On trade-off solution pairs in a special type of transportation problem

Abstract is not available.

An approximate mathematical procedure for the determination of characteristic parameters for a general case in three dimensional photoelasticity

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Anomalous plasma heating by an intense laser beam

Heating of laser produced plasmas by an instability is investigated. For intense laser beams anomalous absorption is found. A comparison is made with the experiment.

A Finite Variable Difference Relaxation Scheme for hyperbolic-parabolic equations

Using the framework of a new relaxation system, which converts a nonlinear viscous conservation law into a system of linear convection-diffusion equations with nonlinear source terms, a finite variable difference method is developed for nonlinear hyperbolic-parabolic equations. The basic idea is to formulate a finite volume method with an optimum spatial difference, using the Locally Exact Numerical Scheme (LENS), leading to a Finite Variable Difference Method as introduced by Sakai [Katsuhiro Sakai, A new finite variable difference method with application to locally exact numerical scheme, journal of Computational Physics, 124 (1996) pp. 301-308.], for the linear convection-diffusion equations obtained by using a relaxation system. Source terms are treated with the well-balanced scheme of Jin [Shi Jin, A steady-state capturing method for hyperbolic systems with geometrical source terms, Mathematical Modeling Numerical Analysis, 35 (4) (2001) pp. 631-645]. Bench-mark test problems for scalar and vector conservation laws in one and two dimensions are solved using this new algorithm and the results demonstrate the efficiency of the scheme in capturing the flow features accurately.

Nonlinear saturation of ion-acoustic instability

It is proposed that the wave mediated indirect wave-particle interaction may be responsible for nonlinear saturation of current driven low frequency ion-acoustic turbulence. This process decreases the growth rate and increases the damping rate of the wave. Comparison has been made with some experiments.

Occupational release of engineered nanoparticles: A review

Characterising the release of different types of Engineered Nanoparticles (ENPs) from various processes is of critical importance for the assessment of human exposure, as well as understanding the possible health effects of these particles. Therefore, the main aim of this chapter is to present a comprehensive review of studies which report on the release of airborne ENPs in different nanotechnology workplaces. The chapter will cover topics of relevance to the occupational characterisation of ENP emissions, ranging from the identification of different particle release sources and scenarios, to measurement methods and working towards a more uniform approach to characterisation. Furthermore, a brief review of ENP exposure control strategies, together with the application of mathematical modelling as an effective tool for the characterisation of emissions at nanotechnology workplaces is included.

Calculating the bound spectrum by path summation in action-angle variables

The density of states n(E) is calculated for a bound system whose classical motion is integrable, starting from an expression in terms of the trace of the time-dependent Green function. The novel feature is the use of action-angle variables. This has the advantages that the trace operation reduces to a trivial multiplication and the dependence of n(E) on all classical closed orbits with different topologies appears naturally. The method is contrasted with another, not applicable to integrable systems except in special cases, in which quantization arises from a single closed orbit which is assumed isolated and the trace taken by the method of stationary phase.

Ion heating by the lower hybrid mode

The lower hybrid mode excited in a plasma with cross-field current and density gradient induces an attractive potential between the negative-and positive-energy modes of the plasma. The growth rate is thereby reduced and becomes comparable with the damping rates due to wave-particle interaction. This leads to the saturation of the turbulent field. Some applications have been made to the turbulent heating experiments in plasma where cross-field current is present.

