Production delays, supply distortions and endogenous price dynamics

It takes time to produce commodities, and different production technologies may take different lengths of time. Suppose that firms may switch between different production technologies that take different lengths of time. A natural implication of such a scenario is that not all firms would then offer their commodities in every period, i.e. firms’ total supply schedule would become a time-varying quantity. Based on a behavioral cobweb framework, we analytically demonstrate that commodity markets become unstable when firms switch too rapidly between production technologies that take different lengths of time. In particular, we observe that supply distortions lead to endogenous commodity price dynamics due to a mismatch between supply and demand

The Emergence ofBull and BearDynamics in a Nonlinear Model of Interacting Markets

We develop a three-dimensional nonlinear dynamic model in which the stock markets of two countries are linked through the foreign exchange market. Connections are due to the trading activity of heterogeneous speculators. Using analytical and numerical tools, we seek to explore how the coupling of the markets may affect the emergence ofbull and bearmarket dynamics. The dimension of the model can be reduced by restricting investors' trading activity, which enables the dynamic analysis to be performed stepwise, from low-dimensional cases up to the full three-dimensional model. In our paper we focus mainly on the dynamics of the one- and two- dimensional cases, with numerical experiments and some analytical results, and also show that the main features persist in the three-dimensional model

Application of an improved global-scale groundwater model for water table estimation across New Zealand

Many studies underline the importance of groundwater assessment at the larger, i.e. global, scale. The groundwater models used for these assessments are dedicated to the global scale and therefore not often applied for studies in smaller areas, e.g. catchments, because of their simplifying assumptions. In New Zealand, advanced numerical groundwater flow models have been applied in several catchments. However, that application is piecemeal: only for a limited amount of aquifers and through a variety of groundwater model suites, formats, and developers. Additionally, there are large areas where groundwater models and data are sparse. Hence, an inter-catchment, inter-regional, or nationwide overview of important groundwater information, such as the water table, does not exist. The investment needed to adequately cover New Zealand with high-resolution groundwater models in a consistent approach would be significant and is therefore not considered possible at this stage. This study proposes a solution that obtains a nationwide overview of groundwater that bridges the gap between the (too-)expensive advanced local models and the (too-)simple global-scale models. We apply an existing, global-scale, groundwater flow model and improve it by feeding in national input data of New Zealand terrain, geology, and recharge, and by slight adjustment of model parametrisation and model testing. The resulting nationwide maps of hydraulic head and water table depths show that the model points out the main alluvial aquifers with fine spatial detail (200&thinsp;m grid resolution). The national input data and finer spatial detail result in better and more realistic variations of water table depth than the original, global-scale, model outputs. In two regional case studies in New Zealand, the hydraulic head shows excellent correlation with the available groundwater level data. Sensitivity and other analyses of our nationwide water tables show that the model is mostly driven by recharge, model resolution, and elevation (gravity), and impeded by the geology (permeability). The use of this first dedicated New Zealand-wide model can aid in provision of water table estimates in data-sparse regions. The national model can also be used to solve inconsistency of models in areas of trans-boundary aquifers, i.e. aquifers that cover more than one region in New Zealand. Comparison of the models, i.e. the national application (National Water Table model: NWT) with the global model (Equilibrium Water Table model: EWT), shows that most improvement is achieved by feeding in better and higher-resolution input data. The NWT model still has a bias towards shallow water tables (but less than the EWT model because of the finer model resolution), which could only be solved by feeding in a very high resolution terrain model that incorporates drainage features. Although this is a model shortcoming, it can also be viewed as a valuable indicator of the pre-human water table, i.e. before 90&thinsp;% of wetlands were drained for agriculture since European settlement in New Zealand. Calibration to ground-observed water level improves model results but can of course only work where there are such data available. Future research should therefore focus on both model improvements and more data-driven, improved estimation of hydraulic conductivity, recharge, and the digital elevation model. We further surmise that the findings of this study, i.e. successful application of a global-scale model at smaller scales, will lead to subsequent improvement of the global-scale model equations.</p

