Method for determining the shear stress in cylindrical systems

We develop a method for determining the elements of the pressure tensor at a radius r in a cylindrically symmetric system, analogous to the so-called method of planes used in planar systems [B. D. Todd, Denis J. Evans, and Peter J. Daivis, Phys. Rev. E 52, 1627 (1995)]. We demonstrate its application in determining the radial shear stress dependence during molecular dynamics simulations of the forced flow of methane in cylindrical silica mesopores. Such expressions are useful for the examination of constitutive relations in the context of transport in confined systems.

Quantum dynamics as a physical resource

How useful is a quantum dynamical operation for quantum information processing? Motivated by this question, we investigate several strength measures quantifying the resources intrinsic to a quantum operation. We develop a general theory of such strength measures, based on axiomatic considerations independent of state-based resources. The power of this theory is demonstrated with applications to quantum communication complexity, quantum computational complexity, and entanglement generation by unitary operations.

Molecular dynamics simulation of organic-inorganic nanocomposites: Layering behavior and interlayer structure of organoclays

Isothermal-isobaric (NPT) molecular dynamics simulation has been performed to investigate the layering behavior and structure of nanoconfined quaternary alkylammoniums in organoclays. This work is focused on systems consisting of two clay layers and a number of alkylammoniums, and involves the use of modified Dreiding force field. The simulated basal spacings of organoclays agree satisfactorily with the experimental results in the literature. The atomic density profiles in the direction normal to the clay surface indicate that the alkyl chains within the interlayer space of montmorillonite exhibit an obvious layering behavior. The headgroups of long alkyl chains are distributed within two layers close to the clay surface, whereas the distributions of methyl and methylene groups are strongly dependent on the alkyl chain length and clay layer charge. Monolayer, bilayer, and pseudo-trilayer structures are found in organoclays modified with single long alkyl chains, which are identical to the structural models based on the measured basal spacings. A pseudo-quadrilayer structure, for the first time to our knowledge, is also identified in organoclays with double long alkyl chains. In the mixture structure of paraffin-type and multilayer, alkyl chains do not lie flat within a single layer but interlace, and also jump to the next layer in pseudo-trilayer as well as next nearest layer in pseudo-quadrilayer.

Quantum dynamics with stochastic gauge simulations

The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite stochastic time-evolution equations, equivalent to master equations, for many systems including quantum time evolution. The method is illustrated with a variety of simple examples ranging from astrophysical molecular hydrogen production, through to the topical problem of Bose-Einstein condensation in an optical trap and the resulting quantum dynamics.

Fungible dynamics: There are only two types of entangling multiple-qubit interactions

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? It has been shown that all two-body Hamiltonian evolutions can be simulated using any fixed two-body entangling n-qubit Hamiltonian and fast local unitaries. By entangling we mean that every qubit is coupled to every other qubit, if not directly, then indirectly via intermediate qubits. We extend this study to the case where interactions may involve more than two qubits at a time. We find necessary and sufficient conditions for an arbitrary n-qubit Hamiltonian to be dynamically universal, that is, able to simulate any other Hamiltonian acting on n qubits, possibly in an inefficient manner. We prove that an entangling Hamiltonian is dynamically universal if and only if it contains at least one coupling term involving an even number of interacting qubits. For odd entangling Hamiltonians, i.e., Hamiltonians with couplings that involve only an odd number of qubits, we prove that dynamic universality is possible on an encoded set of n-1 logical qubits. We further prove that an odd entangling Hamiltonian can simulate any other odd Hamiltonian and classify the algebras that such Hamiltonians generate. Thus, our results show that up to local unitary operations, there are only two fundamentally different types of entangling Hamiltonian on n qubits. We also demonstrate that, provided the number of qubits directly coupled by the Hamiltonian is bounded above by a constant, our techniques can be made efficient.

A multi-scaled approach for simulating chemical reaction systems

In this paper we give an overview of some very recent work, as well as presenting a new approach, on the stochastic simulation of multi-scaled systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge–Kutta methods and the balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and present a new approach which couples the three regimes mentioned above. We then apply this approach to a biologically inspired problem involving the expression and activity of LacZ and LacY proteins in E. coli, and conclude with a discussion on the significance of this work.

Of sheep and rain: large-scale population dynamics of the red kangaroo

1. We analysed time-series data from populations of red kangaroos (Macropus rufus, Desmarest) inhabiting four areas in the pastoral zone of South Australia. We formulated a set of a priori models to disentangle the relative effects of the covariates: rainfall, harvesting, intraspecific competition, and domestic herbivores, on kangaroo population-growth rate. 2. The statistical framework allowed for spatial variation in the growth-rate parameters, response to covariates, and environmental variability, as well as spatially correlated error terms due to shared environment. 3. The most parsimonious model included all covariates but no area-specific parameter values, suggesting that kangaroo densities respond in the same way to the covariates across the areas. 4. The temporal dynamics were spatially correlated, even after taking into account the potentially synchronizing effect of rainfall, harvesting and domestic herbivores. 5. Counter-intuitively, we found a positive rather than negative effect of domestic herbivore density on the population-growth rate of kangaroos. We hypothesize that this effect is caused by sheep and cattle acting as a surrogate for resource availability beyond rainfall. 6. Even though our system is well studied, we must conclude that approximating resources by surrogates such as rainfall is more difficult than previously thought. This is an important message for studies of consumer-resource systems and highlights the need to be explicit about population processes when analysing population patterns.

