Narrow Results

We consider the execution of a complex application on a heterogeneous "grid" computing platform. The complex application consists of a suite of identical, independent problems to be solved. In turn, each problem consists of a set of tasks. There are dependences (precedence constraints) between these tasks and these dependences are organized as a tree. A typical example is the repeated execution of the same algorithm on several distinct data samples. We use a non-oriented graph to model the grid platform, where resources have different speeds of computation and communication. We show how to determine the optimal steady-state scheduling strategy for each processor (the fraction of time spent computing and the fraction of time spent communicating with each neighbor). This result holds for a quite general framework, allowing for cycles and multiple paths in the platform graph.

Morphogens, such as Decapentaplegic (Dpp) in Drosophila wing disc, are locally produced and spread to other regions in organs, forming gradients that control the interrelated pattern and growth of developing organs. During development, morphogen gradients must be robust to changes in intracellular and extracellular environments so as to provide target genes precise information to determine cell fates and the resulting spatial pattern on the proper position and at the proper time. However, how tissue growth affects the robust formation of morphogen gradient remains to be fully explored. Here, we model, using a reaction–advection–diffusion equation, a morphogen transport mechanism including tissue growth. By introducing and analyzing a robustness index that measures the effect of tissue growth on the formation of the morphogen gradient, we demonstrate that tissue growth can enlarge the range of morphogen gradient. In particular, tissue growth in the region near the source can efficiently filter the shift resulting from the changes in the production rate in each of steady-state and pre-steady-state situations, but the efficiency depends on growth rate and spatial position in either situation as well as on the time of development in the pre-steady-state situation. These results indicate that tissue growth is an nonnegligible factor for the robust formation of morphogen gradient.

We study numerically a system of two lasers cross-coupled optoelectronically with a time delay where the output intensity of each laser modulates the pump current of the other laser. We demonstrate control of chaos via variable coupling time delay by converting the laser intensity chaos to the steady-state. We also show that wavelength chaos in an electrically tunable distributed Bragg reflector (DBR) laser diode with a feedback loop that can be controlled via variable feedback time delay.

Trapping of hot electron behavior by trap centers located in the buffer layer of a wurtzite phase GaN MESFET has been simulated using an ensemble Monte Carlo simulation. The simulated results show that trap centers are responsible for current collapse in GaN MESFET at low temperatures. These electrical traps degrade the performance of the device at low temperatures. On the other hand, at high temperatures, the electrical performances are improved due to electron emission from the trap centers. The simulated device geometries and doping are matched to the nominal parameters described for the experimental structures as closely as possible, and the predicted drain current and other electrical characteristics for the simulated device including the trapping center effects show much closer agreement with the available experimental data than without trap center effects.

Monte Carlo simulation of electron transport in a GaN diode of n⁺nn⁺ structure with a 0.4 or 0.6 μm long active layer is described. The anode voltage ranges from 10 to 50 V. The distributions of electron energies and electron velocities, and the profiles of the electron density, electric field, potential and average electron velocity are computed. Based on these data, the near ballistic nature of the electron transport in the 0.4 μm-long diode and the importance of the back-scattering of electrons from the anode n⁺-layer are discussed. Also, the effects of the lattice temperature and doping on the length of the active layer are discussed.

An ensemble Monte Carlo simulation has been used to model bulk electron transport at 300 K for both the natural wurtzite and the zincblende lattice phases of GaN. Electronic states within the conduction band are represented by non-parabolic ellipsoidal valleys centred on important symmetry points of the Brillouin zone, but for zincblende GaN, the simpler spherical parabolic band approximation has also been tested, for comparison. In the case of wurtzite GaN, transport has been modeled with an electric field applied both parallel and perpendicular to the (0001) c-axis. The steady state velocity-field characteristics are in fair agreement with other recent calculations.

An ensemble Monte Carlo simulation is used to compare bulk electron transport in wurtzite phase GaN, AlN and InN materials. Electronic states within the conduction band valleys at the Γ₁, U, M, Γ₃ and K are represented by non-parabolic ellipsoidal valleys centered on important symmetry points of the Brillouin zone. For all materials, it is found that electron velocity overshoot only occurs when the electric field is increased to a value above a certain critical field, unique to each material. This critical field is strongly dependent on the material parameters. Transient velocity overshoot has also been simulated, with the sudden application of fields up to ~5 × 10⁷Vm^-1, appropriate to the gate-drain fields expected within an operational field effect transistor. The electron drift velocity relaxes to the saturation value of ~1.4 × 10⁵ms^-1 within 4 ps, for all crystal structures. The steady state and transient velocity overshoot characteristics are in fair agreement with other recent calculations.

An ensemble Monte Carlo simulation is used to compare high field electron transport in bulk InAs, InP and GaAs. In particular, velocity overshoot and electron transit times are examined. For all materials, we find that electron velocity overshoot only occurs when the electric field is increased to a value above a certain critical field, unique to each material. This critical field is strongly dependent on the material, about 400 kVm^-1 for the case of GaAs, 300 kVm^-1 for InAs and 700 kVm^-1 for InP. We find that InAs exhibits the highest peak overshoot velocity and that this velocity overshoot lasts over the longest distances when compared with GaAs and InP. Finally, we estimate the minimum transit time across a 1 μm GaAs sample to be a bout 3 ps. Similar calculations for InAs and InP yield 2.2 and 5 ps, respectively. The steady-state and transient velocity overshoot characteristics are in fair agreement with other recent calculations.

