scholarly journals Recipes for How to Force Oceanic Model Dynamics

2020 ◽  
Vol 12 (2) ◽  
Author(s):  
Lionel Renault ◽  
S. Masson ◽  
T. Arsouze ◽  
Gurvan Madec ◽  
James C. McWilliams
Keyword(s):  
Model Dynamics ◽  
Oceanic Model

scholarly journals Global Stability Analysis of a Bioreactor Model for Phenol and Cresol Mixture Degradation

Processes ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 124
Author(s):  
Neli Dimitrova ◽  
Plamena Zlateva
Keyword(s):  
Specific Growth ◽  
Equilibrium Points ◽  
Nonlinear Ordinary Differential Equations ◽  
The Novel ◽  
Model Design ◽  
Stirred Bioreactor ◽  
Global Stability Analysis ◽  
Local Asymptotic Stability ◽  
Model Dynamics ◽  
Stability And Bifurcations

We propose a mathematical model for phenol and p-cresol mixture degradation in a continuously stirred bioreactor. The model is described by three nonlinear ordinary differential equations. The novel idea in the model design is the biomass specific growth rate, known as sum kinetics with interaction parameters (SKIP) and involving inhibition effects. We determine the equilibrium points of the model and study their local asymptotic stability and bifurcations with respect to a practically important parameter. Existence and uniqueness of positive solutions are proved. Global stabilizability of the model dynamics towards equilibrium points is established. The dynamic behavior of the solutions is demonstrated on some numerical examples.

scholarly journals Cosmological viable f(R,T) dark energy model: dynamics and stability

2014 ◽  
Vol 356 (1) ◽  
pp. 173-180 ◽  
Author(s):  
E. H. Baffou ◽  
A. V. Kpadonou ◽  
M. E. Rodrigues ◽  
M. J. S. Houndjo ◽  
J. Tossa
Keyword(s):  
Dark Energy ◽  
Dark Energy Model ◽  
Energy Model ◽  
Model Dynamics

Burgers turbulence model for a channel flow

1971 ◽  
Vol 47 (2) ◽  
pp. 321-335 ◽  
Author(s):  
Jon Lee
Keyword(s):  
Channel Flow ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Amplitude Equations ◽  
Fourier Amplitude ◽  
Navier Stokes Equations ◽  
Burgers Model ◽  
Model Dynamics

The truncated Burgers models have a unique equilibrium state which is defined continuously for all the Reynolds numbers and attainable from a realizable class of initial disturbances. Hence, they represent a sequence of convergent approximations to the original (untruncated) Burgers problem. We have pointed out that consideration of certain degenerate equilibrium states can lead to the successive turbulence-turbulence transitions and finite-jump transitions that were suggested by Case & Chiu. As a prototype of the Navier–Stokes equations, Burgers model can simulate the initial-value type of numerical integration of the Fourier amplitude equations for a turbulent channel flow. Thus, the Burgers model dynamics display certain idiosyncrasies of the actual channel flow problem described by a truncated set of Fourier amplitude equations, which includes only a modest number of modes due to the limited capability of the computer at hand.

Direct Sensitivity Analysis of Spatial Multibody Systems With Joint Friction Using Index-1 Formulation

2021 ◽  
Author(s):  
Adwait Verulkar ◽  
Corina Sandu ◽  
Daniel Dopico ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Multibody Systems ◽  
Friction Model ◽  
Design Parameters ◽  
Adjoint Sensitivity ◽  
Joint Friction ◽  
Multibody Dynamic ◽  
Model Dynamics ◽  
Direct Sensitivity

Abstract Sensitivity analysis is one of the most prominent gradient based optimization techniques for mechanical systems. Model sensitivities are the derivatives of the generalized coordinates defining the motion of the system in time with respect to the system design parameters. These sensitivities can be calculated using finite differences, but the accuracy and computational inefficiency of this method limits its use. Hence, the methodologies of direct and adjoint sensitivity analysis have gained prominence. Recent research has presented computationally efficient methodologies for both direct and adjoint sensitivity analysis of complex multibody dynamic systems. The contribution of this article is in the development of the mathematical framework for conducting the direct sensitivity analysis of multibody dynamic systems with joint friction using the index-1 formulation. For modeling friction in multibody systems, the Brown and McPhee friction model has been used. This model incorporates the effects of both static and dynamic friction on the model dynamics. A case study has been conducted on a spatial slider-crank mechanism to illustrate the application of this methodology to real-world systems. Using computer models, with and without joint friction, effect of friction on the dynamics and model sensitivities has been demonstrated. The sensitivities of slider velocity have been computed with respect to the design parameters of crank length, rod length, and the parameters defining the friction model. Due to the highly non-linear nature of friction, the model dynamics are more sensitive during the transition phases, where the friction coefficient changes from static to dynamic and vice versa.

