Two-dimensional defective crystals with non-constant dislocation density and unimodular solvable group structure

In Parry and Zyskin [1] we outlined mathematical methods which seemed to be necessary in order to discuss crystal structures with non-constant dislocation density tensor (ddt). This was part of a programme to investigate the geometry of continuously defective crystals and the symmetries of associated discrete structures -- one can think of the programme as an attempt to generalize the use of crystallographic groups as material symmetries in non-linear elasticity theory, for perfect crystals, to deal with the case where defects are present. The methods used rely on the following fact: when the ddt is non-constant, (given technical assumptions), there is a Lie group that acts on the set of material points, and the dimension of the group is strictly greater than that of the ambient space in which the crystal resides. So there is a non-trivial isotropy group associated with the group action. We develop ideas, and recap the requisite mathematical apparatus, in the context of Davini's model of defective crystals, then focus on a particular case where the ddt is such that a solvable three dimensional Lie group acts on a two dimensional crystal state. We construct the corresponding discrete structures too. The paper is an extension of [1], where the analogous group was nilpotent

Драма-антиутопія: до історії терміна

В статті розглянуто історію терміну "драма-антиутопія" і розкрито його змістове наповнення

Fluid dynamic modeling of nano-thermite reactions

This paper presents a direct numerical method based on gas dynamic equations to predict pressure evolution during the discharge of nanoenergetic materials. The direct numerical method provides for modeling reflections of the shock waves from the reactor walls that generates pressure-time fluctuations. The results of gas pressure prediction are consistent with the experimental evidence and estimates based on the self-similar solution. Artificial viscosity provides sufficient smoothing of shock wave discontinuity for the numerical procedure. The direct numerical method is more computationally demanding and flexible than self-similar solution, in particular it allows study of a shock wave in its early stage of reaction and allows the investigation of “slower” reactions, which may produce weaker shock waves. Moreover, numerical results indicate that peak pressure is not very sensitive to initial density and reaction time, providing that all the material reacts well before the shock wave arrives at the end of the reactor

Estimating the volatility of property assets

When an investor is allocating assets between equities, bonds and property, this allocation needs to provide a portfolio with an appropriate risk/return trade-off: for instance, a pension scheme may prefer a robust portfolio that holds its aggregate value in a number of different situations. In order to do this, some estimate needs to be made of the volatility or uncertainty in the property assets, in order to use that in the same way as the volatilities of equities and bonds are used in the allocation. However, property assets are only valued monthly or quarterly (and are sold only rarely) whereas equities and bonds are priced continuously and recorded daily. Currently many actuaries may assume that the volatility of property assets is between those of equities and bonds, but without quantifying it from real data. The challenge for the Study Group is to produce a model for estimating the volatility or uncertainty in property asset values, for use in portfolio planning. The Study Group examined contexts for the use of volatility estimates, particularly in relation to solvency calculations as required by the Financial Services Authority, fund trustees and corporate boards, and it proposed a number of possible approaches. This report summarises that work, and it suggests directions for further investigation

Modeling and simulation of pressure waves generated by nano-thermite reactions

This paper reports the modeling of pressure waves from the explosive reaction of nano-thermites consisting of mixtures of nanosized aluminum and oxidizer granules. Such nanostructured thermites have higher energy density (up to 26 kJ/cm3) and can generate a transient pressure pulse four times larger than that from trinitrotoluene (TNT) based on volume equivalence. A plausible explanation for the high pressure generation is that the reaction times are much shorter than the time for a shock wave to propagate away from the reagents region so that all the reaction energy is dumped into the gaseous products almost instantaneously and thereby a strong shock wave is generated. The goal of the modeling is to characterize the gas dynamic behavior for thermite reactions in a cylindrical reaction chamber and to model the experimentally measured pressure histories. To simplify the details of the initial stage of the explosive reaction, it is assumed that the reaction generates a one dimensional shock wave into an air-filled cylinder and propagates down the tube in a self-similar mode. Experimental data for Al/Bi2O3 mixtures were used to validate the model with attention focused on the ratio of specific heats and the drag coefficient. Model predictions are in good agreement with the measured pressure histories

How Do We Mitigate Against a Marauding Terrorist?

In recent years, worldwide terrorist strategy has changed from long term plan- ning and high impact attacks, to relatively short-term planning, ’marauding’ attacks. In other words, terrorist attacks from 2010 to present have often consisted of a small number of terrorists in densely populated public spaces actively searching out people to maim and kill with weapons that are har- der to regulate, such as knives and vehicles, with little regard for their own survival. This begs the question, therefore, of how we mitigate against these ’marauding terrorists’. If we assume 3 different types of actors: Public, Ter- rorists, and Responders, and assume the strategy of the Terrorists is to kill as many people as possible before they themselves are killed, how can the strategies of the Public and Responders (police, bouncers etc.) be optimised to minimise loss of life? In this report, the problem at hand and important information are compiled before 3 approaches to model a terrorist attack in a public space are considered - a Particle Model, a Discrete Network Model, and a Game Simulation model. Whilst this is by no means a complete list of possible models of a terrorist attack, these were believed to be models that could be developed the most in a week at the ESGI130 at the University of Warwick. For each model type, we first consider their assumptions and suitability to the problem, then model the scenario. Finally, we consider possible extensions to each model, and also how they may be used to evaluate the most effective strategies of the Public and Responders given the information available to them at any one time

Geometrical structure of two-dimensional crystals with non-constant dislocation density

We outline mathematical methods which seem to be necessary in order to discuss crystal structures with non-constant dislocation density tensor(ddt) in some generality. It is known that, if the ddt is constant (in space), then material points can be identified with elements of a certain Lie group, with group operation determined in terms of the ddt - the dimension of the Lie group equals that of the ambient space in which the body resides, in that case. When the ddt is non-constant, there is also a relevant Lie group (given technical assumptions), but the dimension of the group is strictly greater than that of the ambient space. The group acts on the set of material points, and there is a non-trivial isotropy group associated with the group action. We introduce and discuss the requisite mathematical apparatus in the context of Davini's model of defective crystals, and focus on a particular case where the ddt is such that a three dimensional Lie group acts on a two dimensional crystal state - this allows us to construct corresponding discrete structures too

Improved model of an electric calciner for carbon materials

Teknova have 2D steady-state models of the calciner but wish, in the long term, to have a 3D model that can also cover unsteady conditions, and can can model the loss of axisymmetry that someties occurs. Teknova also wish to understand the processes happening around the tip of the upper electrode, in particular the formation of a lip on it and the the shape of the empty region below it. The Study Group proposed potential models for the degree of graphitization, and for the granular flow. Also the Study Group considered the upper electrode in detail. The proposed model for the lip formation is by sublimation of carbon from the hottest parts of the furnace with redeposition in the region around the electrode, which may stick particles onto the electrode surface. In this model the region below the electrode would be a void, roughly a vertex-down conical cavity. The electric field near the lower rim of the electrode will then have a singularity and so the most intense heating of the charge will be around the rim. We conjecture that the reason why the lower electrode lasts so much longer than the upper is that it is not adjacent to a cavity like this, and therefore does not have a singularity in the field.Dept. of Mathematical Sciences, Durham University, and Smith Institut