Low carbon fuels and commodity chemicals from waste gases – systematic approach to understand energy metabolism in a model acetogen

Gas fermentation using acetogenic bacteria offers a promising route for the sustainable production of low carbon fuels and commodity chemicals from abundant, inexpensive C1 feedstocks including industrial waste gases, syngas, reformed methane or methanol. Clostridium autoethanogenum is a model gas fermenting acetogen that produces fuel ethanol and 2,3-butanediol, a precursor for nylon and rubber. Acetogens have already been used in large scale industrial fermentations, they are ubiquitous and known to play a prominent role in the global carbon cycle. Still, they are considered to live on the thermodynamic edge of life and potential energy constraints when growing on C1 gases pose a major challange for the commercial production of fuels and chemicals. We have developed a systematic platform to investigate acetogenic energy metabolism, exemplified here by experiments contrasting heterotrophic and autotrophic metabolism. The platform is built from complete omics technologies, augmented with genetic tools and complemented by a manually curated genome-scale mathematical model. Together the tools enable the design and development of new, energy efficient pathways and strains for the production of chemicals and advanced fuels via C1 gas fermentation. As a proof-of-platform, we investigated heterotrophic growth on fructose versus autotrophic growth on gas that demonstrate the role of the Rnf complex and Nfn complex in maintaining growth using the Wood–Ljungdahl pathway. Pyruvate carboxykinase was found to control the rate-limiting step of gluconeogenesis and a new specialized glyceraldehyde-3-phosphate dehydrogenase was identified that potentially enhances anabolic capacity by reducing the amount of ATP consumed by gluconeogenesis. The results have been confirmed by the construction of mutant strains.

Mathematical model and rule extraction for tool wear monitoring problem using nature inspired techniques

In this paper, pattern classification problem in tool wear monitoring is solved using nature inspired techniques such as Genetic Programming(GP) and Ant-Miner (AM). The main advantage of GP and AM is their ability to learn the underlying data relationships and express them in the form of mathematical equation or simple rules. The extraction of knowledge from the training data set using GP and AM are in the form of Genetic Programming Classifier Expression (GPCE) and rules respectively. The GPCE and AM extracted rules are then applied to set of data in the testing/validation set to obtain the classification accuracy. A major attraction in GP evolved GPCE and AM based classification is the possibility of obtaining an expert system like rules that can be directly applied subsequently by the user in his/her application. The performance of the data classification using GP and AM is as good as the classification accuracy obtained in the earlier study.

W physics at the ILC with polarized beams as a probe of the Littlest Higgs model

We study the possibility of using W pair production and leptonic decay of one of the W's at the ILC with polarized beams as a probe of the Littlest Higgs Model. We consider cross-sections, polarization fractions of the W's, leptonic decay energy and angular distributions, and left-right polarization asymmetry as probes of the model. With parameter values allowed by present experimental constraints detectable effects on these observables at typical ILC energies of 500 GeV and 800 GeV will be present. Beam polarization is further found to enhance the sensitivity.

The virial expansion of a classical interacting system

We consider N particles interacting pairwise by an inverse square potential in one dimension (Calogero-Sutherland-Moser model). For a system placed in a harmonic trap, its classical partition function for the repulsive regime is recognised in the literature. We start by presenting a concise re-derivation of this result. The equation of state is then calculated both for the trapped and the homogeneous gas. Finally, the classical limit of Wu's distribution function for fractional exclusion statistics is obtained and we re-derive the classical virial expansion of the homogeneous gas using this distribution function.

Wigner distributions for finite-state systems without redundant phase-point operators

We set up Wigner distributions for N-state quantum systems following a Dirac-inspired approach. In contrast to much of the work in this study, requiring a 2N x 2N phase space, particularly when N is even, our approach is uniformly based on an N x N phase-space grid and thereby avoids the necessity of having to invoke a `quadrupled' phase space and hence the attendant redundance. Both N odd and even cases are analysed in detail and it is found that there are striking differences between the two. While the N odd case permits full implementation of the marginal property, the even case does so only in a restricted sense. This has the consequence that in the even case one is led to several equally good definitions of the Wigner distributions as opposed to the odd case where the choice turns out to be unique.

Special issue on Current Trends in Physics

In 1974, the Russian physicist Vitaly Ginzburg wrote a book entitled `Key Problems of Physics and Astrophysics' in which he presented a selection of important and challenging problems along with speculations on what the future holds. The selection had a broad range, was highly personalized, and was aimed at the general scientist, for whom it made very interesting reading