Fundamental Steady State Research Articles

On numerical solution stability of the Laplace equation in absence of the Dirichlet boundary condition: Benchmark problem proposal

A fundamental 1D steady state diffusion problem using only third type boundary condition also named as the Robin or Fourier type is analysed. In the heat transfer problems this boundary condition is called convective boundary condition using heat transfer coefficient ( α ) as a constant. The main idea of the proposed Benchmark problem is to test the solution accuracy in both limiting cases of α approaching to zero and to infinity. The infinite case limits to Dirichlet boundary condition and should not be the problem, while the zero limit leads to trivial solution of zeros in the absence of the Dirichlet boundary condition. The application of the Benchmark would be in freeze drying, where similar boundary conditions occur. The presented BEM numerical solution failed for α > 1 0 13 in double precision computation for two 2D formulations: cartesian and axisymmetric. The low limit results failed for α < 1 0 − 13 for cartesian formulation. This is expected, while the failure of axisymmetric formulation results already at moderate low α < 1 0 − 3 value is not. The solution stability and accuracy are found strong dependent to the fundamental solution integrals accuracy. The effect of system matrix preconditioner is also studied.

Adaptively Adjusted Beliefs About Prices in an Evolutive Muthian Cobweb Model

In the present work, starting from the 1D evolutionary Muthian cobweb model in [Hommes &amp; Wagener, 2010], where the economy is populated by biased firms and unbiased fundamentalist firms, we investigate the effects generated by adaptively adjusted beliefs on the long-period price of the goods produced. As in [Hommes &amp; Wagener, 2010], we focus on the case in which the Muthian model is globally stable in the sense of Guesnerie [2002], stable under naive expectations. Coupling into the details, we first assume that just biased producers, being aware of the systematic errors they make in their forecasts, partially rely on an adaptive adjustment of beliefs, obtaining a 3D model, which has a unique steady state. Although in [Hommes &amp; Wagener, 2010] the fundamental steady state is always stable and at most it can coexist with a period-two cycle, we show that the complexity degree increases in our case, where on increasing the reactivity of the evolutionary mechanism, there may be up to two stability thresholds for the steady state, both corresponding to flip bifurcations, and the equilibrium can coexist with a quasiperiodic attractor. On checking the robustness of such outcomes, we contrast them with those we find for the 4D setting, obtained by assuming that unbiased fundamentalists update their belief about the fundamental value partially relying on the same adaptive adjustment mechanism used by biased producers. The outcomes are similar to those of the 3D framework. For instance, in both cases, there exists just the fundamental equilibrium, which can coexist with a quasiperiodic attractor.

Revisiting Paul de Grauwe’s Chaotic Exchange Rate Model: New Analytical Insights and Agent-Based Explorations

We apply recent stability and bifurcation results to provide an analytical characterization of Paul de Grauwe’s chaotic exchange rate model. We prove that the model’s fundamental steady state becomes unstable due to a Neimark-Sacker bifurcation when chartists extrapolate past exchange rate trends too strongly, a phenomenon that gives rise to cyclical exchange rate dynamics. In contrast, fundamentalists’ mean reversion strength only has a stabilizing effect on the model’s dynamics when the exchange rate is out of equilibrium. We also show that agent-based versions of Paul de Grauwe’s exchange rate model may produce endogenous exchange rate dynamics, too.

On the Stability of Equilibrium in Markets with Heterogeneous Investment Horizons

This study incorporates the difference in agents’ trading intervals into the heterogeneous agent model developed by Brock and Hommes (1998). We show that the effect of a longer investment horizon appears as either an increase or a decrease in the fraction of strategy adopted by long-term traders, depending on the values of the risk-free rate in the economy and the variance perceived by traders. Specifically, when long-term traders are fundamentalists and short-term traders are trend followers, we examine whether an increase in the intensity of choice to switch predictors can lead to market instability, which is the main result obtained by Brock and Hommes (1998). This is robust if costs borne by short-term traders are less than those borne by long-term traders. Furthermore, when there is no cost borne by short-term traders who conduct twice as many transactions as long-term traders, the short-term traders’ belief form for establishing the stability of the fundamental steady state becomes more restrictive. This happens if and only if the ratio of variance in the long-term investment horizon to that in the short-term investment horizon is larger than the risk-free rate in the economy.

Time-varying economic dominance in financial markets: A bistable dynamics approach.

By developing a continuous-time heterogeneous agent financial market model of multi-assets traded by fundamental and momentum investors, we provide a potential mechanism for generating time-varying dominance between fundamental and non-fundamental in financial markets. We show that investment constraints lead to the coexistence of a locally stable fundamental steady state and a locally stable limit cycle around the fundamental, characterized by a Bautin bifurcation. This provides a mechanism for market prices to switch stochastically between the two persistent but very different market states, leading to the coexistence and time-varying dominance of seemingly controversial efficient market and price momentum over different time periods. The model also generates other financial market stylized facts, such as spillover effects in both momentum and volatility, market booms, crashes, and correlation reduction due to cross-sectional momentum trading. Empirical evidence based on the U.S. market supports the main findings. The mechanism developed in this paper can be used to characterize time-varying economic dominance in economics and finance in general.

