The circadian oscillator gene GIGANTEA mediates a long-term response of the Arabidopsis thaliana circadian clock to sucrose.

Circadian clocks are 24-h timing devices that phase cellular responses; coordinate growth, physiology, and metabolism; and anticipate the day-night cycle. Here we report sensitivity of the Arabidopsis thaliana circadian oscillator to sucrose, providing evidence that plant metabolism can regulate circadian function. We found that the Arabidopsis circadian system is particularly sensitive to sucrose in the dark. These data suggest that there is a feedback between the molecular components that comprise the circadian oscillator and plant metabolism, with the circadian clock both regulating and being regulated by metabolism. We used also simulations within a three-loop mathematical model of the Arabidopsis circadian oscillator to identify components of the circadian clock sensitive to sucrose. The mathematical studies identified GIGANTEA (GI) as being associated with sucrose sensing. Experimental validation of this prediction demonstrated that GI is required for the full response of the circadian clock to sucrose. We demonstrate that GI acts as part of the sucrose-signaling network and propose this role permits metabolic input into circadian timing in Arabidopsis.

Earthquakes, influenza and cycles of Indian kala-azar.

It is suggested that previous data indicate 3 major epidemics of kala-azar in Assam between 1875 and 1950, with inter-epidemic periods of 30-45 and 20 years. This deviates from the popular view of regular cycles with a 10-20 year period. A deterministic mathematical model of kala-azar is used to find the simplest explanation for the timing of the 3 epidemics, paying particular attention to the role of extrinsic (drugs, natural disasters, other infectious diseases) versus intrinsic (host and vector dynamics, birth and death rates, immunity) processes in provoking the second. We conclude that, whilst widespread influenza in 1918-1919 may have magnified the second epidemic, intrinsic population processes provide the simplest explanation for its timing and synchrony throughout Assam. The model also shows that the second inter-epidemic period is expected to be shorter than the first, even in the absence of extrinsic agents, and highlights the importance of a small fraction of patients becoming chronically infectious (with post kala-azar dermal leishmaniasis) after treatment during an epidemic.

Parameter measurement for heavy-vehicle fuel consumption modelling

A mathematical model is developed to predict the energy consumption of a heavy vehicle. It includes the important factors of heavy-vehicle energy consumption, namely engine and drivetrain performances, losses due to accessories, aerodynamic drag, rolling resistance, road gradients, and driver behaviour. Novel low-cost testing methods were developed to determine engine and drivetrain characteristics. A simple drive cycle was used to validate the model. The model is able to predict the fuel use for a 371 tractor-semitrailer vehicle over a 4 km drive cycle within 1 per cent. This paper demonstrates that accurate and reliable vehicle benchmarking and model parameter measurement can be achieved without expensive equipment overheads, e.g. engine and chassis dynamometers.

Acoustic radiation force of a Bessel beam on a porous sphere.

The possibility of using acoustic Bessel beams to produce an axial pulling force on porous particles is examined in an exact manner. The mathematical model utilizes the appropriate partial-wave expansion method in spherical coordinates, while Biot's model is used to describe the wave motion within the poroelastic medium. Of particular interest here is to examine the feasibility of using Bessel beams for (a) acoustic manipulation of fine porous particles and (b) suppression of particle resonances. To verify the viability of the technique, the radiation force and scattering form-function are calculated for aluminum and silica foams at various porosities. Inspection of the results has shown that acoustic manipulation of low porosity (<0.3) spheres is similar to that of solid elastic spheres, but this behavior significantly changes at higher porosities. Results have also shown a strong correlation between the backscattered form-function and the regions of negative radiation force. It has also been observed that the high-order resonances of the particle can be effectively suppressed by choosing the beam conical angle such that the acoustic contribution from that particular mode vanishes. This investigation may be helpful in the development of acoustic tweezers for manipulation of micro-porous drug delivery carrier and contrast agents.

Quantification of the effects of antibodies on the extra- and intracellular dynamics of Salmonella enterica.

