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The aim of this paper is to investigate whether a Nash equilibrium of a two-country trading economy is symmetry-breaking or not.

The approach to tackle this topic is a theoretical treatment by the general equilibrium trade theory and game theory.

If each government's domestic policy serving private production is diminishing to the private production scale, the Nash equilibrium is not symmetry-breaking.

In the existing study of Chatterjee (2017), a similar result is derived by focusing on the properties of each country's GDP function. The authors, however, consider an economy where each country's PPF is strictly concave and show that the Nash equilibrium uniquely exists and this equilibrium is symmetry.

The two‐dimensional flow field is numerically investigated using a compact finite difference and a pseudo‐spectral method when two fluids with different physical properties are mixing under gravity as well as flow rate. The gravity and the viscous mobility affect the fingering instability, i.e. the mixing range shrinks much at the large viscous mobility or the strong gravity. When the gravitation acts parallel to the main stream, the flow decelerates or accelerates according to its direction. The fingertip velocity is exactly expressed by a pure cosine function and especially invariant when the gravity acts along the −y direction at the high Peclet number. The maximum and fingertip velocities at the very low Peclet number are nearly symmetric with respect to the −y direction perpendicular to the main flow direction x. When the gravity acts along the −y direction, the flow field shows the asymmetry, and a pair of vortices is generated at both the very high Peclet number and less viscous mobility number. As the viscous mobility becomes large, the vortex scale enlarges at the small Peclet number, while the vortices are slightly destroyed at the relatively high Peclet number. As the gravitational angle changes clockwise from downstream to upstream, a pair of vortices evolves through a process of asymmetry.

A two‐dimensional laser surface remelting problem is numerically simulated. The mathematical formulation of this multiphase problem is obtained using a continuum model, constructed from classical mixture theory. This formulation permits the construction of a set of continuum conservation equations for pure or binary, solid‐liquid phase change systems. The numerical resolution of this set of coupled partial differential equations is performed using a finite volume method associated with a PISO algorithm. The numerical results show the modifications caused by an increase of the free surface shear stress (represented by the Reynolds number R_e) upon the stability of the thermocapillary flow in the melting pool. The solutions exhibit a symmetry‐breaking flow transition, oscillatory behaviour at higher values of R_e. Spectral analysis of temperature and velocity signals for particular points situated in the melted pool, show that these oscillations are at first mono‐periodic them new frequencies appear generating a quasi‐periodic behaviour. These oscillations of the flow in the melted pool could induce the deformation of the free surface which in turn could explain the formation of surface ripples observed during laser surface treatments (surface remelting, cladding) or laser welding.

A numerical scheme is proposed to solve double‐diffusive problems using a boundary‐fitted coordinate system to introduce finer grids in the boundary layer regions and an accurate high‐order difference method. Numerical stability is improved by using fourth‐order accurate upwind‐biased differences to approximate the convection terms. The other terms in the governing differential equations are discretized using fourth‐order central difference. To demonstrate the versatility of the boundary‐fitted coordinate system, natural convection in an eccentric annulus is first simulated. The numerical results are consistent with the experimental results by Kuehn and Goldstein and better than the numerical results by Projahn et al. for eccentric cases. Secondly, the symmetry breaking and overturning states in thermohaline‐driven flows in a two‐dimensional rectangular cavity are simulated first to validate the numerical scheme. The numerical results agree well with those by Dijkstra and Molemaker and Quon and Ghil. Finally, the effect of the Lewis number on the flow system is investigated in detail. Depending on the value of the Lewis number, the flow pattern is either stable and symmetric, periodic and oscillatory, or unsymmetric and random.

The purpose of this paper is to simulate and analyze the excitation and propagation of surface plasmon polaritons (SPPs) on sinusoidal metallic gratings in conical mounting.

Chandezon's method has been implemented in MATLAB environment in order to compute the optical response of metallic gratings illuminated under azimuthal rotation. The code allows describing the full optical features both in far- and near-field terms, and the performed analyses highlight the fundamental role of incident polarization on SPP excitation in the conical configuration.

Results of far-field polarization conversion and plasmonic near-field computation clearly show that azimuthally rotated metallic gratings can support propagating surface plasmon with generic polarization.

The recent papers experimentally demonstrated the benefits in sensitivity and the polarization phenomenology that are originated by an azimuthal rotation of the grating. In this work, numerical simulations confirm these experimental results and complete the analysis with a study of the excited SPP near-field on the metal surface.

