose sets have (pairwise) disjoint convex hulls. The results rely on deriving necessary and sufficient conditions for a point to be an extreme point of a corresponding polytope.Research of this author was partially supported by NSF Grant ECS-83-10213 and by a Grant for the Promotion of Research at the Technion.     

Synthesis and structure of the incomplete cuboidal clusters [W3Se4H3(dmpe)3]+, [W3Se4H(3-x)(OH)x(dmpe)3]+ and [W3Se4(OH)3(dmpe)3]+, and the mechanism of the acid-assisted substitution of the coordinated hydrides

The novel incomplete cuboidal cluster [W3Se4H3(dmpe)3](PF6), [1](PF6), has been prepared by reduction of [W3Se4Br3(dmpe)3](PF6) with LiBH4 in THF solution. The trihydroxo complex [W3Se4(OH)3(dmpe)3](PF6), [2](PF6), was obtained by reacting [W3Se4Br3(dmpe)3](PF6) with NaOH in MeCN-H2O solution. The complexes [1](PF6) and [2](PF6) were converted to their BPh4- salts by treatment with NaBPh4. Recrystallisation of [1](BPh4) in the presence of traces of water affords the mixed dihydride hydroxo complex [W3Se4H2(OH)(dmpe)3](BPh4). The crystal structures of [1](BPh4), [2](BPh4) and [W3Se4H2(OH)(dmpe)3](BPh4) have been resolved. Although the [1]+ trihydride does not react with an excess of halide salts, reaction with HX leads to [W3Se4X3(dmpe)3]+ (X = Cl, Br). The kinetics of this reaction has been studied at 25 degrees C in MeCN-H2O solution (1:1, v/v) and found to occur with two consecutive kinetic steps. The first step is independent of the nature and concentration of the X(-) anion but shows a first order dependence on the concentration of acid (k1 = 12.0 mol(-1) dm(3) s(-1)), whereas the second one is independent of the nature and concentration of both the acid and added salts (k2 = 0.024 s(-1)). In contrast, the reaction of [2]+ with acids occurs in a single step with kobs = 0.63 s(-1)(HCl) and 0.17 s(-1)(HBr). These kinetic results are discussed on the basis of the mechanism previously proposed for the reactions of the analogous [W3S4H3(dmpe)3]+ cluster, with special emphasis on the effects caused by the change of S by Se on the rate constants for the different processes involved.     

Effects produced by metal-coated near-field probes on the performance of silicon waveguides and resonators

We study the effects of metal-coated fiber near-field probes on the performance of nanophotonic devices. Employing a heterodyne near-field scanning optical microscope and analyzing transmission characteristics, we find that a metal-coated probe can typically introduce a 3 dB intensity loss and a 0.2 rad phase shift during characterization of a straight waveguide made in a silicon-on-insulator system. In resonant nanophotonic structures such as a 5 mum radius microring resonator, we demonstrate that the probe induces a 1 nm shift in resonant wavelength and decreases the resonator quality factor, Q, from 1100 to 480.     

Improved Bounds for Acyclic Job Shop Scheduling

In acyclic job shop scheduling problems there are n jobs and m machines. Each job is composed of a sequence of operations to be performed on different machines. A legal schedule is one in which within each job, operations are carried out in order, and each machine performs at most one operation in any unit of time. If D denotes the length of the longest job, and C denotes the number of time units requested by all jobs on the most loaded machine, then clearly lb = max[C,D] is a lower bound on the length of the shortest legal schedule. A celebrated result of Leighton, Maggs, and Rao shows that if all operations are of unit length, then there always is a legal schedule of length O(lb), independent of n and m. For the case that operations may have different lengths, Shmoys, Stein and Wein showed that there always is a legal schedule of length , where the notation is used to suppress terms. We improve the upper bound to . We also show that our new upper bound is essentially best possible, by proving the existence of instances of acyclic job shop scheduling for which the shortest legal schedule is of length . This resolves (negatively) a known open problem of whether the linear upper bound of Leighton, Maggs, and Rao applies to arbitrary job shop scheduling instances (without the restriction to acyclicity and unit length operations). Received June 30, 1998 RID="*" ID="*" Incumbent of the Joseph and Celia Reskin Career Development Chair RID="†" ID="†" Research was done while staying at the Weizmann Institute, supported by a scholarship from the Minerva foundation.     

A tight upper bound on the cover time for random walks on graphs

We prove that the expected time for a random walk to visit all n vertices of a connected graph is at most 4/27n³ + o(n³).     

Characterizations of optimal scalings of matrices

A scaling of a non-negative, square matrixA ≠ 0 is a matrix of the formDAD ^?1, whereD is a non-negative, non-singular, diagonal, square matrix. For a non-negative, rectangular matrixB ≠ 0 we define a scaling to be a matrixCBE ^?1 whereC andE are non-negative, non-singular, diagonal, square matrices of the corresponding dimension. (For square matrices the latter definition allows more scalings.) A measure of the goodness of a scalingX is the maximal ratio of non-zero elements ofX. We characterize the minimal value of this measure over the set of all scalings of a given matrix. This is obtained in terms of cyclic products associated with a graph corresponding to the matrix. Our analysis is based on converting the scaling problem into a linear program. We then characterize the extreme points of the polytope which occurs in the linear program.     

Is multiscaling an artifact in the stochastically forced Burgers equation?

We study turbulence in the one-dimensional Burgers equation with a white-in-time, Gaussian random force that has a Fourier-space spectrum approximately 1/k, where k is the wave number. From very high-resolution numerical simulations, in the limit of vanishing viscosity, we find evidence for multiscaling of velocity structure functions which cannot be falsified by standard tests. We find a new artifact in which logarithmic corrections can appear disguised as anomalous scaling and conclude that bifractal scaling is likely.