Time-Varying Economic Dominance Through Bistable Dynamics

By developing a continuous-time heterogeneous agent model of multi-assets traded by fundamental and momentum investors, we provide a potential mechanism in generating time-varying dominance between fundamental and non-fundamental in financial market. The deterministic skeleton of the nonlinear model tends to have bistable dynamics, characterized by a Bautin bifurcation, in which a locally stable fundamental steady state coexists with a locally stable limit cycle around the fundamental, leading to two very different market states. Market prices switch stochastically between the two persistent market states, leading to the coexistence of seemingly controversial efficient market and price momentum over different time periods. The model also generates other financial market stylized facts, such as spillover effects in both momentum and volatility, market booms, crashes, and correlation reduction due to cross-sectional momentum trading. Empirical evidence based on US market supports the main findings.

Modified Models and Database for Calculating Cooling Degree-Days for the Egyptian Climates

Abstract: Degree-days techniques are fundamental steady state methods for cooling frameworks analysis. The significance of such techniques shows up in the most recent couple of decades where vitality consumption increments altogether while the world energy assets turn out to be rare. Additionally, these techniques can provide a straightforward approach for the estimation of monthly or annual energy consumptions of air conditioning systems.The issue of building up a cooling degree-days unit for summer air conditioning systems similar to that for heating system has been entangled by the way that energy consumption for summer air conditioning systems is influenced not just by sensible heat transmission (because of dry bulb temperature contrast) but additionally by latent heat load. Endeavors, have been done to make sense of a cooling degree-days unit by including the estimations of the inconvenience list (incorporates both dry bulb and wet bulb temperatures with certain weights) at different time periods daily, then subtracting certain value (usually called base temperature) from this sum.This requires comprehensive temperature records and does not take into account the internal sources of the latent loads (inhabitants, supplies, and so on). Another intricacy is the effect of solar radiation on cooling loads, which is not directly related to any of the ambient temperatures. Besides, many works exhibited comes about for cooling degree-days units utilizing wet bulb temperatures only.In this work, cooling degree-days models are exhibited and connected to most cities in Egypt covering every climatic zone of the country. The models considers the impact of both the sensible heat transmission and the latent (inward and outside) cooling load. They additionally consider the impact of solar heat gain on the cooling degree-days unit. What's more, the impact of base temperature is examined. Correlations between the consequences of the introduced model and cooling degree-days units computed from direct surrounding temperature records are shown.

Path dependent coordination of expectations in asset pricing experiments: A behavioral explanation

In the learning-to-forecast laboratory experiments in Hommes et al. (2005), three different types of aggregate asset price behavior have been observed: monotonic convergence to the stable fundamental steady state, dampened price oscillations and permanent price oscillations. We present a simple behavioral 2-type heuristics switching model explaining individual as well as aggregate behavior in the experiment. Based on relative performance, agents switch between a simple trend following and an anchor and adjustment heuristic that differ in how much weight is given to the long run average price level. The nonlinear switching model exhibits path dependence through co-existence of a locally stable fundamental steady state and a stable (quasi-)periodic orbit, created via a so-called Chenciner bifurcation. Depending on initial states, agents coordinate individual expectations either on a stable fundamental steady state path or on almost self-fulfilling persistent price fluctuations around the fundamental steady state.

On the inherent instability of international financial markets: natural nonlinear interactions between stock and foreign exchange markets

We develop a novel financial market model in which the stock markets of two countries are linked via and with the foreign exchange market. To be precise, there are domestic and foreign speculators in each of the two stock markets which rely either on linear technical or linear fundamental trading strategies to determine their orders. Since foreign stock market speculators require foreign currency to conduct their trades, all three markets are connected. Our setup entails a natural nonlinearity which may cause persistent endogenous price dynamics. Moreover, we analytically show that market interactions can destabilize the model’s fundamental steady state.

Thermodynamic simulation and evaluation of sugar refinery evaporators using a steady state modelling approach

Abstract In a sugar refinery, the juice is concentrated through evaporation, with the objective of concentrating the juice to syrup as rapidly as possible. Because the heat of vaporization of water is relatively high, the evaporation process can be highly energy intensive, and therefore the economical use of steam is important in the refinery. This paper reports on the development of a simulation model for the evaporation sections of two Mauritian sugar refineries. The first objective was to use the simulation model to carry out an energy balance over the evaporators in order to assess the economy of steam usage over the refinery. The second objective was to examine to what extent a fundamental steady state model, based on thermodynamics (not kinetics) was capable of predicting the material and energy flows in two operating sugar refineries and thereby to evaluate the applicability of the modelling framework. The simulation model was validated using historical data as well as data from the plant DCS system. The simulation results generally correlated well with the measured values, except for one of the evaporators on one refinery. Some suggestions were made as to the cause of the discrepancy. On balance, it was found that both refineries are extremely efficient in terms of steam and equipment usage and that there is not much scope for energy optimisation within the present configuration – nor for much spare steam capacity for an additional refinery. It was also shown that steady state process simulation, using thermodynamic models, can generate a very useful representation of a working refinery. Besides being able to use the model to “benchmark” the operation and thus evaluate its performance as a whole as well as across individual units, it could also be used to evaluate refinery performance across refineries, nationally as well as globally.

