Universal simulation of Hamiltonian dynamics for quantum systems with finite-dimensional state spaces

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd [Phys. Rev. A 65, 040301(R) (2002)] provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems are qudits, that is, have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries.

Catalytically active Dengue virus NS3 protease forms aggregates that are separable by size exclusion chromatography

An active form of the Dengue virus protease NS3 (CF40.Gly.NS3pro) was expressed in Escherichia coli. This construct consists of a critical 40 amino acid cofactor domain from NS2B fused to the N-terminal 184 amino acid protease domain of NS3 via a flexible, covalent linker (Gly(4)SerGly(4)). The recombinantly produced protein is soluble and has a hexa-histidine tag engineered at the N-terminus for ease of purification using metal affinity chromatography. However, the presence of lower molecular weight impurities after affinity chromatography indicated the need for additional purification steps. The consistent appearance of these impurities suggested that they may be the products of proteolysis and/or auto-proteolysis. The latter possibility was subsequently excluded by the observation of the same impurities in a purified, catalytically inactive form of the recombinant protease (CF40.Gly.NS3pro.SA). Further analysis indicated that these impurities may represent premature translation termination products. Regardless of their origin, they were shown to form various sized aggregates with full-length CF40.Gly.NS3pro that can be separated by size exclusion chromatography, yielding fractions of active protease of sufficient purity for crystallisation trials. The ultimate goal of these studies is to obtain a crystal structure of a catalytically active form of the Dengue virus NS3 protease for structure-based drug design. (C) 2002 Elsevier Science (USA). All rights reserved.

Modelling of microstructure formation and evolution during solidification

A comprehensive probabilistic model for simulating microstructure formation and evolution during solidification has been developed, based on coupling a Finite Differential Method (FDM) for macroscopic modelling of heat diffusion to a modified Cellular Automaton (mCA) for microscopic modelling of nucleation, growth of microstructures and solute diffusion. The mCA model is similar to Nastac's model for handling solute redistribution in the liquid and solid phases, curvature and growth anisotropy, but differs in the treatment of nucleation and growth. The aim is to improve understanding of the relationship between the solidification conditions and microstructure formation and evolution. A numerical algorithm used for FDM and mCA was developed. At each coarse scale, temperatures at FDM nodes were calculated while nucleation-growth simulation was done at a finer scale, with the temperature at the cell locations being interpolated from those at the coarser volumes. This model takes account of thermal, curvature and solute diffusion effects. Therefore, it can not only simulate microstructures of alloys both on the scale of grain size (macroscopic level) and the dendrite tip length (mesoscopic level), but also investigate nucleation mechanisms and growth kinetics of alloys solidified with various solute concentrations and solidification morphologies. The calculated results are compared with values of grain sizes and solidification morphologies of microstructures obtained from a set of casting experiments of Al-Si alloys in graphite crucibles.

A uniform white-noise model for fixed-point roundoff errors in digital systems

Fixed-point roundoff noise in digital implementation of linear systems arises due to overflow, quantization of coefficients and input signals, and arithmetical errors. In uniform white-noise models, the last two types of roundoff errors are regarded as uniformly distributed independent random vectors on cubes of suitable size. For input signal quantization errors, the heuristic model is justified by a quantization theorem, which cannot be directly applied to arithmetical errors due to the complicated input-dependence of errors. The complete uniform white-noise model is shown to be valid in the sense of weak convergence of probabilistic measures as the lattice step tends to zero if the matrices of realization of the system in the state space satisfy certain nonresonance conditions and the finite-dimensional distributions of the input signal are absolutely continuous.

Finite difference time domain (FDTD) method for modeling the effect of switched gradients on the human body in MRI

Numerical modeling of the eddy currents induced in the human body by the pulsed field gradients in MRI presents a difficult computational problem. It requires an efficient and accurate computational method for high spatial resolution analyses with a relatively low input frequency. In this article, a new technique is described which allows the finite difference time domain (FDTD) method to be efficiently applied over a very large frequency range, including low frequencies. This is not the case in conventional FDTD-based methods. A method of implementing streamline gradients in FDTD is presented, as well as comparative analyses which show that the correct source injection in the FDTD simulation plays a crucial rule in obtaining accurate solutions. In particular, making use of the derivative of the input source waveform is shown to provide distinct benefits in accuracy over direct source injection. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and the source injection method has been verified against examples with analytical solutions. Results are presented showing the spatial distribution of gradient-induced electric fields and eddy currents in a complete body model.

Adsorption of aromatic compounds by activated carbon: Effects of functional groups and molecular size

The adsorption of three aromatic compounds on to an untreated carbon was investigated. The solution pH was lowered in all experiments so that all the solutes were in their molecular forms. It was shown that the difference in the maximum adsorption of the solutes was mainly a result of the difference in the sizes of the molecules and their functional groups. Further-more, it was illustrated that the packing arrangement was most likely edge-to-face (sorbate-sorbent) with various tilt angles. On the other hand, the affinity and heterogeneity of the adsorption systems were apparently related to the pK(a) values of the solutes.