scholarly journals Development and evaluation of a high-resolution reanalysis of the East Australian Current region using the Regional Ocean Modelling System (ROMS 3.4) and Incremental Strong-Constraint 4-Dimensional Variational (IS4D-Var) data assimilation

2016 ◽  
Vol 9 (10) ◽  
pp. 3779-3801 ◽  
Author(s):  
Colette Kerry ◽  
Brian Powell ◽  
Moninya Roughan ◽  
Peter Oke
Keyword(s):  
High Resolution ◽  
Data Assimilation ◽  
Water Column ◽  
Marked Improvement ◽  
Sea Surface ◽  
East Australian Current ◽  
Strong Constraint ◽  
Ocean Modelling ◽  
Model Dynamics ◽  
Modelling System

Abstract. As with other Western Boundary Currents globally, the East Australian Current (EAC) is highly variable making it a challenge to model and predict. For the EAC region, we combine a high-resolution state-of-the-art numerical ocean model with a variety of traditional and newly available observations using an advanced variational data assimilation scheme. The numerical model is configured using the Regional Ocean Modelling System (ROMS 3.4) and takes boundary forcing from the BlueLink ReANalysis (BRAN3). For the data assimilation, we use an Incremental Strong-Constraint 4-Dimensional Variational (IS4D-Var) scheme, which uses the model dynamics to perturb the initial conditions, atmospheric forcing, and boundary conditions, such that the modelled ocean state better fits and is in balance with the observations. This paper describes the data assimilative model configuration that achieves a significant reduction of the difference between the modelled solution and the observations to give a dynamically consistent “best estimate” of the ocean state over a 2-year period. The reanalysis is shown to represent both assimilated and non-assimilated observations well. It achieves mean spatially averaged root mean squared (rms) residuals with the observations of 7.6 cm for sea surface height (SSH) and 0.4 °C for sea surface temperature (SST) over the assimilation period. The time-mean rms residual for subsurface temperature measured by Argo floats is a maximum of 0.9 °C between water depths of 100 and 300 m and smaller throughout the rest of the water column. Velocities at several offshore and continental shelf moorings are well represented in the reanalysis with complex correlations between 0.8 and 1 for all observations in the upper 500 m. Surface radial velocities from a high-frequency radar array are assimilated and the reanalysis provides surface velocity estimates with complex correlations with observed velocities of 0.8–1 across the radar footprint. A comparison with independent (non-assimilated) shipboard conductivity temperature depth (CTD) cast observations shows a marked improvement in the representation of the subsurface ocean in the reanalysis, with the rms residual in potential density reduced to about half of the residual with the free-running model in the upper eddy-influenced part of the water column. This shows that information is successfully propagated from observed variables to unobserved regions as the assimilation system uses the model dynamics to adjust the model state estimate. This is the first study to generate a reanalysis of the region at such a high resolution, making use of an unprecedented observational data set and using an assimilation method that uses the time-evolving model physics to adjust the model in a dynamically consistent way. As such, the reanalysis potentially represents a marked improvement in our ability to capture important circulation dynamics in the EAC. The reanalysis is being used to study EAC dynamics, observation impact in state-estimation, and as forcing for a variety of downscaling studies.

scholarly journals Interconnections Accelerate Collapse in a Socio-Ecological Metapopulation

2019 ◽  
Vol 11 (7) ◽  
pp. 1852 ◽  
Author(s):  
Zachary Dockstader ◽  
Chris Bauch ◽  
Madhur Anand
Keyword(s):  
Theoretical Models ◽  
Ecological Sustainability ◽  
Human Populations ◽  
Metapopulation Model ◽  
Single Population ◽  
Metapopulation Structure ◽  
Model Dynamics ◽  
Simplifying Assumptions ◽  
Over Exploitation ◽  
The Impact

