Normative Conflict & Feuds: The Limits of Self-Enforcement

A normative conflict arises when there exist multiple plausible norms of behavior. In such cases, norm enforcement can lead to a sequence of mutual retaliatory sanctions, which we refer to as a feud. We investigate the hypothesis that normative conflict enhances the likelihood of a feud in a public-good experiment. We find that punishment is much more likely to trigger counter-punishment and start a feud when there is a normative conflict, than in a setting in which no conflict exists. While the possibility of a feud sustains cooperation,the cost of feuding fully offsets the efficiency gains from increased cooperation.normative conflict; peer punishment; feuds; counter-punishment; social norms

Can Real-Effort Investments Inhibit the Convergence of Experimental Markets?

Evidence shows that real-effort investments can affect bilateral bargaining outcomes. This paper investigates whether similar investments can inhibit equilibrium convergence of experimental markets. In one treatment, sellers’ relative effort affects the allocation of production costs, but a random productivity shock ensures that the allocation is not necessarily equitable. In another treatment, sellers’ effort increases the buyers’ valuation of a good. We find that effort investments have a short-lived impact on trading behavior when sellers’ effort benefits buyers, but no effect when effort determines cost allocation. Efficiency rates are high and do not differ across treatments.Property Rights; Real Effort; Posted Offer Markets; Random Shock; Surplus Creation

The evolution of the temperature field during cavity collapse in liquid nitromethane. Part I: inert case

We study the effect of cavity collapse in non-ideal explosives as a means of controlling their sensitivity. The aim is to understand the origin of localised temperature peaks (hot spots) which play a key role at the early stages of ignition. Thus we perform 2D and 3D numerical simulations of shock induced gas-cavity collapse in nitromethane. Ignition is the result of a complex interplay between fluid dynamics and exothermic chemical reaction. To understand the relative contribution between these two processes we consider in this first part of the work the evolution of the physical system in the absence of chemical reactions. We employ a multi-phase mathematical formulation which accounts for the large density difference across the gas-liquid interface without generating spurious temperature peaks. The mathematical and physical models are validated against experimental, analytic and numerical data. Previous studies identified the impact of the upwind side of the cavity wall to the downwind one as the main reason for the generation of a hot-spot outside of the cavity; this is also observed in this work. However, it is apparent that the topology of the temperature field is more complex than previously thought and additional hot spots locations exist, arising from the generation of Mach stems rather than jet impact. To explain the generation mechanisms and topology of the hot spots we follow the complex wave patterns generated and identify the temperature elevation or reduction generated by each wave. This allows to track each hot spot back to its origins. We show that the highest hot spot temperatures can be more than twice the post-incident shock temperature of the neat material and can thus lead to ignition. By comparing the maximum temperature observed in the domain in 2D and 3D simulations we show that 3D calculations are necessary to avoid belated ignition times in reactive scenarios

A multi-physics methodology for the simulation of reactive flow and elastoplastic structural response

We propose a numerical methodology for the numerical simulation of distinct, interacting physical processes described by a combination of compressible, inert and reactive forms of the Euler equations, multiphase equations and elastoplastic equations. These systems of equations are usually solved by coupling finite element and CFD models. Here we solve them simultaneously, by recasting all the equations in the same, hyperbolic form and solving them on the same grid with the same finite-volume numerical schemes. The proposed compressible, multiphase, hydrodynamic formulation can employ a hierarchy of five reactive and non-reactive flow models, which allows simple to more involved applications to be directly described by the appropriate selection. The communication between the hydrodynamic and elastoplastic systems is facilitated by means of mixed-material Riemann solvers at the boundaries of the systems, which represent physical material boundaries. To this end we derive approximate mixed Riemann solvers for each pair of the above models based on characteristic equations. The components for reactive flow and elastoplastic solid modelling are validated separately before presenting validation for the full, coupled systems. Multi-dimensional use cases demonstrate the suitability of the reactive flow-solid interaction methodology in the context of impact-driven initiation of reactive flow and structural response due to violent reaction in automotive (e.g. car crash) or defence (e.g. explosive reactive armour) applications. Several types of explosives (C4, Detasheet, nitromethane, gaseous fuel) in gaseous, liquid and solid state are considered.This work was supported by Jaguar Land Rover and the UK-EPSRC grant EP/K014188/1 as part of the jointly funded Programme for Simulation Innovation

The evolution of the temperature field during cavity collapse in liquid nitromethane. Part II: reactive case

