Consistent Dynamic Model Research Articles

Dynamic Analysis of Non-Uniform Functionally Graded Beams on Inhomogeneous Foundations Subjected to Moving Distributed Loads

Inhomogeneous materials, variable foundations, non-uniform cross-sections, and non-uniformly distributed loads are common in engineering structures and typically complicate their mechanical analysis considerably. This paper presents an accurate and efficient numerical method for the dynamic analysis of non-uniform functionally graded beams resting on inhomogeneous viscoelastic foundations subjected to non-uniformly distributed moving load and investigates the effects of non-uniformities and inhomogeneities on material, foundation, and load. Based on the Timoshenko beam theory and a Chebyshev spectral method, a consistent discrete dynamic model is derived, which can deal with all axially varying properties. A series of numerical experiments are carried out to validate the convergence and accuracy of the proposed method. The results are compared with those obtained through finite element analysis or in the literature, and excellent agreement is observed. Then, the dynamic response of an axially functionally graded beam resting on an inhomogeneous viscoelastic foundation and subjected to a non-uniformly distributed moving load is investigated. The results show that the material gradient and the inhomogeneous foundation can alter the vibration amplitudes and critical speeds of the beam significantly. Compared with more realistic non-uniformly distributed moving load models, idealized concentrated and uniformly distributed moving load models produce apparent computation errors in vibration amplitudes.

The complex dynamics of the 2023 Kahramanmaraş, Turkey, Mw 7.8-7.7 earthquake doublet.

The destructive 2023 moment magnitude (Mw) 7.8-7.7 earthquake doublet ruptured multiple segments of the East Anatolian Fault system in Turkey. We integrated multiscale seismic and space-geodetic observations with multifault kinematic inversions and dynamic rupture modeling to unravel the events' complex rupture history and stress-mediated fault interactions. Our analysis reveals three subshear slip episodes during the initial Mw 7.8 earthquake with a delayed rupture initiation to the southwest. The Mw 7.7 event occurred 9 hours later with a larger slip and supershear rupture on its western branch. Mechanically consistent dynamic models accounting for fault interactions can explain the unexpected rupture paths and require a heterogeneous background stress. Our results highlight the importance of combining near- and far-field observations with data-driven and physics-based models for seismic hazard assessment.

An electro-mechanical dynamic model for flexoelectric energy harvesters

Flexoelectricity is a universal electro-mechanical coupling effect that occurs in dielectrics of all symmetric groups and becomes dominant at the micro- and nano-scales. It plays an important role in evaluating micro-electro-mechanical systems (MEMS) such as energy harvesters which convert vibrational energy to electric energy. At finer length scales, micro-inertia effects significantly contribute to the behavior of flexoelectric materials due to the mechanical dispersion. Hence, to properly characterize the vibrational behavior of MEMS, a reliable theoretical approach is required accounting for all possible phenomena that affect the output of the system such as voltage or power density. In this work, we present a consistent (dynamic) model and associated computational framework for flexoelectric structures to study the characteristics of the vibrational behavior of energy harvesters showing the dominance of the flexoelectric effect at micro- and nano-scales. In this context, we quantify the impact of the micro-inertia length scale and the flexoelectric dynamic parameter on both frequency and time responses of energy harvesters.

Assessing the Marshall–Lerner condition within a stock-flow consistent model

Abstract We derive the general equilibrium condition for the terms of trade in a two-country economy model. We show that the Marshall–Lerner condition is only a special case of this condition, in which a full exchange rate pass-through to import prices is assumed. In fact, the Marshall–Lerner condition is not even a ‘useful approximation’ of the general condition. For the full pass-through assumption has destabilising, rather than stabilizing, effects, when it is introduced in a stock-flow consistent dynamic model. More generally, the higher (lower) the pass-through, the slower (quicker) is the adjustment of the economy towards the equilibrium. This is tantamount to saying that the speed of adjustment is a positive function of the strategic behaviour of the exporters, who attempt to retain their market share by keeping their foreign currency-denominated prices unchanged.

