COMPARISON OF ACCURACY AND PERFORMANCE FOR LATTICE BOLTZMANN AND FINITE DIFFERENCE SIMULATIONS OF STEADY VISCOUS FLOW

The lattice Boltzmann method (LBM) is used to simulate flow in an infinite periodic array of octagonal cylinders. Results are compared with those obtained by a finite difference (FD) simulation solved in terms of streamfunction and vorticity using an alternating direction implicit scheme. Computed velocity profiles are compared along lines common to both the lattice Boltzmann and finite difference grids. Along all such slices, both streamwise and transverse velocity predictions agree to within 0ċ5% of the average streamwise velocity. The local shear on the surface of the cylinders also compares well, with the only deviations occurring in the vicinity of the corners of the cylinders, where the slope of the shear is discontinuous. When a constant dimensionless relaxation time is maintained, LBM exhibits the same convergence behaviour as the FD algorithm, with the time step increasing as the square of the grid size. By adjusting the relaxation time such that a constant Mach number is achieved, the time step of LBM varies linearly with the grid size. The efficiency of LBM on the CM-5 parallel computer at the National Center for Supercomputing Applications (NCSA) is evaluated by examining each part of the algorithm. Overall, a speed of 13ċ9 GFLOPS is obtained using 512 processors for a domain size of 2176×2176.     

A Signalling Problem for Near-Equilibrium Flows in the Fickett-Majda Model of Combustion

The signalling problem for chemico-acoustic interactions ina simplified model of combustion and detonation is considered.The problem is examined in different limits, depending uponthe sensitivity of the reaction rate with the degree of reactioncoordinate and with the thermodynamic state. In one limit, theproblem is singular, and singular perturbation techniques areused to obtain an approximate solution. In the general case,a combination Riemann function-Laplace transform method is usedto obtain exact solutions with arbitrary boundary data. Thiscombined method allows the Riemann method to be applied to certainwave problems with discontinuous data.     

ACCOUNTING FOR TEMPERATURE IN PREDATOR FUNCTIONAL RESPONSES

ABSTRACT. A rational mechanism that integrates temperature‐mediated activity cycles into standard predator functional responses is presented. Daily temperature variations strongly influence times that predators can search for prey, and they affect the activity periods of prey, thereby modifying their detection by predators. Thus, key parameters in the functional response, the search time and the detection, become temperature‐dependent. These temperature mediated responses are included in discrete‐time population growth models, and it is shown how environmental temperature variations, such as those that may occur under global climate change, can affect population levels. As an illustration, a logistic growth model with a stochastic, temperature‐dependent predation term is examined, and the response to both average temperature levels and temperature variability is quantified. We infer, through simulations, that predation and prey abundance are strongly affected by mean temperature, temperature amplitudes, and increasing uncertainty in predicting temperature levels and variation, thus confirming many qualitative conclusions in the ecological literature. In particular, we show that increased temperature variability increases oscillations in the system and leads to increased probability of extinction of the prey.     

Properties of Continous Models of Transfer Lines with Unreliable Machines and Finite Buffers

We consider a transfer line consisting of a series of machinesseparated by buffers of finite capacity. The processing of apart on a machine requires a fixed amount of time. In thesesystems, blocking and starvation, which occur as a consequenceof machine failures, are important phenomena. Except for transferlines without buffer storage, no exact models of such systemshave been reported in the literature, even in the case of two-machinelines. Two approximate models have been proposed: the discrete-timemodel and the continuous-flow model. Exact solutions of theemodels have been reported in the case of two-machine Lines,and approximations have been proposed for longer lines. Thepurpose of this paper is to provide properties of the continuous-flowmodel. The main result of the paper is to show that lower andupper bounds on the exact production rate of the transfer linecan be obtained using the continuous flow model. These boundsare obtained by making an appropriate choice of the buffer capacities     

Implicit algorithms and their linearization for the transient incompressible Navier-Stokes equations

Email: na.asmith2{at}na-net.ornl.gov Email: na.silvester{at}na-net.ornl.gov The issue of appropriate time discretization methods for theunsteady incompressible Navier-Stokes equations is consideredfrom a practical perspective. Conventional implicit time-steppingalgorithms are not feasible for long-time simulations sincethey inherit the quadratic nonlinearity of the steady-stateequations. As a result, two new linearized versions of the ‘pure’algorithms are analyzed herein. These have similar stabilityproperties and comparable accuracy to the underlying nonlinearmethods.     

