Molecular dynamics in arbitrary geometries : parallel evaluation of pair forces

A new algorithm for calculating intermolecular pair forces in molecular dynamics (MD) simulations on a distributed parallel computer is presented. The arbitrary interacting cells algorithm (AICA) is designed to operate on geometrical domains defined by an unstructured, arbitrary polyhedral mesh that has been spatially decomposed into irregular portions for parallelisation. It is intended for nano scale fluid mechanics simulation by MD in complex geometries, and to provide the MD component of a hybrid MD/continuum simulation. The spatial relationship of the cells of the mesh is calculated at the start of the simulation and only the molecules contained in cells that have part of their surface closer than the cut-off radius of the intermolecular pair potential are required to interact. AICA has been implemented in the open source C++ code OpenFOAM, and its accuracy has been indirectly verified against a published MD code. The same system simulated in serial and in parallel on 12 and 32 processors gives the same results. Performance tests show that there is an optimal number of cells in a mesh for maximum speed of calculating intermolecular forces, and that having a large number of empty cells in the mesh does not add a significant computational overhead

Adversarial blockchain queues and trading on a CFMM

We describe a plausible probabilistic model for a blockchain queueing environment in which rational, profit-maximising schedulers impose adversarial disciplines on incoming messages containing a payload that encodes a state transition in a machine. The model can be specialised to apply to chains with fixed or variable block times, traditional priority queue disciplines with `honest' schedulers, or adversarial public mempools. We find conditions under which the model behaves as a bulk-service queue with priority discipline and derive practical expressions for the relative block and message number of a transaction. We study this setup in the context of orders to a CFMM DEX where the execution price a user receives may be quite sensitive to its positioning in the chain -- in particular, to a string of transactions scheduled for prior execution which is not knowable at the time of order creation. We derive statistical models for the price impact of this order flow both in the presence and absence of MEV extraction activity.Comment: 20 pages. Keywords: queue, blockchain, mempool, cfmm, mev, dex, priority discipline, model, sandwich, slippag

A bivariant Yoneda lemma and (∞,2)(\infty,2)-categories of correspondences

Everyone knows that if you have a bivariant homology theory satisfying a base change formula, you get an representation of a category of correspondences. For theories in which the covariant and contravariant transfer maps are in mutual adjunction, these data are actually equivalent. In other words, a 2-category of correspondences is the universal way to attach to a given 1-category a set of right adjoints that satisfy a base change formula . Through a bivariant version of the Yoneda paradigm, I give a definition of correspondences in higher category theory and prove an extension theorem for bivariant functors. Moreover, conditioned on the existence of a 2-dimensional Grothendieck construction, I provide a proof of the aforementioned universal property. The methods, morally speaking, employ the `internal logic' of higher category theory: they make no explicit use of any particular model.Comment: 60 page

Advanced electrostatic ion thruster for space propulsion

The suitability of the baseline 30 cm thruster for future space missions was examined. Preliminary design concepts for several advanced thrusters were developed to assess the potential practical difficulties of a new design. Useful methodologies were produced for assessing both planetary and earth orbit missions. Payload performance as a function of propulsion system technology level and cost sensitivity to propulsion system technology level are among the topics assessed. A 50 cm diameter thruster designed to operate with a beam voltage of about 2400 V is suggested to satisfy most of the requirements of future space missions