From abstract to concrete: some tips for developing an empirical stock–flow consistent model

The main purpose of this paper is to show how a simple (medium-scale) empirical stock–flow consistent dynamic model can be developed from scratch. Eurostat data and conventional statistical packages (notably EViews, Excel and R) are used. On the theoretical side, the work builds upon the pioneering work of Godley/Lavoie (2007). Sectoral transactions–flow matrices and balance sheets are explicitly modelled and their evolution over time under different scenarios is analysed. On the empirical side, the model draws upon the applied work of Burgess et al. (2016). The case of Italy is considered, but the model can be replicated for other countries. Eurostat annual data (from 1995 to 2016) are used to estimate or calibrate most model parameter values (for example, consumption function and housing investment parameters). Remaining parameters are borrowed from the available literature or taken from a range of realistic values (for example, weight on past errors in agents' expectations). The model is then used to impose and compare alternative scenarios for Italian sectoral financial balances, based on different shocks to government spending.

From abstract to concrete: some tips for developing an empirical stock–flow consistent model

The main purpose of this paper is to show how a simple (medium-scale) empirical stock–flow consistent dynamic model can be developed from scratch. Eurostat data and conventional statistical packages (notably EViews, Excel and R) are used. On the theoretical side, the work builds upon the pioneering work of Godley/Lavoie (2007). Sectoral transactions–flow matrices and balance sheets are explicitly modelled and their evolution over time under different scenarios is analysed. On the empirical side, the model draws upon the applied work of Burgess et al. (2016). The case of Italy is considered, but the model can be replicated for other countries. Eurostat annual data (from 1995 to 2016) are used to estimate or calibrate most model parameter values (for example, consumption function and housing investment parameters). Remaining parameters are borrowed from the available literature or taken from a range of realistic values (for example, weight on past errors in agents’ expectations). The model is then used to impose and compare alternative scenarios for Italian sectoral financial balances, based on different shocks to government spending.

Integrating Material Stock Dynamics Into Economy-Wide Material Flow Accounting: Concepts, Modelling, and Global Application for 1900–2050

Assessing progress towards environmental sustainability requires a robust and systematic knowledge base. Economy-wide material flow accounting (ew-MFA) is an established method to monitor resource use across scales and its headline indicators are widely used in policy. However, ew-MFA is currently limited by its empirical focus on annual flows of material and energy, because it neglects the pivotal role of in-use material stocks of manufactured capital. Explicitly integrating in-use stocks enables new insights into a range of Ecological Economics' topics, such as the biophysical assessment of socio-economic systems, the circular economy and stock-flow consistent scenarios.Herein, we conceptually and practically expand the ew-MFA framework towards jointly addressing material flows, in-use stocks of manufactured capital and waste, using a fully consistent dynamic model of Material Inputs, Stocks and Outputs (MISO-model). We review the stock modelling literature, propose a novel distinction of stock-driven versus inflow-driven approaches and situate the MISO-model as the latter. We then investigate the global dynamics of socio-metabolic flows and in-use stocks from 1900 to 2014, explore model sensitivities and quantify and attribute uncertainty. Two exemplary scenarios are presented. Through these innovations for ew-MFA, we enable a dynamic and comprehensive assessment of resource use, stocks and all wastes in the socio-economic metabolism.

Mathematical Modelling and Parameter Estimation of an Industrial Steam Turbine-Generator Based on Operational Data

In this paper, mathematical modeling and identification of an industrial, 200 MW steam turbine and generator are taken into consideration based on operational data. This data is acquired by the measuring devices and data acquisition systems from precisely designed tests. Due to the significance of power systems dynamic studies, steam turbine-generator as the main part of this system deserves an accurate and consistent dynamical model. After introducing the operation and the main parts of the studied steam turbine-generator, an appropriate mathematical model which best describes the behavior of the real system is proposed. In the next step, parameters of the suggested model and the generator are estimated using the nonlinear least squares (NLS) method. The accuracy of the suggested model with the estimated parameters is investigated by comparing the model response with the real data.

