An obstruction based approach to the Kochen-Specker theorem

In [1] it was shown that the Kochen Specker theorem can be written in terms of the non-existence of global elements of a certain varying set over the partially ordered set of boolean subalgebras of projection operators on some Hilbert space. In this paper, we show how obstructions to the construction of such global elements arise, and how this provides a new way of looking at proofs of the theorem.Comment: 14 pages, 6 figure

Spherically Symmetric Solutions to Fourth-Order Theories of Gravity

Gravitational theories generated from Lagrangians of the form f(R) are considered. The spherically symmetric solutions to these equations are discussed, paying particular attention to features that differ from the standard Schwarzschild solution. The asymptotic form of solutions is described, as is the lack of validity of Birkhoff's theorem. Exact solutions are presented which illustrate these points and their stability and geodesics are investigated.Comment: 10 pages, published versio

Dynamics of a lattice Universe

We find a solution to Einstein field equations for a regular toroidal lattice of size L with equal masses M at the centre of each cell; this solution is exact at order M/L. Such a solution is convenient to study the dynamics of an assembly of galaxy-like objects. We find that the solution is expanding (or contracting) in exactly the same way as the solution of a Friedman-Lema\^itre-Robertson-Walker Universe with dust having the same average density as our model. This points towards the absence of backreaction in a Universe filled with an infinite number of objects, and this validates the fluid approximation, as far as dynamics is concerned, and at the level of approximation considered in this work.Comment: 14 pages. No figure. Accepted version for Classical and Quantum Gravit

Experimental studies on cyclic behaviour of steel base plate connections considering anchor bolts post tensioning

This paper presents the experimental tests on cyclic behaviour of the base plate connections that are connected to the foundation with and without fully post tensioned anchor rods. The main aim is to evaluate these connections that are designed with available design procedures from the low damage aspect. Also, the effect of post tensioning on the seismic performance of this type of connection is presented. To characterize the base plate connection damageability, each column base was designed for a particular major inelastic deformation mode such as anchor rod yielding, yielding of the column, or column and base plate yielding. It is shown that considered joints are not able to be categorized as “a low damage”. Also, post tensioning of the base plate increases the rotational stiffness of the base, and results in more ductility of the column with low axial forc

Cosmological solutions with charged black holes

RB aknowledges support from the Higher Education Commission (HEC) of Pakistan, which provided funding to visit QMUL while this work was performed. TC and JD are supported by the STFC

Experimental investigation of the shearing resistance of SODA-Lime glass at pressures of 9 GPa and strain rates of 10^6 s^(-1)

Pressure-Shear Plate Impact (PSPI) experiments were conducted to measure the high-rate shearing resistance of soda-lime glass at pressures of 9 GPa and at shearing rates of approximately 10^6 s^(−1). Samples of soda lime glass, 5 µm thick, were sandwiched between pure tungsten carbide (WC) plates and impacted by pure WC flyers. Impacting plates were inclined to the direction of approach by an angle of 18°. Normal stress and shearing resistance of the sample were calculated from measured free surface velocities using 1D elastic wave theory. The experimental results show that, at a pressure of 9GPa, the shear stress increases almost linearly up to 1 GPa and then falls quickly to approximately 0.3 GPa — after which it decreases slowly to approximately 0.17 GPa. Comparisons with results of previous experiments on nominally identical samples, impacted to generate lower peak pressures, showed the peak shearing resistance to be much higher at higher pressures; however, the sharp fall in shearing resistance occurs at comparable shear strains (1.5-2)

Experimental investigation of the shearing resistance of SODA-Lime glass at pressures of 9 GPa and strain rates of 10^6 s^(-1)

Pressure-Shear Plate Impact (PSPI) experiments were conducted to measure the high-rate shearing resistance of soda-lime glass at pressures of 9 GPa and at shearing rates of approximately 10^6 s^(−1). Samples of soda lime glass, 5 µm thick, were sandwiched between pure tungsten carbide (WC) plates and impacted by pure WC flyers. Impacting plates were inclined to the direction of approach by an angle of 18°. Normal stress and shearing resistance of the sample were calculated from measured free surface velocities using 1D elastic wave theory. The experimental results show that, at a pressure of 9GPa, the shear stress increases almost linearly up to 1 GPa and then falls quickly to approximately 0.3 GPa — after which it decreases slowly to approximately 0.17 GPa. Comparisons with results of previous experiments on nominally identical samples, impacted to generate lower peak pressures, showed the peak shearing resistance to be much higher at higher pressures; however, the sharp fall in shearing resistance occurs at comparable shear strains (1.5-2)

Teaching and Doing Strategy as an Intentional Strategic Innovation Mindset

There are many important keys in learning, teaching, and doing strategy today. We propose rethinking the learning strategies employed at the MBA level to make the degree more relevant. Recent calls from academia and practice indicate the need to stress adaptability using soft knowledge and skills to make MBA courses more aligned with the realities of strategic decision-making in today’s business environments. We emphasize that while traditional strategic framework models and diagrams have their place, today’s professionals must be prepared to make decisions in unstructured and highly ambiguous situations that traditional models do not address

Cosmologies with Energy Exchange

We provide a simple mathematical description of the exchange of energy between two fluids in an expanding Friedmann universe with zero spatial curvature. The evolution can be reduced to a single non-linear differential equation which we solve in physically relevant cases and provide an analysis of all the possible evolutions. Particular power-law solutions exist for the expansion scale factor and are attractors at late times under particular conditions. We show how a number of problems studied in the literature, such as cosmological vacuum energy decay, particle annihilation, and the evolution of a population of evaporating black holes, correspond to simple particular cases of our model. In all cases we can determine the effects of the energy transfer on the expansion scale factor. We also consider the situation in the presence of anti-decaying fluids and so called phantom fluids which violate the dominant energy conditions.Comment: 12 pages, 1 figur