The silicon trypanosome

African trypanosomes have emerged as promising unicellular model organisms for the next generation of systems biology. They offer unique advantages, due to their relative simplicity, the availability of all standard genomics techniques and a long history of quantitative research. Reproducible cultivation methods exist for morphologically and physiologically distinct life-cycle stages. The genome has been sequenced, and microarrays, RNA-interference and high-accuracy metabolomics are available. Furthermore, the availability of extensive kinetic data on all glycolytic enzymes has led to the early development of a complete, experiment-based dynamic model of an important biochemical pathway. Here we describe the achievements of trypanosome systems biology so far and outline the necessary steps towards the ambitious aim of creating a , a comprehensive, experiment-based, multi-scale mathematical model of trypanosome physiology. We expect that, in the long run, the quantitative modelling enabled by the Silicon Trypanosome will play a key role in selecting the most suitable targets for developing new anti-parasite drugs

Minimal Brownian Ratchet: An Exactly Solvable Model

We develop an exactly-solvable three-state discrete-time minimal Brownian ratchet (MBR), where the transition probabilities between states are asymmetric. By solving the master equations we obtain the steady-state probabilities. Generally the steady-state solution does not display detailed balance, giving rise to an induced directional motion in the MBR. For a reduced two-dimensional parameter space we find the null-curve on which the net current vanishes and detailed balance holds. A system on this curve is said to be balanced. On the null-curve, an additional source of external random noise is introduced to show that a directional motion can be induced under the zero overall driving force. We also indicate the off-balance behavior with biased random noise.Comment: 4 pages, 4 figures, RevTex source, General solution added. To be appeared in Phys. Rev. Let

Unifying thermodynamic and kinetic descriptions of single-molecule processes: RNA unfolding under tension

We use mesoscopic non-equilibrium thermodynamics theory to describe RNA unfolding under tension. The theory introduces reaction coordinates, characterizing a continuum of states for each bond in the molecule. The unfolding considered is so slow that one can assume local equilibrium in the space of the reaction coordinates. In the quasi-stationary limit of high sequential barriers, our theory yields the master equation of a recently proposed sequential-step model. Non-linear switching kinetics is found between open and closed states. Our theory unifies the thermodynamic and kinetic descriptions and offers a systematic procedure to characterize the dynamics of the unfolding processComment: 13 pages, 3 figure

Generalized Smoluchowski equation with correlation between clusters

In this paper we compute new reaction rates of the Smoluchowski equation which takes into account correlations. The new rate K = KMF + KC is the sum of two terms. The first term is the known Smoluchowski rate with the mean-field approximation. The second takes into account a correlation between clusters. For this purpose we introduce the average path of a cluster. We relate the length of this path to the reaction rate of the Smoluchowski equation. We solve the implicit dependence between the average path and the density of clusters. We show that this correlation length is the same for all clusters. Our result depends strongly on the spatial dimension d. The mean-field term KMFi,j = (Di + Dj)(rj + ri)d-2, which vanishes for d = 1 and is valid up to logarithmic correction for d = 2, is the usual rate found with the Smoluchowski model without correlation (where ri is the radius and Di is the diffusion constant of the cluster). We compute a new rate: the correlation rate K_{i,j}^{C} (D_i+D_j)(r_j+r_i)^{d-1}M{\big(\frac{d-1}{d_f}}\big) is valid for d \leq 1(where M(\alpha) = \sum+\infty i=1i\alphaNi is the moment of the density of clusters and df is the fractal dimension of the cluster). The result is valid for a large class of diffusion processes and mass radius relations. This approach confirms some analytical solutions in d 1 found with other methods. We also show Monte Carlo simulations which illustrate some exact new solvable models

Langevin dynamics with dichotomous noise; direct simulation and applications

We consider the motion of a Brownian particle moving in a potential field and driven by dichotomous noise with exponential correlation. Traditionally, the analytic as well as the numerical treatments of the problem, in general, rely on Fokker-Planck description. We present a method for direct numerical simulation of dichotomous noise to solve the Langevin equation. The method is applied to calculate nonequilibrium fluctuation induced current in a symmetric periodic potential using asymmetric dichotomous noise and compared to Fokker-Planck-Master equation based algorithm for a range of parameter values. Our second application concerns the study of resonant activation over a fluctuating barrier.Comment: Accepted in Journal of Statistical Mechanics: Theory and Experimen