Position-space renormalization for systems with weak long-range interactions and the breakdown of hyperscaling

Exact renormalization group equations are derived for a position-space renormalization of spin systems with weak long-range forces. It is shown how an apparent dependence of the critical exponents on the choice of the renormalization group can be resolved via the mechanism of dangerous irrelevant variables and that this same mechanism is responsible for the breakdown of hyperscaling. The dimensiond=4 can be seen to be a borderline dimension above which classical critical exponents are expected.     

Measurement of rheological properties of corn stover suspensions

Corn stover is currently being evaluated as a feedstock for ethanol production. The corn stover suspensions fed to reactors typically range between 10 and 40% solids. To simulate and design bioreactors for processing highly loaded corn stover suspensions, the rheologic properties of the suspension must be measured. In systems with suspended solids, rheologic measurements are difficult to perform owing to settling in the measurement devices. In this study, viscosities of corn stover suspensions were measured using a helical ribbon impeller viscometer. A calibration procedure is required for the impeller method in order to obtain the shear rate constant, k, which is dependent on the geometry of the measurement system. The corn stover suspensions are described using a power law flow model.     

RATE OF INTRA-MOLECULAR CONTACT FORMATION IN SHORT TWO-DIMENSIONAL COMPACT POLYMERS CHAINS

It is important to know the rate of intra-molecular contact formation in proteins in order to understand how proteins fold clearly. Here we investigate the rate of intra-molecular contact formation in short two-dimensional compact polymer chains by calculating the probability distribution p(r) of end-to-end distance r using the enumeration calculation method and HP model on two-dimensional square lattice. The probability distribution of end-to-end distance p(r) of short two-dimensional compact polymers chains may consist of two parts, i.e. p(r) = p1(r) p2(r), where p1(r) and p2(r) are different for small r. The rate of contact formation decreases monotonically with the number of bonds N, and the rate approximately conforms to the scaling relation of k(N) ∝ N-α. Here the value of α increases with the contact radius a and it also depends on the percentage of H (hydrophobic) residues in the sequences of compact chains and the energy parameters of εHH, εHP and εPP . Some comparisons of theoretical predictions with experimental results are also made. This investigation may help us to understand the protein folding.     

Cathode of a fuel cell with a solid polymer electrolyte: Calculating overall currents in the presence of a gas-diffusion layer

Mathematical apparatus, which makes it possible to perform calculations of the current-voltage characteristics of cathodes of fuel cells with a solid polymer electrolyte in conditions where there are present extraneous diffusion restrictions is proposed. In so doing, the partial pressure of oxygen and the absolute pressure of gas in the gas chamber may assume any values. First of all presented are the results of calculations of the current-voltage characteristics intrinsic to active layers of the air and oxygen cathodes, which are performed under the assumption that the extraneous diffusion restrictions are absent altogether. Thereafter, in the same conditions (at the same parameters that characterize the active layer of a cathode), obtained are results of a calculation of the current-voltage characteristics inherent in the air and oxygen cathodes in the presence of extraneous diffusion restrictions. Afterward there is performed an analysis of the way a gas-diffusion layer restricts the process of generation of current in a cathode and of what measures should be taken in order for the extraneous diffusion restrictions to become less significant.     

Deviation from Ohm's law in electric field assisted capillary liquid chromatography

Earlier studies of electric field assisted LC (EF-LC) have shown that the effect on charged analytes of the application of an electric field over a capillary LC column is relatively small. Charged analytes can only be affected by the electric field while present in the mobile phase, which makes the effective time for influence of the electric field t(0) independent of retention time. Because the charged analytes only can be affected for a short time the electric field strength ought to be high in order to increase the impact of the electric field on the separation. We have, however, found that only a relatively low electric field strength can be used in EF-LC when pressure is used as main driving force. The useful field strength was limited by a dramatic increase in the current. This increase in current was found to origin from an increased concentration of buffer ions that have an electrophoretic mobility towards the pumped flow.     