Long-run consequences of debt

Empirical evidence suggests that both public and private debt may have long-run detrimental effects on the economy. However, theoretical works have not provided a unique explanation to the issue. In this paper, therefore, we propose a framework that is able to describe the long-run effects of different kinds of debt. We introduce a stock-flow consistent dynamic model where the economy is represented as a network of trading relationships among agents. Debt contracts are one of such relationships. The model is characterized by a unique and stable steady-state and predicts that: (i) aggregate income is always limited from the above by the money supply; (ii) debts cause in the long-run a redistribution of borrowers’ wealth and income in favor of lenders; (iii) the redistribution is magnified by the level of the interest rate and (iv) by the degree of debt persistence. In the aggregate this may also lower the average marginal propensity to spend and nominal income, providing therefore a clear-cut explanation to the empirical evidence.

Cohort aggregation modelling for complex forest stands: Spruce–aspen mixtures in British Columbia

Mixed-species growth models are needed as a synthesis of ecological knowledge and for guiding forest management. Individual-tree models have been commonly used, but the difficulties of reliably scaling from the individual to the stand level are often underestimated. Emergent properties and statistical issues limit their effectiveness. A more holistic modelling of aggregates at the whole stand level is a potentially attractive alternative. This work explores methodology for developing biologically consistent dynamic mixture models where the state is described by aggregate stand-level variables for species or age/size cohorts. The methods are demonstrated and tested with a two-cohort model for spruce–aspen mixtures named SAM. The models combine single-species submodels and submodels for resource partitioning among the cohorts. The partitioning allows for differences in competitive strength among species and size classes, and for complementarity effects. Height growth reduction in suppressed cohorts is also modelled. SAM fits well the available data, and exhibits behaviors consistent with current ecological knowledge. The general framework can be applied to any number of cohorts, and should be useful as a basis for modelling other mixed-species or uneven-aged stands.

Dynamical analysis of fluid lines coupled to mechanical systems taking into account fluid frequency-dependent damping and non-conventional constitutive models: part 1 – Modeling fluid lines

The design of hydraulic transmission systems for control and actuation requires accurate knowledge of their dynamic response: some standard techniques are known to obtain a consistent dynamic model of a fluid line, including the contribution of inertia, compressibility and friction. In this paper an efficient procedure is developed for simulating the dynamic response of a fluid line in both the frequency and time domains, focusing the attention on the modal analysis of a discretized model, in view of coupling with mechanical systems. A bi-dimensional approach is adopted, and the laminar flow frequency-dependent friction is modeled using non-integer order differential laws, which may improve the accuracy of the simulated responses in comparison with more traditional Newtonian models.

Dynamical analysis of fluid lines coupled to mechanical systems taking into account fluid frequency-dependent damping and non-conventional constitutive models: Part 2 – Coupling with mechanical systems

The design of hydraulic transmission systems for control and actuation requires accurate knowledge of their dynamic response: some standard techniques are known to obtain a consistent dynamic model of a fluid line, including the contribution of inertia, compressibility and friction. In this study an efficient procedure is developed for simulating the dynamic response of a fluid line coupled with mechanical systems, in both the frequency and time domains. A bi-dimensional approach is adopted for the fluid line, and the laminar flow frequency-dependent friction is modeled using non-integer order differential laws, which may improve the accuracy in comparison with more traditional Newtonian models. The coupling problem with mechanical systems is studied by means of both continuous models of the fluid line (yielding frequency response functions in exact analytical form), and discretized models of the fluid line (to express time response functions in approximate analytical form), focusing on the damping properties of the resulting vibrating systems.

