Numerical exploration of Kaldorian interregional macrodynamics: stability and the trade threshold for business cycles under fixed exchange rates

The stability of equilibrium and the possibility of generation of business cycles in a discrete interregional Kaldorian macrodynamic model with fixed exchange rates are explored using numerical methods. One of the aims is to illustrate the feasibility and effectiveness of the numerical approach for dynamical systems of moderately high dimensionality and several parameters. The model considered is five-dimensional with four parameters, the speeds of adjustment of the goods markets and the degrees of economic interactions between the regions through trade and capital movement. Using a grid search method for the determination of the region of stability of equilibrium in two-dimensional parameter subspaces, and coefficient criteria for the flip bifurcation - and Hopf bifurcation - curve, we determine the stability region in several parameter ranges and identify Hopf bifurcation curves when they exist. It is found that interregional cycles emerge only for sufficient interregional trade. The relevant threshold is predicted by the model at 14 - 16 % of trade transactions. By contrast, no minimum level of capital mobility exists in a global sense as a requirement for the emergence of interregional cycles; the main conclusion being, therefore, that cycles may occur for very low levels of capital mobility if trade is sufficient. Examples of bifurcation and Lyapunov exponent diagrams illustrating the occurrence of cycles or period doubling, and examples of the development of the occurring cycles, are given. Both supercritical and subcritical bifurcations are found to occur, the latter type indicating coexistence of a point and a cyclical attractor.     

Kinematic Simulation of Fully Developed Turbulent Channel Flow

We detail a new method of generating kinematic simulation fields in a channel. We employ a new decomposition for kinematic simulation which ensures that the boundary conditions are automatically satisfied while preserving incompressibility. We impose statistics up to second order, including the Reynolds shear-stress and one-dimensional spectral densities. We observe streak-like structures kinematically similar to those observed in the laboratory, with a similar scaling with the wall-normal distance. We explain the appearance and scaling of the streak-like structures in terms of the two-dimensional spectra imposed on the fields.     

An Integrated Market for Electricity and Natural Gas Systems with Stochastic Power Producers

In energy systems with high shares of weather-driven renewable power sources, gas-fired power plants can serve as a back-up technology to ensure security of supply and provide short-term flexibility. Therefore, a tighter coordination between electricity and natural gas networks is foreseen. In this work, we examine different levels of coordination in terms of system integration and time coupling of trading floors. We propose an integrated operational model for electricity and natural gas systems under uncertain power supply by applying two-stage stochastic programming. This formulation co-optimizes day-ahead and real-time dispatch of both energy systems and aims at minimizing the total expected cost. Additionally, two deterministic models, one of an integrated energy system and one that treats the two systems independently, are presented. We utilize a formulation that considers the linepack of the natural gas system, while it results in a tractable mixed-integer linear programming (MILP) model. Our analysis demonstrates the effectiveness of the proposed model in accommodating high shares of renewables and the importance of proper natural gas system modeling in short-term operations to reveal valuable flexibility of the natural gas system. Moreover, we identify the coordination parameters between the two markets and show their impact on the system’s operation and dispatch.     

Improving chaos-based pseudo-random generators in finite-precision arithmetic

Nonlinear Dynamics - One of the widely-used ways in chaos-based cryptography to generate pseudo-random sequences is to use the least significant bits or digits of finite-precision numbers defined...     

Fast algorithms for greedy triangulation

We present the first quadratic-time algorithm for the greedy triangulation of a finite planar point set, and the first linear-time algorithm for the greedy triangulation of a convex polygon.     

Synthesis of potentially allergenic chiral α-(hydroxyalkyl) acrylates.

The title compounds have been synthesized with 75% enantiomeric excess from Chiral p-tolylsulfoxides 1 and aldehydes, followed by thermal elimination of the sulfoxide.     

The Chen-Type of the Spiral Surfaces

We show that a spiral surface M in E³ is of finite type if and only if M is minimal Also, the plane is the only spiral surface in E³ whose the Gauss map G is of finite type, or satisfies the condition ΔG = ΛG, where Λ ∈ R^3×3.     

Efficient parallel algorithms for shortest paths in planar digraphs

Efficient parallel algorithms are presented, on the CREW PRAM model, for generating a succinct encoding of all pairs shortest path information in a directed planar graphG with real-valued edge costs but no negative cycles. We assume that a planar embedding ofG is given, together with a set ofq faces that cover all the vertices. Then our algorithm runs inO(log² n) time and employsO(nq+M(q)) processors (whereM(t) is the number of processors required to multiply twot×t matrices inO(logt) time). Let us note here that wheneverq<n then our processor bound is better than the best previous one (M(n)).O(log² n) time,n-processor algorithms are presented for various subproblems, including that of generating all pairs shortest path information in a directedouterplanar graph. Our work is based on the fundamental hammock-decomposition technique of G. Frederickson. We achieve this decomposition inO(logn log*n) parallel time by usingO(n) processors. The hammock-decomposition seems to be a fundamental operation that may help in improving efficiency of many parallel (and sequential) graph algorithms.This work was partially supported by the EEC ESPRIT Basic Research Action No. 3075 (ALCOM) and by the Ministry of Industry, Energy and Technology of Greece.     

Structural characterization of polybenzyls by high field 13C-NMR spectroscopy

¹³C-NMR Spectroscopy has been used for the structural characterization of polybenzyls synthesized from the polymerization of benzyl chloride catalyzed by arene chromium tricarbonyls. The ¹³C-chemical shifts for various mono-, di-, tri-, and tetrasubstituted phenyl groups in a polybenzyl have been calculated by the use of additivity parameters and compared with their observed shifts. Although from a theroetical point of view, polysubstitution on a phenyl ring gives rise to a number of isomers, the results indicate the preferential formation of only a few of them due to steric and electronic considerations. Based on quantitative ¹³C-NMR data, several important structural parameters including the percentage of mono-, di-, tri-, and tetrasubstituted phenyl rings in the polybenzyl can be calculated. The extent of branching in a number of polybenzyls prepared under different experimental conditions was determined. The results indicate an increase in branching with the increase in reaction temperature.