Over-exploitation of natural resources can have profound effects on both ecosystems and their resident human populations. Simple theoretical models of the dynamics of a population of human harvesters and the abundance of a natural resource being harvested have been studied previously, but relatively few models consider the effect of metapopulation structure (i.e., a population distributed across discrete patches). Here we analyze a socio-ecological metapopulation model based on an existing single-population model used to study persistence and collapse in human populations. Resources grow logistically on each patch. Each population harvests resources on its own patch to support population growth, but can also harvest resources from other patches when their own patch resources become scarce. We show that when populations are allowed to harvest resources from other patches, the peak population size is higher, but subsequent population collapse is significantly accelerated and across a broader parameter regime. As the number of patches in the metapopulation increases, collapse is more sudden, more severe, and occurs sooner. These effects persist under scenarios of asymmetry and inequality between patches. Our model makes simplifying assumptions in order to facilitate insight and understanding of model dynamics. However, the robustness of the model prediction suggests that more sophisticated models should be developed to ascertain the impact of metapopulation structure on socio-ecological sustainability.

Quantum cosmology: From hidden symmetries towards a new (supersymmetric) perspective

2016 ◽  
Vol 25 (03) ◽  
pp. 1630009 ◽  
Author(s):  
S. Jalalzadeh ◽  
T. Rostami ◽  
P. V. Moniz
Keyword(s):  
New York ◽  
Boundary Conditions ◽  
Quantum Cosmology ◽  
Ad Hoc ◽  
Hidden Symmetries ◽  
Shape Invariance ◽  
Hidden Symmetry ◽  
Shape Invariant ◽  
Model Dynamics ◽  
Lecture Notes

We review pedagogically some of the basic essentials regarding recent results intertwining boundary conditions, the algebra of constraints and hidden symmetries in quantum cosmology. They were extensively published in Refs. [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 89 (2014), S. Jalalzadeh, T. Rostami and P. V. Moniz, Eur. Phys. J. C 75 (2015) 38, arXiv:gr-qc/1412.6439 and T. Rostami, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 92 (2015) 023526, arXiv:gr-qc/1507.04212], where complete discussions and full details can be found. More concretely, in Refs. [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 89 (2014) and S. Jalalzadeh, T. Rostami and P. V. Moniz, Eur. Phys. J. C 75 (2015) 38, arXiv:gr-qc/1412.6439] it has been shown that specific boundary conditions can be related to the algebra of Dirac observables. Moreover, a process afterwards associated to the algebra of existent hidden symmetries, from which the boundary conditions can be selected, was introduced. On the other hand, in Ref. [T. Rostami, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 92 (2015) 023526, arXiv:gr-qc/1507.04212] it was subsequently argued that some factor ordering choices can be extracted from the hidden symmetries structure of the minisuperspace model.In Refs. [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 89 (2014), S. Jalalzadeh, T. Rostami and P. V. Moniz, Eur. Phys. J. C 75 (2015) 38, arXiv:gr-qc/1412.6439 and T. Rostami, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 92 (2015) 023526, arXiv:gr-qc/1507.04212], we proceeded gradually towards less simple models, ranging from a FLRW model with a perfect fluid [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541] up to a conformal scalar field content [T. Rostami, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 92 (2015) 023526, arXiv:gr-qc/1507.04212]. We envisage that we could extend this framework towards a class of shape invariant potentials, which could include well known analytically solvable cosmological cases. Provided, we identify integrability in terms of the shape invariance conditions, we could eventually consider to import features of supersymmetric quantum mechanics towards quantum cosmology [P. V. Moniz, Quantum Cosmology-the Supersymmetric Perspective-Vol. 1: Fundamentals, Lecture Notes in Physics, Vol. 803 (Springer-Verlag, Berlin, 2010), P. V. Moniz, Quantum Cosmology-the Supersymmetric Perspective-Vol. 2: Advanced Topics, Lecture Notes in Physics, Vol. 804 (Springer, New York, 2010)], which we will also discuss in this review.Another point to emphasize is that by means of a hidden symmetry and then an algebra of Dirac observables, boundary conditions are extracted (and not ad hoc formulated) within a framework intrinsic to each model dynamics. Therefore, meeting DeWitt’s conjecture [B. S. DeWitt, Phys. Rev. 160 (1967) 1113] that “the constraints are everything” and nothing else but the constraints should be needed.

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