Influence of heating rate on kinetic quantities of solid phase thermal decomposition

Thermogravimetric analyses of thermal decomposition (pyrolysis, thermal dissociation and combustion) of 9 different samples were carried out in dynamic conditions at different heating rates. The kinetic parameters (E, A and k_m) of thermal decomposition were determined and interrelations between the parameters and heating rate q were analyzed. There were also relations between Arrhenius and Eyring equations analyzed for thermal decomposition of solid phase. It was concluded that Eyring theory is an element, which interconnects used thermokinetic equations containing Arrhenius law and suggests considering kinetic quantities in way relative to 3 kinetic constants (E, A and k_m). Analysis of quantities other than km (i.e. E, A, Δ⁺H, Δ⁺S) in relation to heating rate is an incomplete method and does not lead to unambiguous conclusions. It was ascertained that in ideal case, assuming constant values of kinetic parameters (E and A) towards heating rate and satisfying both Kissinger equations, reaction rate constant k_m should take on values intermediate between constants (k_m)₁ and (k_m)₂ determined from these equations. Whereas behavior of parameters E and A towards q were not subjected to any rule, then plotting relation k_m vs. q in the background of (k_m)₁ and (k_m)₂ made possible classification of differences between thermal decomposition processes taking place in oxidizing and oxygen-free atmosphere.     

Vapor-liquid equilibria for the nitrogen-isobutane system

Vapor-liquid equilibria have been investigated experimentally for the nitrogen-isobutane system at temperatures from 120 K to 220 K and at pressures up to 150 bar. Below 126.5 K, two liquid phases were observed as pressure was increased to near the vapor pressure of pure nitrogen. The equilibrium ratio of nitrogen in the binary system and the Henry’s law constants for nitrogen in isobutane were determined from experimental data. The experimental phase equilibrium data were correlated by means of the Peng-Robinson equation of state.     

Comparative analysis of affine scaling algorithms based on simplifying assumptions

We analyze several affine potential reduction algorithms for linear programming based on simplifying assumptions. We show that, under a strong probabilistic assumption regarding the distribution of the data in an iteration, the decrease in the primal potential function will be with high probability, compared to the guaranteed(1). ( 2n is a parameter in the potential function andn is the number of variables.) Under the same assumption, we further show that the objective reduction rate of Dikin's affine scaling algorithm is with high probability, compared to no guaranteed convergence rate.Research supported in part by NSF Grant DDM-8922636.     

A review ofL=λW and extensions

A fundamental principle of queueing theory isL=W (Little's law), which states that the time-average or expected time-stationary number of customers in a system is equal to the product of the arrival rate and the customer-average or expected customer-stationary time each customer spends in the system. This principle is now well known and frequently applied. However, in recent years there have been extensions, such as H=G and the continuous, distributional, ordinal and central-limit-theorem versions, which show that theL=W relation, when viewed properly, has much more power than was previously realized. Moreover, connections have been established between H=G and other fundamental relations, such as the rate conservation law and PASTA (Poisson arrivals see time averages), which show that there is a much greater unity in the overall theory than was previously realized. This paper provides a review.This paper is dedicated to the memory of our colleague Professor Peter Franken (1937–1989), who contributed greatly to the subject of this paper and to queueing theory more generally.     

The domain of partial attraction of a Poisson law

Groshev gave a characterization of the union of domains of partial attraction of all Poisson laws in 1941. His classical condition is expressed by the underlying distribution function and disguises the role of the mean of the attracting distribution. In the present paper we start out from results of the recent probabilistic approach and derive characterizations for any fixed >0 in terms of the underlying quantile function. The approach identifies the portion of the sample that contributes the limiting Poisson behavior of the sum, delineates the effect of extreme values, and leads to necessary and sufficient conditions all involving . It turns out that the limiting Poisson distributions arise in two qualitatively different ways depending upon whether >1 or <1. A concrete construction, illustrating all the results, also shows that in the boundary case when =1 both possibilities may occur.