PHOTOSENSITIZATION BY SYNTHETIC DIPORPHYRINS AND DICHLORINS in vivo AND in vitro

A group of polycarboxylic diporphyrins, two dichlorins and a porphyrin-chlorine dimer, with rings linked by methylene groups, were examined to help identify structures which can mediate photodynamic tumor eradication in vivo. Among the features sought were short persistence of normal tissue photosensitization and substantial absorbance at wavelengths longer than 630 nm. Both objectives were achieved, with pertinent structure-activity relationships partly characterized. The relative hydrophobicity of the different sensitizers was an important determinant of their accumulation in cell culture, but not of in vivo effectiveness. These compounds showed affinity for protein and high-density lipoprotein components of serum. Their distribution may be mediated by a different mechanism than that which occurs with more hydrophobic sensitizers like hematoporphyrin derivative which have greater affinity for low-density lipoproteins and less for protein components of serum, as compared with the products examined in this study.     

ANALOGS AND DERIVATIVES OF FIREFLY OXYLUCIFERIN, THE LIGHT EMITTER IN FIREFLY BIOLUMINESCENCE

Abstract— The 5-methyl analog of firefly oxyluciferin, two isomeric O-methyl ether derivatives of it and an O, O Ó-dimethyl ether derivative were synthesized and their UV absorption and fluorescence emission spectra were determined. Comparisons of the emission data with the emission wavelength in bioluminescence indicate that the mono-anions of firefly oxyluciferin are candidates for the light-emitters in bioluminescence. Further, we have found that the chemiluminescence of active esters of firefly luciferin produces (from the keto form of oxyluciferin) only red light emission under a variety of conditions; a yellow-green light emission (from the enolic forms of the oxyluciferin product) could not be elicited.     

THE TIME COURSE OF CUTANEOUS PORPHYRIN PHOTOSENSITIZATION IN THE MURINE EAR

This study was designed to investigate the time course of acute cutaneous photosensitivity following administration of Photofrin II using the murine ear swelling response (ESR) as an in vivo end-point. Ros:(ICR) mice were injected with 5 mg/kg Photofrin II and illuminated 7.5 h to 31 days later with 630-nm laser light; ESR was measured 24 h after illumination. There was a direct correlation between ESR and the concentration of [14C]Photofrin II in blood, while no relationship between ESR and the level of [14C]Photofrin II in the ear tissue of exsanguinated mice was evident. Photosensitivity in the mouse foot can be suppressed by preexposure to low doses of light via a photochemical destruction of tissue-bound sensitizer (Boyle and Potter, 1987, Photochem. Photobiol. 46, 997-1001). However, mouse ears pretreated with 84 J/cm2 of 630-nm light (28 J/cm2/day, given 2, 4 and 6 d after injection), a dose sufficient to reduce porphyrin fluorescence in ear tissue by about 75%, prior to the usual light dose (88.6 J/cm2, 630 nm, day 9 after injection) showed a mean ESR not significantly different (P less than 0.5) from that for ears which received only a single dose of 88.6 J/cm2 on day 9. It is concluded, for this animal model, that circulating porphyrin is the source of photoinduced ear-tissue edema and that photobleaching of tissue-bound sensitizer does not attenuate ear-tissue photosensitivity.     

On a Penalty-Perturbation Theory for Plate Problems

A penalty-perturbation method previously proposed by Westbrook(J. Inst. Maths Applics (1974) 14, 79–82) for the solutionsof static bending problems for elastic plates is analysed here.The method replaces the single fourth-order biharmonic equationby a system of three second-order equations which is "singularly"perturbed with respect to a small penalty parameter . The existenceof solutions of the perturbed problem for each > 0 is establishedand the behaviour of these solutions as 0 0 is studied. Inparticular, the results show that while these solutions arecontinuous in at = 0, analyticity in at = 0 is lost exceptin special cases.