Are wing size, wing shape and asymmetry related to field fitness of Trichogramma egg parasitoids?

The effects of wing shape, wing size, and fluctuating asymmetry in these measures oil the field fitness of T. nr. brassicae and T. pretiosum were investigated. Trichogramma wasps mass-reared on eggs of the factitious host Sitotroga cerealella were released in tomato paddocks and those females ovipositing on Helicoverpo spp. eggs were recaptured. Comparisons of the recaptured group with a sample from the release population were used to assess fitness. Wing data were obtained by positioning landmarks on mounted forewings. Size was then measured as the centroid size computed from landmark distances, while Procrustes analysis followed by principal component analysis was used to assess wing shape. Similar findings were obtained for both Trichogramma species: fitness of wasps was strongly related to wing size and some shape dimensions, but not to the asymmetries of these measures. Wasps which performed well in the field had larger wings and a different wing shape compared to wasps from the mass reared population. Both size and the shape dimensions were linearly associated with fitness although there was also some evidence for non-linear selection on shape. The results suggest that wing shape and wing size are reliable predictors of field fitness for these Trichogramma wasps.

Composition and energy density of eggs from two species of freshwater turtle with twofold ranges in egg size

Lipid, protein, ash, carbohydrate and water content and energy density of eggs were measured from different clutches over a range of egg size in two species of freshwater turtle. Dry egg contents consisted of protein (54-60%), lipid (25-31%) and ash (5-6%) while carbohydrate was found to be negligible (

Geographic range size, life history and rates of diversification in Australian mammals

What causes species richness to vary among different groups of organisms? Two hypotheses are that large geographical ranges and fast life history either reduce extinction rates or raise speciation rates, elevating a clade's rate of diversification. Here we present a comparative analysis of these hypotheses using data on the phylogenetic relationships, geographical ranges and life history of the terrestrial mammal fauna of Australia. By comparing species richness patterns to null models, we show that species are distributed nonrandomly among genera. Using sister-clade comparisons to control for clade age, we then find that faster diversification is significantly associated with larger geographical ranges and larger litters, but there is no evidence for an effect of body size or age at first breeding on diversification rates. We believe the most likely explanation for these patterns is that larger litters and geographical ranges increase diversification rates because they buffer species from extinction. We also discuss the possibility that positive effects of litter size and range size on diversification rates result from elevated speciation rates.

Species richness in agamid lizards: chance, body size, sexual selection or ecology?

Why does species richness vary so greatly across lineages? Traditionally, variation in species richness has been attributed to deterministic processes, although it is equally plausible that it may result from purely stochastic processes. We show that, based on the best available phylogenetic hypothesis, the pattern of cladogenesis among agamid lizards is not consistent with a random model, with some lineages having more species, and others fewer species, than expected by chance. We then use phylogenetic comparative methods to test six types of deterministic explanation for variation in species richness: body size, life history, sexual selection, ecological generalism, range size and latitude. Of eight variables we tested, only sexual size dimorphism and sexual dichromatism predicted species richness. Increases in species richness are associated with increases in sexual dichromatism but reductions in sexual size dimorphism. Consistent with recent comparative studies, we find no evidence that species richness is associated with small body size or high fecundity. Equally, we find no evidence that species richness covaries with ecological generalism, latitude or range size.

Difference equations in Banach spaces

Difference equations which discretely approximate boundary value problems for second-order ordinary differential equations are analysed. It is well known that the existence of solutions to the continuous problem does not necessarily imply existence of solutions to the discrete problem and, even if solutions to the discrete problem are guaranteed, they may be unrelated and inapplicable to the continuous problem. Analogues to theorems for the continuous problem regarding a priori bounds and existence of solutions are formulated for the discrete problem. Solutions to the discrete problem are shown to converge to solutions of the continuous problem in an aggregate sense. An example which arises in the study of the finite deflections of an elastic string under a transverse load is investigated. The earlier results are applied to show the existence of a solution; the sufficient estimates on the step size are presented. (C) 2003 Elsevier Science Ltd. All rights reserved.

Modelling the size of the crushed zone around a blasthole

A new model to predict the extent of crushing around a blasthole is presented. The model is based on the back-analysis of a comprehensive experimental program that included the direct measurement of the zone of crushing from 92 blasting tests on concrete blocks using two commercial explosives. The concrete blocks varied from low, medium to high strength and measured 1.5 in in length, 1.0 m in width and 1.1 m in height. A dimensionless parameter called the crushing zone index (CZI) is introduced. This index measures the crushing potential of a charged blasthole and is a function of the borehole pressure, the unconfined compressive strength of the rock material, dynamic Young's modulus and Poisson's ratio. It is shown that the radius of crushing is a function of the CZI and the blasthole radius. A good correlation between the new model and measured results was obtained. A number of previously proposed models could not approximate the conditions measured in the experimental work and there are noted discrepancies between the different approaches reviewed, particularly for smaller diameter holes and low strength rock conditions. The new model has been verified with full scale tests reported in the literature. Results from this validation and model evaluations show its applicability to production blasting. (C) 2003 Elsevier Science Ltd. All rights reserved.