Antibodies are known to be essential in controlling Salmonella infection, but their exact role remains elusive. We recently developed an in vitro model to investigate the relative efficiency of four different human immunoglobulin G (IgG) subclasses in modulating the interaction of the bacteria with human phagocytes. Our results indicated that different IgG subclasses affect the efficacy of Salmonella uptake by human phagocytes. In this study, we aim to quantify the effects of IgG on intracellular dynamics of infection by combining distributions of bacterial numbers per phagocyte observed by fluorescence microscopy with a mathematical model that simulates the in vitro dynamics. We then use maximum likelihood to estimate the model parameters and compare them across IgG subclasses. The analysis reveals heterogeneity in the division rates of the bacteria, strongly suggesting that a subpopulation of intracellular Salmonella, while visible under the microscope, is not dividing. Clear differences in the observed distributions among the four IgG subclasses are best explained by variations in phagocytosis and intracellular dynamics. We propose and compare potential factors affecting the replication and death of bacteria within phagocytes, and we discuss these results in the light of recent findings on dormancy of Salmonella.

The night purging of a two-storey atrium building

We examine the fluid mechanics of night purging in a two-storey naturally ventilated atrium building. We develop a mathematical model of a simplified atrium building and focus on the rate at which warm air purges from each storey and the atrium by displacement ventilation into a still cool night environment of a constant temperature. To develop a first insight into how the geometry of the building influences the rate at which warm air purges from each storey via the atrium we neglect heat exchange with the fabric (so there is no thermal buffering) and furthermore assume that the warm air layers in each storey and the atrium are of uniform temperature. The plumes of warm air that rise from the storeys into the atrium, causing the atrium to fill with warm air, have a very strong influence on the night purge. Modelling these as axisymmetric turbulent plumes, we identify three forms of purging behaviour. Each purge is characterised by five key times identified in the progression of the night purge and physical rationale for these differing behaviours is given. An interface velocity deficit and volumetric purge deficit are introduced as measures of the efficiency of a night purge. © 2010 Elsevier Ltd.

The fluid mechanics of a two-dimensional Aaberg exhaust hood

In this paper a study of the air flow pattern created by a two-dimensional Aaberg exhaust hood local ventilation system is presented. A mathematical model of the flow, in terms of the stream function ψ, is derived analytically for both laminar and turbulent injections of fluid. Streamlines and lines of constant speed deduced from the model are examined for various values of the governing dimensionless operating parameter and predictions are given as to the area in front of the hood from which the air can be sampled. The effect of the injection of fluid on the centre-line velocity of the flow is examined and a comparison of the results with the available experimental data is given. © 1992.

Optimisation of passive and semi-active heavy vehicle suspensions

An investigation into the potential for reducing road damage by optimising the design of heavy vehicle suspensions is described. In the first part of the paper two simple mathematical models are used to study the optimisation of conventional passive suspensions. Simple modifications are made to the steel spring suspension of a tandem axle trailer and it is found experimentally that RMS dynamic tyre forces can be reduced by 15% and theoretical road damage by 5.2%. A mathematical model of an air-sprung articulated vehicle is validated, and its suspension is optimised according to the simple models. This vehicle generates about 9% less damage than the leaf-sprung vehicle in the unmodified state and it is predicted that, for the operating conditions examined, the road damage caused by this vehicle can be reduced by a further 5.4%. Finally, it is shown experimentally that computer-controlled semi-active dampers have the potential to reduce road damage by a further 5-6%, compared to an air suspension with optimum passive damping. © Copyright 1994 Society of Automotive Engineers, Inc.

Robotics and neuroscience: A rhythmic interaction

At the crossing between motor control neuroscience and robotics system theory, the paper presents a rhythmic experiment that is amenable both to handy laboratory implementation and simple mathematical modeling. The experiment is based on an impact juggling task, requiring the coordination of two upper-limb effectors and some phase-locking with the trajectories of one or several juggled objects. We describe the experiment, its implementation and the mathematical model used for the analysis. Our underlying research focuses on the role of sensory feedback in rhythmic tasks. In a robotic implementation of our experiment, we study the minimum feedback that is required to achieve robust control. A limited source of feedback, measuring only the impact times, is shown to give promising results. A second field of investigation concerns the human behavior in the same impact juggling task. We study how a variation of the tempo induces a transition between two distinct control strategies with different sensory feedback requirements. Analogies and differences between the robotic and human behaviors are obviously of high relevance in such a flexible setup. © 2008 Elsevier Ltd. All rights reserved.

Modeling nonlinearities in MEMS oscillators

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude¿frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier-based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases. © 1986-2012 IEEE.