On minimal models of process systems

Minimal representations are known to have no redundant elements, and are therefore of great importance. Based on the notions of performance and size indices and measures for process systems, the paper proposes conditions for a process model being minimal in a set of functionally equivalent models with respect to a size norm. Generalized versions of known procedures to obtain minimal process models for a given modelling goal, model reduction based on sensitivity analysis and incremental model building are proposed and discussed. The notions and procedures are illustrated and compared on a simple example, that of a simple nonlinear fermentation process with different modelling goals and on a case study of a heat exchanger modelling. (C) 2004 Elsevier Ltd. All rights reserved.

Simulating Hamiltonian dynamics using many-qudit Hamiltonians and local unitary control

When can a quantum system of finite dimension be used to simulate another quantum system of finite dimension? What restricts the capacity of one system to simulate another? In this paper we complete the program of studying what simulations can be done with entangling many-qudit Hamiltonians and local unitary control. By entangling we mean that every qudit is coupled to every other qudit, at least indirectly. We demonstrate that the only class of finite-dimensional entangling Hamiltonians that are not universal for simulation is the class of entangling Hamiltonians on qubits whose Pauli operator expansion contains only terms coupling an odd number of systems, as identified by Bremner [Phys. Rev. A 69, 012313 (2004)]. We show that in all other cases entangling many-qudit Hamiltonians are universal for simulation.

Optimal unravellings for feedback control in linear quantum systems

For quantum systems with linear dynamics in phase space much of classical feedback control theory applies. However, there are some questions that are sensible only for the quantum case: Given a fixed interaction between the system and the environment what is the optimal measurement on the environment for a particular control problem? We show that for a broad class of optimal (state- based) control problems ( the stationary linear-quadratic-Gaussian class), this question is a semidefinite program. Moreover, the answer also applies to Markovian (current-based) feedback.

Universality of quantum critical dynamics in a planar optical parametric oscillator

We analyze the critical quantum fluctuations in a coherently driven planar optical parametric oscillator. We show that the presence of transverse modes combined with quantum fluctuations changes the behavior of the quantum image critical point. This zero-temperature nonequilibrium quantum system has the same universality class as a finite-temperature magnetic Lifshitz transition.

Characterization of complex quantum dynamics with a scalable NMR information processor

We present experimental results on the measurement of fidelity decay under contrasting system dynamics using a nuclear magnetic resonance quantum information processor. The measurements were performed by implementing a scalable circuit in the model of deterministic quantum computation with only one quantum bit. The results show measurable differences between regular and complex behavior and for complex dynamics are faithful to the expected theoretical decay rate. Moreover, we illustrate how the experimental method can be seen as an efficient way for either extracting coarse-grained information about the dynamics of a large system or measuring the decoherence rate from engineered environments.

Advances in distributed parameter approach to the dynamics and control of activated sludge processes for wastewater treatment

This paper presents a review of modelling and control of biological nutrient removal (BNR)-activated sludge processes for wastewater treatment using distributed parameter models described by partial differential equations (PDE). Numerical methods for solution to the BNR-activated sludge process dynamics are reviewed and these include method of lines, global orthogonal collocation and orthogonal collocation on finite elements. Fundamental techniques and conceptual advances of the distributed parameter approach to the dynamics and control of activated sludge processes are briefly described. A critical analysis on the advantages of the distributed parameter approach over the conventional modelling strategy in this paper shows that the activated sludge process is more adequately described by the former and the method is recommended for application to the wastewater industry (c) 2006 Elsevier Ltd. All rights reserved.

Adverse feedback sequences in exploited marine systems: Are deliberate interruptive actions warranted?

Several mechanisms for self-enhancing feedback instabilities in marine ecosystems are identified and briefly elaborated. It appears that adverse phases of operation may be abruptly triggered by explosive breakouts in abundance of one or more previously suppressed populations. Moreover, an evident capacity of marine organisms to accomplish extensive geographic habitat expansions may expand and perpetuate a breakout event. This set of conceptual elements provides a framework for interpretation of a sequence of events that has occurred in the Northern Benguela Current Large Marine Ecosystem (off south-western Africa). This history can illustrate how multiple feedback loops might interact with one another in unanticipated and quite malignant ways, leading not only to collapse of customary resource stocks but also to degradation of the ecosystem to such an extent that disruption of customary goods and services may go beyond fisheries alone to adversely affect other major global ecosystem concerns (e.g. proliferations of jellyfish and other slimy, stingy, toxic and/or noxious organisms, perhaps even climate change itself, etc.). The wisdom of management interventions designed to interrupt an adverse mode of feedback operation is pondered. Research pathways are proposed that may lead to improved insights needed: (i) to avoid potential 'triggers' that might set adverse phases of feedback loop operation into motion; and (ii) to diagnose and properly evaluate plausible actions to reverse adverse phases of feedback operation that might already have been set in motion. These pathways include the drawing of inferences from available 'quasi-experiments' produced either by short-term climatic variation or inadvertently in the course of biased exploitation practices, and inter-regional applications of the comparative method of science.

First-principles quantum dynamics in interacting Bose gases II: stochastic gauges

First principles simulations of the quantum dynamics of interacting Bose gases using the stochastic gauge representation are analysed. In a companion paper, we showed how the positive-P representation can be applied to these problems using stochastic differential equations. That method, however, is limited by increased sampling error as time evolves. Here, we show how the sampling error can be greatly reduced and the simulation time significantly extended using stochastic gauges. In particular, local stochastic gauges (a subset) are investigated. Improvements are confirmed in numerical calculations of single-, double- and multi-mode systems in the weak-mode coupling regime. Convergence issues are investigated, including the recognition of two modes by which stochastic equations produced by phase-space methods in general can diverge: movable singularities and a noise-weight relationship. The example calculated here displays wave-like behaviour in spatial correlation functions propagating in a uniform 1D gas after a sudden change in the coupling constant. This could in principle be tested experimentally using Feshbach resonance methods.