Membrane Distillation Process Modeling: Dynamical Approach

This paper presents a complete dynamic modeling of a membrane distillation process. The model contains two consistent dynamic models. A 2D advection-diffusion equation for modeling the whole process and a modified heat equation for modeling the membrane itself. The complete model describes the temperature diffusion phenomenon across the feed, membrane, permeate containers and boundary layers of the membrane. It gives an online and complete temperature profile for each point in the domain. It explains heat conduction and convection mechanisms that take place inside the process in terms of mathematical parameters, and justify process behavior during transient and steady state phases. The process is monitored for any sudden change in the performance at any instance of time. In addition, it assists maintaining production rates as desired, and gives recommendations during membrane fabrication stages. System performance and parameters can be optimized and controlled using this complete dynamic model. Evolution of membrane boundary temperature with time, vapor mass transfer along the process, and temperature difference between membrane boundary layers are depicted and included. Simulations were performed over the complete model with real membrane specifications. The plots show consistency between 2D advection-diffusion model and the expected behavior of the systems as well as literature. Evolution of heat inside the membrane starting from transient response till reaching steady state response for fixed and varying times is illustrated. Keywords— Membrane distillation, Dynamical modeling, Advection-diffusion equation, Thermal equilibrium, Heat equation.

Computer package for selecting high voltage insulators for different contamination conditions

This paper presents an interactive computer package enabling to choose insulators used in polluted conditions. This is accomplished by integrating a self consistent dynamic model we developed in previous works and that includes the successive development of the arc on insulator surface based on an equivalent electrical network model and an analytic arc propagation criterion. This package enables to compute the different characteristic parameters of the temporal evolution of discharge (arc) propagating over polluted insulators (current and electrical charge, discharge length, potential, discharge propagation velocity, resistance of discharge channel and time to flashover). Numerous shapes of insulators are incorporated into the package. The package is capable of handling AC, DC and impulse voltages, in addition to different pollution severities. It constitutes a useful tool to choose insulation device for a given voltage system, and as a maintenance tool to determine the critical contamination level (in terms of pollution conductivity) that will cause flashover of insulator at the operating voltage.

A Unification between Dynamical System Theory and Thermodynamics Involving an Energy, Mass, and Entropy State Space Formalism

In this paper, we combine the two universalisms of thermodynamics and dynamical systems theory to develop a dynamical system formalism for classical thermodynamics. Specifically, using a compartmental dynamical system energy flow model involving heat flow, work energy, and chemical reactions, we develop a state-space dynamical system model that captures the key aspects of thermodynamics, including its fundamental laws. In addition, we show that our thermodynamically consistent dynamical system model is globally semistable with system states converging to a state of temperature equipartition. Furthermore, in the presence of chemical reactions, we use the law of mass-action and the notion of chemical potential to show that the dynamic system states converge to a state of temperature equipartition and zero affinity corresponding to a state of chemical equilibrium.

Dynamic modeling of taut strings carrying a traveling mass

In this paper, a new consistent dynamic model is proposed, aimed at studying linear vibrations induced in an elastic wire by a bilaterally constrained single mass moving with a constant velocity. Starting from a variational formulation, through the Hadamard’s condition, a corrective term to the local linear stiffness is determined in the continuum model as a function of the moving mass velocity; in this way, the boundary conditions are properly found. The representation of the solutions of the hyperbolic equations governing the motion of the wire presents some difficulties, which are solved by means of a suitable coordinate transformation in a time-invariant domain and a judicious choice of the set of shape functions, to be used in the discrete formulation of the problem. This new description allows an easy estimation of high-order deformations that are neglected by a purely linear approach. When the mass velocity is sufficiently high, displacements near the supports show high gradients: in these cases, it is necessary to use an unknown velocity or introduce an advanced mechanical model in order to correctly describe the motion of the mass. Numerical examples confirm the stability of the proposed solution in all conditions examined.