The steady-state and transient electron transport in ZnO field effect transistor have been studied using an ensemble Monte Carlo simulation which takes into account the hot-electron transport phenomena. The simulated device geometries and doping are matched to the nominal parameters described for the experimental structures as closely as possible, and the predicted I–V and transfer charateristics for the intrinsic devices show fair agreement with the available experimental data. Simulations of the effect of modulating the gate bias have also been carried out to test the device response and derived the frequency bandwidth. The value of 80 ± 5 GHz has been derived for the intrinsic current gain cut-off frequency of the ZnO MESFETs.

This paper is concerned with the spatiotemporal heterogeneity in a modified Leslie–Gower predator–prey system with Beddington–DeAngelis functional response and prey-taxis. Using Crandall–Rabinowitz bifurcation theory, we investigate the steady-state bifurcation of the nonlinear system by choosing the prey-tactic sensitivity coefficient as a bifurcating parameter. It is rigorously proved that a branch of nonconstant solution exists near the positive equilibrium when the prey-tactic sensitivity is repulsive. Moreover, we study the existence, direction and stability of periodic orbits around the interior constant equilibrium by selecting the intrinsic growth rate of the prey as a bifurcating parameter. A priori estimates play a critical role in the verification procedure. Some numerical simulations are carried out to support our main theoretical results.

We define two conformal structures on S¹ which give rise to a different view of the affine curvature flow and a new curvature flow, the "Q-curvature flow". The steady states of these flows are studied. More specifically, we prove four sharp inequalities, which state the existence of the corresponding extremal metrics.

This paper is concerned with the thermoelastic analysis of a functionally graded rotating annular disk subjected to a nonuniform steady-state thermal load. Material properties are assumed to be temperature independent and continuously varying in the radial direction of the annular disk. The variations of Young's modulus, material density, thermal expansion and conductivity coefficients are represented by a novel exponential-law distribution through the radial direction of the disk, but Poission's ratio is kept constant. The governing differential equations are exactly satisfied at every point of the disk. Exact solutions for the temperature and stress fields are derived in terms of an exponential integral and Whittaker's functions. Presented are some results for stress, strain and displacement components due to thermal bending of the rotating disk. The effects of angular velocity, inner and outer temperature loads and material properties on the stress, strain and displacement components are discussed.

The free energy perturbation technique employing molecular dynamics simulations is more powerful than may be at first apparent. Intrinsically, one can obtain energies and possibly other expectation values even under decidedly non-equilibrium conditions. Interesting questions are thereby raised about irreversible processes, ergodicity, and time-ordering. Techniques and formulas are presented herein with which to extend the power of simulations into the far-from-equilibrium regime to identify "natural" steady-state regimes, where, ordinarily, one would expect the effects of nonergodicity to limit the utility of such simulations.

The steady-state chronoamperometric current for an EC′ reactions at spheroidal ultramicroelectrodes is derived from the non-steady-state diffusion limited current. The polynomial expressions pertaining to two extreme limits of reaction rates are combined for all reaction rates. Starting with the result for spheroidal electrode, equations are obtained for the steady-state currents at disc, oblate, hemisphere and prolate electrodes. Tabular compilation of dimensionless current for disc electrodes are reported. A good agreement with previously available simulation results is noticed.

The software WinStes, developed by our group, is used to derive the strict steady-state initial rate equation of the reaction mechanism of CTP:sn-glycerol-3-phosphate cytidylyltransferase [EC 2.7.7.39] from Bacillus subtilis. This enzyme catalyzes a reaction with two substrates and operates by a random ordered binding mechanism with two molecules of each substrate. The accuracy of the steady-state rate equation derived is checked by comparing the rate values it provides with those obtained from the simulated progress curves. To analyze the kinetics of this enzyme using the strict steady-state initial rate equation, several curves for different substrate concentrations and different rate constants are generated. A comparison of these curves with the curves obtained from the rapid equilibrium initial rate equation, with different substrate concentration values, serves to analyze how the strict steady-state rate equation values are closer to those of rapid equilibrium rate equations when rapid equilibrium conditions are fulfilled.

With the recent advances in experimental technologies, such as gas chromatography and mass spectrometry, the number of metabolites that can be measured in biofluids of individuals has markedly increased. Given a set of such measurements, a very common task encountered by biologists is to identify the metabolic mechanisms that lead to changes in the concentrations of given metabolites and interpret the metabolic consequences of the observed changes in terms of physiological problems, nutritional deficiencies, or diseases. In this paper, we present the steady-state metabolic network dynamics analysis (SMDA) approach in detail, together with its application in a cystic fibrosis study. We also present a computational performance evaluation of the SMDA tool against a mammalian metabolic network database. The query output space of the SMDA tool is exponentially large in the number of reactions of the network. However, (i) larger numbers of observations exponentially reduce the output size, and (ii) exploratory search and browsing of the query output space is provided to allow users to search for what they are looking for.