On a class of linearizable Monge-Amp\`ere equations

Monge-Amp\`ere equations of the form, $u_{xx}u_{yy}-u_{xy}^2=F(u,u_x,u_y)$ arise in many areas of fluid and solid mechanics. Here it is shown that in the special case $F=u_y^4f(u, u_x/u_y)$, where $f$ denotes an arbitrary function, the Monge-Amp\`ere equation can be linearized by using a sequence of Amp\`ere, point, Legendre and rotation transformations. This linearization is a generalization of three examples from finite elasticity, involving plane strain and plane stress deformations of the incompressible perfectly elastic Varga material and also relates to a previous linearization of this equation due to Khabirov [7]

Two views on neutral money: Wieser and Hayek versus Menger and Mises

Neutral money plays a central role in contemporary macroeconomic theory, and is a live issue in recent monetary policy discussions. We challenge the opinion that Hayek’s writings on neutral money have been influenced by, and are similar to, the work of Menger and Mises. We show, first, the significant alternative influence of Friedrich von Wieser on Hayek’s work on the subject. Second, we rehabilitate a neglected method of monetary theorizing specific to Menger and Mises that rejects money neutrality both as a tool for investigating monetary phenomena and as the standard by which monetary regimes, and the market economy itself, should be evaluated. Examining this chapter in the history of economic thought can aid in a deeper reconsideration of the doctrinal foundations of modern monetary theory and policy

Extreme fluctuations in noisy task-completion landscapes on scale-free networks

We study the statistics and scaling of extreme fluctuations in noisy task-completion landscapes, such as those emerging in synchronized distributed-computing networks, or generic causally-constrained queuing networks, with scale-free topology. In these networks the average size of the fluctuations becomes finite (synchronized state) and the extreme fluctuations typically diverge only logarithmically in the large system-size limit ensuring synchronization in a practical sense. Provided that local fluctuations in the network are short-tailed, the statistics of the extremes are governed by the Gumbel distribution. We present large-scale simulation results using the exact algorithmic rules, supported by mean-field arguments based on a coarse-grained description.Comment: 16 pages, 6 figures, revte

Mobility induces global synchronization of oscillators in periodic extended systems

We study synchronization of locally coupled noisy phase oscillators which move diffusively in a one-dimensional ring. Together with the disordered and the globally synchronized states, the system also exhibits several wave-like states which display local order. We use a statistical description valid for a large number of oscillators to show that for any finite system there is a critical spatial diffusion above which all wave-like solutions become unstable. Through Langevin simulations, we show that the transition to global synchronization is mediated by the relative size of attractor basins associated to wave-like states. Spatial diffusion disrupts these states and paves the way for the system to attain global synchronization

High shock release in ultrafast laser irradiated metals: Scenario for material ejection

We present one-dimensional numerical simulations describing the behavior of solid matter exposed to subpicosecond near infrared pulsed laser radiation. We point out to the role of strong isochoric heating as a mechanism for producing highly non-equilibrium thermodynamic states. In the case of metals, the conditions of material ejection from the surface are discussed in a hydrodynamic context, allowing correlation of the thermodynamic features with ablation mechanisms. A convenient synthetic representation of the thermodynamic processes is presented, emphasizing different competitive pathways of material ejection. Based on the study of the relaxation and cooling processes which constrain the system to follow original thermodynamic paths, we establish that the metal surface can exhibit several kinds of phase evolution which can result in phase explosion or fragmentation. An estimation of the amount of material exceeding the specific energy required for melting is reported for copper and aluminum and a theoretical value of the limit-size of the recast material after ultrashort laser irradiation is determined. Ablation by mechanical fragmentation is also analysed and compared to experimental data for aluminum subjected to high tensile pressures and ultrafast loading rates. Spallation is expected to occur at the rear surface of the aluminum foils and a comparison with simulation results can determine a spall strength value related to high strain rates

Commensurability and beyond: from Mises and Neurath to the future of the socialist calculation debate

Mises' 'calculation argument' against socialism argues that monetary calculation is indispensable as a commensurable unit for evaluating factors of production. This is not due to his conception of rationality being purely 'algorithmic,' for it accommodates non-monetary, incommensurable values. Commensurability is needed, rather, as an aid in the face of economic complexity. The socialist Neurath's response to Mises is unsatisfactory in rejecting the need to explore possible non-market techniques for achieving a certain degree of commensurability. Yet Neurath's contribution is valuable in emphasizing the need for a balanced, comparative approach to the question of market versus non-market that puts the commensurability question in context. These central issues raised by adversaries in the early socialist calculation debate have continued relevance for the contemporary discussion

Quantum-like Representation of Extensive Form Games: Wine Testing Game

We consider an application of the mathematical formalism of quantum mechanics (QM) outside physics, namely, to game theory. We present a simple game between macroscopic players, say Alice and Bob (or in a more complex form - Alice, Bob and Cecilia), which can be represented in the quantum-like (QL) way -- by using a complex probability amplitude (game's ``wave function'') and noncommutative operators. The crucial point is that games under consideration are so called extensive form games. Here the order of actions of players is important, such a game can be represented by the tree of actions. The QL probabilistic behavior of players is a consequence of incomplete information which is available to e.g. Bob about the previous action of Alice. In general one could not construct a classical probability space underlying a QL-game. This can happen even in a QL-game with two players. In a QL-game with three players Bell's inequality can be violated. The most natural probabilistic description is given by so called contextual probability theory completed by the frequency definition of probability