Nonlinear Dynamics for Local Fractional Burgers Equation Arising in Fractal Flow

The local fractional Burgers’ equation (LFBE) is investigated from the point of view of local fractional conservation laws envisaging a nonlinear local fractional transport equation with a linear non-differentiable diffusion term. The local fractional derivative transformations and the LFBE conversion to a linear local fractional diffusion equation are analyzed.

Optimization of radial jets mixing in cross-flow of combustion chambers using computational fluid dynamics

Cross-Flow, Radial Jets Mixing, Temperature Homogenization, Optimization, Combustion Chamber, CFD

Telomere length dynamics in human lymphocyte subpopulations measured by flow cytometry.

To measure the average length of telomere repeats at chromosome ends in individual cells we developed a flow cytometry method using fluorescence in situ hybridization (flow FISH) with labeled peptide nucleic acid (PNA) probes. Results of flow FISH measurements correlated with results of conventional telomere length measurements by Southern blot analysis (R = 0.9). Consistent differences in telomere length in CD8+ T-cell subsets were identified. Naive and memory CD4+ T lymphocytes in normal adults differed by around 2.5 kb in telomere length, in agreement with known replicative shortening of telomeres in lymphocytes in vivo. T-cell clones grown in vitro showed stabilization of telomere length after an initial decline and rare clones capable of growing beyond 100 population doublings showed variable telomere length. These results show that flow FISH can be used to measure specific nucleotide repeat sequences in single cells and indicate that the very large replicative potential of lymphocytes is only indirectly related to telomere length.

Dynamics of flow: a nonlinear perspective

The aims of this study are to consider the experience of flow from a nonlinear dynamics perspective. The processes and temporal nature of intrinsic motivation and flow, would suggest that flow experiences fluctuate over time in a dynamical fashion. Thus it can be argued that the potential for chaos is strong. The sample was composed of 20 employees (both full and part time) recruited from a number of different organizations and work backgrounds. The Experience Sampling Method (ESM) was used for data collection. Once obtained the temporal series, they were subjected to various analyses proper to the com- plexity theory (Visual Recurrence Analysis and Surrogate Data Analysis). Results showed that in 80% of the cases, flow presented a chaotic dynamic, in that, flow experiences delineated a complex dynamic whose patterns of change were not easy to predict. Implications of the study, its limitations and future research are discussed.

The dynamics of biofilm bacterial communities is driven by flow wax and wane in a temporary stream

Biofilm communities are exposed to long periods of desiccation in temporary streams. We investigated how water flow intermittency affected the bacterial community structure colonizing three different streambed compartments in a Mediterranean stream. Massive parallel sequencing revealed different bacterial communities in biofilms from sand sediments and cobbles. Bacterial communities were similar (62% of shared operational taxonomic units) in the epipsammic and hyporheic biofilms, and more diverse than those in the epilithic biofilms. The non-flow phase caused a decrease of bacterial diversity in the biofilms, when communities included only bacterial taxa assumed to be adapted to water stress. The most sensitive bacterial communities to flow intermittency were in the epilithic, where the exposure to physical stress was the highest. In sand sediments a wide group of bacterial taxa was tolerant to desiccation. During non-flow the proliferation of opportunistic taxa in the superficial compartments evidenced the biological link with the terrestrial environment. Bacterial communities better tolerate rewetting than desiccation, since a major number of taxa tolerant to rewetting occurred in all biofilms. Overall, bacterial communities in sandy compartments showed higher resistance to flow intermittency than those in epilithic biofilms

Studies on the dynamics and rheology of dilute suspensions of Brownian particles in simple shear flow under the action of an external force

We present a novel approach to computing the orientation moments and rheological properties of a dilute suspension of spheroids in a simple shear flow at arbitrary Peclct number based on a generalised Langevin equation method. This method differs from the diffusion equation method which is commonly used to model similar systems in that the actual equations of motion for the orientations of the individual particles are used in the computations, instead of a solution of the diffusion equation of the system. It also differs from the method of 'Brownian dynamics simulations' in that the equations used for the simulations are deterministic differential equations even in the presence of noise, and not stochastic differential equations as in Brownian dynamics simulations. One advantage of the present approach over the Fokker-Planck equation formalism is that it employs a common strategy that can be applied across a wide range of shear and diffusion parameters. Also, since deterministic differential equations are easier to simulate than stochastic differential equations, the Langevin equation method presented in this work is more efficient and less computationally intensive than Brownian dynamics simulations.We derive the Langevin equations governing the orientations of the particles in the suspension and evolve a procedure for obtaining the equation of motion for any orientation moment. A computational technique is described for simulating the orientation moments dynamically from a set of time-averaged Langevin equations, which can be used to obtain the moments when the governing equations are harder to solve analytically. The results obtained using this method are in good agreement with those available in the literature.The above computational method is also used to investigate the effect of rotational Brownian motion on the rheology of the suspension under the action of an external force field. The force field is assumed to be either constant or periodic. In the case of con- I stant external fields earlier results in the literature are reproduced, while for the case of periodic forcing certain parametric regimes corresponding to weak Brownian diffusion are identified where the rheological parameters evolve chaotically and settle onto a low dimensional attractor. The response of the system to variations in the magnitude and orientation of the force field and strength of diffusion is also analyzed through numerical experiments. It is also demonstrated that the aperiodic behaviour exhibited by the system could not have been picked up by the diffusion equation approach as presently used in the literature.The main contributions of this work include the preparation of the basic framework for applying the Langevin method to standard flow problems, quantification of rotary Brownian effects by using the new method, the paired-moment scheme for computing the moments and its use in solving an otherwise intractable problem especially in the limit of small Brownian motion where the problem becomes singular, and a demonstration of how systems governed by a Fokker-Planck equation can be explored for possible chaotic behaviour.

Viscous Flow and Fluid Dynamics

Exam questions and solutions for a third year maths course. Diagrams for the questions are all together in the support.zip file, as .eps files

Orography in a contour dynamics model of large-scale atmospheric flow

The influence of orography on the structure of stationary planetary Rossby waves is studied in the context of a contour dynamics model of the large-scale atmospheric flow. Orography of infinitesimal and finite amplitude is studied using analytical and numerical techniques. Three different types of orography are considered: idealized orography in the form of a global wave, idealized orography in the form of a local table mountain, and the earth's orography. The study confirms the importance of resonances, both in the infinitesimal orography and in the finite orography cases. With finite orography the stationary waves organize themselves into a one-dimensional set of solutions, which due to the resonances, is piecewise connected. It is pointed out that these stationary waves could be relevant for atmospheric regimes.

Managing the complexity of information flow for construction small and medium-sized enterprises (CSMEs) using system dynamics and collaborative technologies

With the increase in e-commerce and the digitisation of design data and information,the construction sector has become reliant upon IT infrastructure and systems. The design and production process is more complex, more interconnected, and reliant upon greater information mobility, with seamless exchange of data and information in real time. Construction small and medium-sized enterprises (CSMEs), in particular,the speciality contractors, can effectively utilise cost-effective collaboration-enabling technologies, such as cloud computing, to help in the effective transfer of information and data to improve productivity. The system dynamics (SD) approach offers a perspective and tools to enable a better understanding of the dynamics of complex systems. This research focuses upon system dynamics methodology as a modelling and analysis tool in order to understand and identify the key drivers in the absorption of cloud computing for CSMEs. The aim of this paper is to determine how the use of system dynamics (SD) can improve the management of information flow through collaborative technologies leading to improved productivity. The data supporting the use of system dynamics was obtained through a pilot study consisting of questionnaires and interviews from five CSMEs in the UK house-building sector.