Computer simulations were done extensively in order to study non‐linear dynamics of laser‐plasma interaction in InSb semiconductor. We constructed the modified Duffing kind of non‐linear semiconductor plasma oscillator equation. Collision frequency is found to be dominant parameter to influence the bifurcation, chaos, hysteresis and bistable effects of plasma wave. Small windows of higher period cascade above the critical value of laser parameter (α₁α₂) in the chaos region are observed. Laser‐plasma exhibits too much chaotic regime at lower value of laser driving frequency (δ). Hysteresis and bistable regions of plasma wave are presented and the conditions for their occurence are identified. The unstable regions completely merge at higher value of effective collision frequency (γ).

This article notes the growing attractiveness of concepts “borrowed” from chaos theory in organizational studies. Many of these interpretations display sentiments broadly congruent with a “postmodern” approach to organization. Indeed chaos theory itself is presented as part of a similar postmodern shift within natural science. However, these sentiments have been subject to stinging criticism by scientists. Here, the deterministic underpinning of chaos theory is used to show that chaos theory is an entirely modernist enterprise. In this case the indeterministic messages taken by organizational theorists are something of a misunderstanding. Consequently, I discuss whether this is enough to threaten the interdisciplinary status of chaos theory, particularly when it is used in a self-consciously ‘metaphorical’ fashion.

Sets out to discuss laminar free convection characteristics of air confined to a square cavity and a horizontal rectangular cavity (aspect ratio A=2) along with the viable isosceles triangular cavities and right‐angle triangular cavities that may be inscribed inside the two original cavities.

The three distinct cavities shared the base wall as the heated wall, while the remaining sides and upper walls are cold. The finite volume method is used to perform the numerical computation of the transient conservation equations of mass, momentum and energy. The methodology takes into account the second‐order‐accurate quick scheme for the discretization of the convective term, whereas the pressure‐velocity coupling is handled with the simple scheme. The working fluid is air, which is not assumed as a Boussinesqian gas, so that all influencing thermophysical properties of air are taken as temperature‐dependent. The cavity problem is examined over a variety of height‐based Grashof numbers ranging from 10³ to 10⁶.

Numerical results are reported for the velocity fields, the temperature field as well as the local and mean wall heat fluxes along the heated base wall. It was found that the airflow remains symmetric for the isosceles triangular cavity with aspect ratio A=1 even at high Grashof numbers. In contrast, for an isosceles triangular cavity with an aspect ratio A=2, a pitchfork bifurcation begins to form at a critical Grashof number of 2 × 10⁵, breaking the airflow symmetry. The computed local and mean heat fluxes along the hot base wall are compared for the three configurations under study and the corresponding maximum heat transfer levels are clearly identified for the two aspect ratios A=1 and 2.

As a continuity of this work, there are two avenues that future research could explore and indeed are presently being explored by the authors within these geometries. The first deals with heat transfer enhancement using mixture of gases. The second is to re‐examine the problem under turbulent conditions.

The present study seeks to maximize the convection heat transport in cavities and minimize their sizes. The peculiarity of the derived cavities is their cross‐section area being half of the cross‐section area of the basic cavities.

One important issue that modern communication theory does not deal with is the physical substratum of information. We advance here the thesis that information is generated by the ever increasing complexity of a “self”‐organizing hierarchical system—which evolves via cascading bifurcations giving rise to broken symmetry. We call “Language” the process which reveals that information, namely the cognitive gadget which “compresses” the complexity generated by broken symmetry‐thereby providing “minimal length” algorithms for triggering an “internal representation” or the replication of the physical system involved. This compressibility has an obvious “survival value” since it allows the possessor of language to reduce and predict a rapidly changing environment. In characterizing language, like any open system far from equilibrium, the usual concept of free energy mediating a conflict between internal energy and entropy—is not only irrelevant but also wrong. The concepts of “complexity” and organization seem here more pertinent.

Our recent results on stability and multiplicity of flow states for confined flows of an incompressible Newtonian fluid are surveyed. The considered laminar flows are caused by either thermal, mechanical, or electromagnetic effects and beyond the stability limit exhibit multiplicity of stable, steady or oscillatory, asymptotic states. Stability diagrams as well as examples of multiple flow states are given. It is concluded that beyond the critical value of the characteristic non‐dimensional parameter, and below the threshold to stochastic or turbulent state, multiple stable asymptotic flow states can be expected. This means that at such flow regimes, any computational (experimental) result may be strongly dependent on its initial condition and/or computational (experimental) path. Uncertainties of experimental and numerical modeling, which follow from this conclusion, are discussed. The global spectral Galerkin method using divergence free basis functions has been employed for the spatial approximation of the velocity and temperature fields. Several numerical experiments were performed comparing the present and other formulations, each of which confirmed the computational efficiency of the present approach over other classical numerical methods.