We study effect of cavity collapse in non-ideal explosives as a means of controlling their sensitivity. The main aim is to understand the origin of localised temperature peaks (hot spots) that play a leading order role at early ignition stages. Thus, we perform 2D and 3D numerical simulations of shock induced single gas-cavity collapse in nitromethane. Ignition is the result of a complex interplay between fluid dynamics and exothermic chemical reaction. In part I of this work we focused on the hydrodynamic effects in the collapse process by switching off the reaction terms in the mathematical model. Here, we reinstate the reactive terms and study the collapse of the cavity in the presence of chemical reactions. We use a multi-phase formulation which overcomes current challenges of cavity collapse modelling in reactive media to obtain oscillation-free temperature fields across material interfaces to allow the use of a temperature-based reaction rate law. The mathematical and physical models are validated against experimental and analytic data. We identify which of the previously-determined (in part I of this work) high-temperature regions lead to ignition and comment on their reactive strength and reaction growth rate. We quantify the sensitisation of nitromethane by the collapse of the cavity by comparing ignition times of neat and single-cavity material; the ignition occurs in less than half the ignition time of the neat material. We compare 2D and 3D simulations to examine the change in topology, temperature and reactive strength of the hot spots by the third dimension. It is apparent that belated ignition times can be avoided by the use of 3D simulations. The effect of the chemical reactions on the topology and strength of the hot spots in the timescales considered is studied by comparing inert and reactive simulations and examine maximum temperature fields and their growth rates

A numerical scheme for non-Newtonian fluids and plastic solids under the GPR model

A method for modeling non-Newtonian fluids (dilatants and pseudoplastics) by a power law under the Godunov-Peshkov-Romenski model is presented, along with a new numerical scheme for solving this system. The scheme is also modified to solve the corresponding system for power-law elastoplastic solids. The scheme is based on a temporal operator splitting, with the homogeneous system solved using a finite volume method based on a WENO reconstruction, and the temporal ODEs solved using an analytical approximate solution. The method is found to perform favorably against problems with known exact solutions, and numerical solutions published in the open literature. It is simple to implement, and to the best of the authors’ knowledge it is currently the only method for solving this modified version of the GPR model.EPSRC Centre for Doctoral Training in Computational Methods for Materials Science under grant EP/L015552/

A unified Eulerian framework for multimaterial continuum mechanics

A framework for simulating the interactions between multiple different continua is presented. Each constituent material is governed by the same set of equations, differing only in terms of their equations of state and strain dissipation functions. The interfaces between any combination of fluids, solids, and vacuum are handled by a new Riemann Ghost Fluid Method, which is agnostic to the type of material on either side (depending only on the desired boundary conditions). The Godunov-Peshkov-Romenski (GPR) model is used for modelling the continua (having recently been used to solve a range of problems involving Newtonian and non-Newtonian fluids, and elastic and elastoplastic solids), and this study represents a novel approach for handling multimaterial problems under this model. The resulting framework is simple, yet capable of accurately reproducing a wide range of different physical scenarios. It is demonstrated here to accurately reproduce analytical results for known Riemann problems, and to produce expected results in other cases, including some featuring heat conduction across interfaces, and impact-induced deformation and detonation of combustible materials. The framework thus has the potential to streamline development of simulation software for scenarios involving multiple materials and phases of matter, by reducing the number of different systems of equations that require solvers, and cutting down on the amount of theoretical work required to deal with the interfaces between materials.EPSRC Centre for Doctoral Training in Computational Methods for Materials Science under grant EP/L015552/

A dimensionally split Cartesian cut cell method for the compressible Navier–Stokes equations

We present a dimensionally split method for computing solutions to the compressible Navier-Stokes equations on Cartesian cut cell meshes. The method is globally second order accurate in the L1 norm, fully conservative, and allows the use of time steps determined by the regular grid spacing. We provide a description of the three-dimensional implementation of the method and evaluate its numerical performance by computing solutions to a number of test problems ranging from the nearly incompressible to the highly compressible flow regimes. All the computed results show good agreement with reference results from theory, experiment and previous numerical studies. To the best of our knowledge, this is the first presentation of a dimensionally split cut cell method for the compressible Navier-Stokes equations in the literature

Numerical simulations of immiscible generalised Newtonian fluids

We present a numerical methodology for three-dimensional large-scale simulations of two-fluid flow for generalised Newtonian fluids exhibiting non-Newtonian behaviour such as a non-zero yield stress and power-law dependency on strain-rate. The incompressible continuity and Cauchy momentum equations, along with appropriate rheological models, are solved using a computational framework initially developed at Lawrence Berkeley National Laboratory. The solver uses second-order Godunov method- ology for the advective terms and semi-implicit diffusion in the context of an approximate projection method to evolve the system in time. We have extended the algorithm to en- able the simulation of Herschel-Bulkley fluids by means of a mathematical regularisation of the constitutive equation which describes the fluid rheology. Additionally, interfaces between fluids with different properties are treated using a passively advected indicator function. The performance of the software is validated for two-dimensional displacement flow and tested on a three-dimensional viscoplastic dambreak.Funding and technical support from BP through the BP International Centre for Advanced Materials (BP-ICAM) which made this research possible