A simplified stock-flow consistent dynamic model of the systemic financial fragility in the ‘New Capitalism’

In the last few years, many financial analysts and heterodox economists (but even some ‘dissenters’ among orthodox economists) have referred to the contribution of Hyman P. Minsky as a fundamental reading for understanding the current crisis. However, it is well known that the traditional formulation of Minsky's ‘financial instability hypothesis’ raises a number of theoretical issues. Furthermore, Minsky's analysis of capitalism must be updated on the basis of the deep changes which, during the last three decades, have concerned the world economy. In order to address these theoretical and empirical issues, the paper, first, introduces the reader to the ‘mechanics’ of the financial instability theory, according to the formulation of the traditional Minskian literature (Section 2). Second, it shows that Minsky's theory, in this formulation, cannot be regarded as a general theory of the business cycle (Section 3). Third, the paper attempts to supply a consistent, although simplified, updating of Minsky's theory by cross-breeding it with inputs coming from the ‘New Cambridge’ theories and the current ‘formal Minskian literature’. The aim of this is to analyse the impact of both capital-asset inflation and consumer credit on the financial ‘soundness’ of the business sector (Sections 4–7). Some concluding remarks are provided in the last part of the paper (Section 8).

Dynamically driven star formation in models of NGC 7252

We present new dynamical models of the merger remnant NGC 7252 which include star formation simulated according to various phenomenological rules. By using interactive software to match our model with the observed morphology and gas velocity field, we obtain a consistent dynamical model for NGC 7252. In our models, this proto-elliptical galaxy formed by the merger of two similar gas-rich disk galaxies which fell together with an initial pericentric separation of ~2 disk scale lengths approximately 620 Myr ago. Results from two different star formation rules--- density-dependent and shock-induced--- show significant differences in star formation during and after the first passage. Shock-induced star formation yields a prompt and wide-spread starburst at the time of first passage, while density-dependent star formation predicts a more slowly rising and centrally concentrated starburst. A comparison of the distributions and ages of observed clusters with results of our simulations favors shock-induced mechanism of star formation in NGC 7252. We also present simulated color images of our model of NGC 7252, constructed by incorporating population synthesis with radiative transfer and dust attenuation. Overall the predicted magnitudes and colors of the models are consistent with observations, although the simulated tails are fainter and redder than observed. We suggest that a lack of star formation in the tails, reflected by the redder colors, is due to an incomplete description of star formation in our models rather than insufficient gas in the tails.

Credit Models and the Crisis, or: How I Learned to Stop Worrying and Love the CDOs

We follow a long path for Credit Derivatives and Collateralized Debt Obligations (CDOs) in particular, from the introduction of the Gaussian copula model and the related implied correlations to the introduction of arbitrage-free dynamic loss models capable of calibrating all the tranches for all the maturities at the same time. En passant, we also illustrate the implied copula, a method that can consistently account for CDOs with different attachment and detachment points but not for different maturities. The discussion is abundantly supported by market examples through history. The dangers and critics we present to the use of the Gaussian copula and of implied correlation had all been published by us, among others, in 2006, showing that the quantitative community was aware of the model limitations before the crisis. We also explain why the Gaussian copula model is still used in its base correlation formulation, although under some possible extensions such as random recovery. Overall we conclude that the modeling effort in this area of the derivatives market is unfinished, partly for the lack of an operationally attractive single-name consistent dynamic loss model, and partly because of the diminished investment in this research area.

A consistent dynamical model for pion-photoproduction

Abstract Pion-photoproduction amplitude is calculated within a consistent isobar model already used to fix the Δ + + ( 1232 MeV ) parameters in pion–nucleon scattering and bremsstrahlung. This amplitude is expressed in terms of (physical) on-shell quantities and off-shell contributions coming from final state interactions. These latter are isolated in principal value integrals on the non-polar part of the pion–nucleon K -matrix, being the main effect of them to dress the bare form factors present in the γ N → Δ vertex. First, we hide the dressing into effective form factors getting at k γ 2 = 0 , G M = 2.97 ± 0.08 and G E = 0.055 ± 0.010 in full consistence with recent chiral effective field theory calculations. Then, different models to regularize the mentioned integrals are analyzed. We choose those better describing the non-resonant multipoles, in order to get model independent results for the resonant ones. Finally, we try to predict the bare form factors getting G M 0 = 1.69 ± 0.02 and G E 0 = 0.028 ± 0.008 , which are consistent with recent lattice quark calculations and other more sophisticated dynamical models.