Active control of high frequency vibration in uncertain structures

The active suppression of structural vibration is normally achieved by either feedforward or feedback control. In the absence of a suitable reference signal feedforward control cannot be employed and feedback control is the only viable approach. Conventional feedback control algorithms (e.g. LQR and LQG) are designed on the basis of a mathematical model of the system and ideally the performance of the system should be robust against uncertainties in this model. The aim of this paper is to numerically investigate the robustness of LQR and LQG algorithms by designing the controller for a nominal system, and then assessing (via Monte Carlo simulation) the effects of uncertainties in the system. The ultimate concern is with the control of high frequency vibrations, where the short wavelength of the structural deformation induces a high sensitivity to imperfection. It is found that standard algorithms such as LQR and LQG are generally unfeasible for this case. This leads to a consideration of design strategies for the robust active control of high frequency vibrations. The system chosen for the numerical simulation concerns two coupled plates, which are randomized by the addition of point masses at random locations.

Lymph Node Colonization Dynamics after Oral Salmonella Typhimurium Infection in Mice

An understanding of how pathogens colonize their hosts is crucial for the rational design of vaccines or therapy. While the molecular factors facilitating the invasion and systemic infection by pathogens are a central focus of research in microbiology, the population biological aspects of colonization are still poorly understood. Here, we investigated the early colonization dynamics of Salmonella enterica subspecies 1 serovar Typhimurium (S. Tm) in the streptomycin mouse model for diarrhea. We focused on the first step on the way to systemic infection - the colonization of the cecal lymph node (cLN) from the gut - and studied roles of inflammation, dendritic cells and innate immune effectors in the colonization process. To this end, we inoculated mice with mixtures of seven wild type isogenic tagged strains (WITS) of S. Tm. The experimental data were analyzed with a newly developed mathematical model describing the stochastic immigration, replication and clearance of bacteria in the cLN. We estimated that in the beginning of infection only 300 bacterial cells arrive in the cLN per day. We further found that inflammation decreases the net replication rate in the cLN by 23%. In ccr7-/- mice, in which dendritic cell movement is impaired, the bacterial migration rate was reduced 10-fold. In contrast, cybb-/- mice that cannot generate toxic reactive oxygen species displayed a 4-fold higher migration rate from gut to cLN than wild type mice. Thus, combining infections with mixed inocula of barcoded strains and mathematical analysis represents a powerful method for disentangling immigration into the cLN from replication in this compartment. The estimated parameters provide an important baseline to assess and predict the efficacy of interventions. © 2013 Kaiser et al.

Automated computational modelling for solid mechanics

We present some recent developments in automated computational modelling with an emphasis on solid mechanics applications. The automation process permits an abstract mathematical model of a physical problem to be translated into computer code rapidly and trivially, and can lead to computer code which is faster than hand-written and optimised code. Crucial to the approach is ensuring that mathematical abstractions inherent in the mathematical model are inherited by the software library. © Springer Science+Business Media B.V. 2008.

Training and assignment of multi-skilled workers for implementing seru production systems

Confronted with high variety and low volume market demands, many companies, especially the Japanese electronics manufacturing companies, have reconfigured their conveyor assembly lines and adopted seru production systems. Seru production system is a new type of work-cell-based manufacturing system. A lot of successful practices and experience show that seru production system can gain considerable flexibility of job shop and high efficiency of conveyor assembly line. In implementing seru production, the multi-skilled worker is the most important precondition, and some issues about multi-skilled workers are central and foremost. In this paper, we investigate the training and assignment problem of workers when a conveyor assembly line is entirely reconfigured into several serus. We formulate a mathematical model with double objectives which aim to minimize the total training cost and to balance the total processing times among multi-skilled workers in each seru. To obtain the satisfied task-to-worker training plan and worker-to-seru assignment plan, a three-stage heuristic algorithm with nine steps is developed to solve this mathematical model. Then, several computational cases are taken and computed by MATLAB programming. The computation and analysis results validate the performances of the proposed mathematical model and heuristic algorithm. © 2013 Springer-Verlag London.

Stack ventilation in multi-storey atrium buildings: A dimensionless design approach

Using a simplified mathematical model, a preliminary design strategy for steady stack ventilation in multi-storey atrium buildings is developed. By non-dimensionalising the governing equations of flow, two key dimensionless parameters are identified - a ventilation performance indicator, λ, and atrium enhancement parameter, E - which quantify the performance of the ventilation system and the effectiveness of the atrium in assisting flows. Analytical expressions are determined to inform the vent sizes needed to provide the desired balance between indoor air temperature, ventilation flow rate and heat inputs for any distribution of occupants within the building, and also to ensure unidirectional flow. Dimensionless charts for determining the required combination of design variables are presented with a view to informing first-order design guidance for naturally ventilated buildings. © 2013 Elsevier Ltd.