Does eductive stability imply evolutionary stability?

This note presents a simple example of a model in which the unique rational expectations (RE) steady state equilibrium is eductively stable in the sense of Guesnerie (2002), but where evolutionary learning, as introduced in Brock and Hommes (1997), does not necessarily converge to the RE steady state price. The example is a Muthian cobweb model where producers have heterogeneous expectations and select forecasting strategies based upon recent realized profits. By means of a simple three types example we show that a locally stable RE fundamental steady state may co-exists with a locally stable two-cycle. We also study the Muthian model with a large number of different producer types, and investigate conditions under which an evolutionary adaptive learning process based upon recent realized profits enforces global convergence to the stable RE steady state and when persistent periodic price fluctuations can arise.

Asset price and wealth dynamics in a financial market with heterogeneous agents

This paper considers a discrete-time model of a financial market with one risky asset and one risk-free asset, where the asset price and wealth dynamics are determined by the interaction of two groups of agents, fundamentalists and chartists. In each period each group allocates its wealth between the risky asset and the safe asset according to myopic expected utility maximization, but the two groups have heterogeneous beliefs about the price change over the next period: the chartists are trend extrapolators, while the fundamentalists expect that the price will return to the fundamental. We assume that investors’ optimal demand for the risky asset depends on wealth, as a result of CRRA utility. A market maker is assumed to adjust the market price at the end of each trading period, based on excess demand and on changes of the underlying reference price. The model results in a nonlinear discrete-time dynamical system, with growing price and wealth processes, but it is reduced to a stationary system in terms of asset returns and wealth shares of the two groups. It is shown that the long-run market dynamics are highly dependent on the parameters which characterize agents’ behaviour as well as on the initial condition. Moreover, for wide ranges of the parameters a (locally) stable fundamental steady state coexists with a stable ‘non-fundamental’ steady state, or with a stable closed orbit, where only chartists survive in the long run: such cases require the numerical and graphical investigation of the basins of attraction. Other dynamic scenarios include periodic orbits and more complex attractors, where in general both types of agents survive in the long run, with time-varying wealth fractions.

A robust rational route to randomness in a simple asset pricing model

We investigate asset pricing dynamics in an adaptive evolutionary asset pricing model with fundamentalists, trend followers and a market maker. Agents can choose between a fundamentalist strategy at positive information cost or choose a trend following strategy for free. Price adjustment is proportional to the excess demand in the asset market. Agents asynchronously update their strategy according to realized net profits in the recent past. As agents become more sensitive to differences in strategy performance, the fundamental steady state becomes unstable and multiple steady states may arise. As the traders’ sensitivity to differences in fitness increases, a bifurcation route to chaos sets in due to homoclinic bifurcations of stable and unstable manifolds of the fundamental steady state.

An Evolutionary Adaptive Learning Model with Fundamentalists and Moving Average Traders

In this paper a financial market model with heterogeneous adaptively learning agents is developed. The agents can choose between a fundamental forecasting rule and a technical trading rule. The fundamental forecasting rule predicts that the price returns back to the fundamental value with a certain speed, whereas the technical trading rule is based on moving averages. The model in this paper extends the Brock and Hommes (1998) heterogeneous agents model by adding a moving-average technical trading strategy to the set of beliefs the agents can choose from, but deviates by assuming constant relative risk aversion, so that agents choosing the same forecasting rule invest the same fraction of their wealth in the risky asset. The local dynamical behavior of the model around the fundamental steady state is studied by varying the values of the model parameters. A mixture of theoretical and numerical methods is used to analyze the dynamics. In particular we show that the fundamental steady state may become unstable due to a Hopf bifurcation. The interaction between fundamentalists and technical traders may thus cause prices to deviate from their fundamental value. In this heterogeneous world the fundamental traders are not able to drive the moving average traders out of the market, but fundamentalists and technical analysts coexist forever with the irrelative importance changing over time.

Non-linear effects in the support motion of an elastically mounted slider crank mechanism

A study is made of an in-line slider crank mechanism in which the sliding mass is elastically supported. The ratio of crank length to connecting rod length is not assumed small and relatively large displacements of the support are allowed. Ordinary and parametric non-linear terms are thus retained in the equations of motion. It is shown that the presence of parametric terms gives rise to additional conditions for resonance in the support motion. Approximate solutions are obtained for the fundamental and half subharmonic steady state responses and the effect of the non-linear and parametric terms examined. The stability of the steady state responses is considered and it is shown that instability is associated with a negative slope of the amplitude frequency characteristic.