scholarly journals Estimating range expansion of wildlife in heterogeneous landscapes: A spatially explicit state‐space matrix model coupled with an improved numerical integration technique

2018 ◽  
Author(s):  
Yutaka Osada ◽  
Takeo Kuriyama ◽  
Masahiko Asada ◽  
Hiroyuki Yokomizo ◽  
Tadashi Miyashita
Keyword(s):  
State Space ◽  
Numerical Integration ◽  
Matrix Model ◽  
Range Expansion ◽  
Spatially Explicit ◽  
Integration Technique ◽  
Heterogeneous Landscapes ◽  
Space Matrix

Comparison of spectral methods for the evaluation of Stokes integral  

2021 ◽  
Author(s):  
Avadh Bihari Narayan ◽  
Ashutosh Tiwari ◽  
Govind Sharma ◽  
Balaji Devaraju ◽  
Onkar Dikshit
Keyword(s):  
Boundary Value Problems ◽  
Numerical Integration ◽  
Spectral Methods ◽  
Boundary Value ◽  
Fundamental Equation ◽  
Computation Time ◽  
Spherical Approximation ◽  
Integration Technique ◽  
Gravity Measurements ◽  
Stokes Integral

<p>The spherical approximation of the fundamental equation of geodesy defines the boundary value problems. Stokes’s integral provides the solution of boundary value problems that enables the computation of geoid from the properly reduced gravity measurements to the geoid. The stokes integral can be evaluated by brute-force numerical integration, spectral methods, and least-squares collocation. There is a trade-off between computation time and accuracy when we chose numerical integration technique or any spectral method. This research will compare time complexity and the accuracy of different spectral methods (1D-FFT, 2D-FFT, Multi-band FFT) and numerical integration technique for the region in the lower Himalaya, around Nainital, Uttarakhand, India. </p>

Efficient Updated-Lagrangian Simulations in Forming Processes

2015 ◽  
Vol 651-653 ◽  
pp. 1294-1300
Author(s):  
Diego Canales ◽  
Adrien Leygue ◽  
Francisco Chinesta ◽  
Elias Cueto ◽  
Eric Feulvarch ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Numerical Integration ◽  
General Purpose ◽  
Integration Technique ◽  
Numerical Examples ◽  
Nodal Integration ◽  
Out Of Plane ◽  
Material Forming ◽  
Updated Lagrangian ◽  
Stabilized Conforming Nodal Integration

A new efficient updated-Lagrangian strategy for numerical simulations of material forming processes is presented in this work. The basic ingredients are the in-plane-out-of-plane PGD-based decomposition and the use of a robust numerical integration technique (the Stabilized Conforming Nodal Integration). This strategy is of general purpose, although it is especially well suited for plateshape geometries. This paper is devoted to show the feasibility of the technique through some simple numerical examples.

scholarly journals A spatial theory for characterizing predator–multiprey interactions in heterogeneous landscapes

2015 ◽  
Vol 282 (1812) ◽  
pp. 20150973 ◽  
Author(s):  
Daniel Fortin ◽  
Pietro-Luciano Buono ◽  
Oswald J. Schmitz ◽  
Nicolas Courbin ◽  
Chrystel Losier ◽  
...  
Keyword(s):  
Prey Species ◽  
Landscape Heterogeneity ◽  
Spatially Explicit ◽  
Human Disturbances ◽  
Predator Prey ◽  
Heterogeneous Landscapes ◽  
Empirically Supported ◽  
Predator Interactions ◽  
Predator Prey Models ◽  
Species Specific

Trophic interactions in multiprey systems can be largely determined by prey distributions. Yet, classic predator–prey models assume spatially homogeneous interactions between predators and prey. We developed a spatially informed theory that predicts how habitat heterogeneity alters the landscape-scale distribution of mortality risk of prey from predation, and hence the nature of predator interactions in multiprey systems. The theoretical model is a spatially explicit, multiprey functional response in which species-specific advection–diffusion models account for the response of individual prey to habitat edges. The model demonstrates that distinct responses of alternative prey species can alter the consequences of conspecific aggregation, from increasing safety to increasing predation risk. Observations of threatened boreal caribou, moose and grey wolf interacting over 378 181 km 2 of human-managed boreal forest support this principle. This empirically supported theory demonstrates how distinct responses of apparent competitors to landscape heterogeneity, including to human disturbances, can reverse density dependence in fitness correlates.

scholarly journals Continuous state-space representation of a bucket-type rainfall-runoff model: a case study with the GR4 model using state-space GR4 (version 1.0)

2018 ◽  
Vol 11 (4) ◽  
pp. 1591-1605 ◽  
Author(s):  
Léonard Santos ◽  
Guillaume Thirel ◽  
Charles Perrin
Keyword(s):  
Water Balance ◽  
State Space ◽  
Operator Splitting ◽  
Space Representation ◽  
Rainfall Runoff ◽  
Integration Technique ◽  
State Space Representation ◽  
Rainfall Runoff Model ◽  
Unit Hydrographs ◽  
Runoff Model

Abstract. In many conceptual rainfall–runoff models, the water balance differential equations are not explicitly formulated. These differential equations are solved sequentially by splitting the equations into terms that can be solved analytically with a technique called “operator splitting”. As a result, only the solutions of the split equations are used to present the different models. This article provides a methodology to make the governing water balance equations of a bucket-type rainfall–runoff model explicit and to solve them continuously. This is done by setting up a comprehensive state-space representation of the model. By representing it in this way, the operator splitting, which makes the structural analysis of the model more complex, could be removed. In this state-space representation, the lag functions (unit hydrographs), which are frequent in rainfall–runoff models and make the resolution of the representation difficult, are first replaced by a so-called “Nash cascade” and then solved with a robust numerical integration technique. To illustrate this methodology, the GR4J model is taken as an example. The substitution of the unit hydrographs with a Nash cascade, even if it modifies the model behaviour when solved using operator splitting, does not modify it when the state-space representation is solved using an implicit integration technique. Indeed, the flow time series simulated by the new representation of the model are very similar to those simulated by the classic model. The use of a robust numerical technique that approximates a continuous-time model also improves the lag parameter consistency across time steps and provides a more time-consistent model with time-independent parameters.

A Method for the Calculation of Natural Frequencies of Orthotropic Axisymmetrically Loaded Shells of Revolution

1994 ◽  
Vol 116 (1) ◽  
pp. 16-25 ◽  
Author(s):  
A. Kayran ◽  
J. R. Vinson ◽  
E. Selcuk Ardic
Keyword(s):  
Numerical Integration ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Shell Of Revolution ◽  
Initial Stresses ◽  
Integration Technique ◽  
Shells Of Revolution ◽  
Axisymmetric Loading

A methodology is presented for the calculation of the natural frequencies of orthotropic axisymmetrically loaded shells of revolution including the effect of transverse shear deformation. The fundamental system of equations governing the free vibration of the stress-free shells of revolution are modified such that the initial stresses due to the axisymmetric loading are incorporated into the analysis. The linear equations on the vibration about the deformed state are solved by using the transfer matrix method which makes use of the multisegment numerical integration technique. This method is commonly known as frequency trial method. The solution for the initial stresses due to axisymmetric loading is omitted; since the application of the transfer matrix method, making use of multisegment numerical integration technique for both linear and nonlinear equations are available in the literature. The method is verified by applying it to the solution of the natural frequencies of spinning disks, for which exact solutions exist in the literature, and a deep paraboloid for which approximate solutions exist. The governing equations for a shell of revolution are used to approximate circular disks by decreasing the curvature of the shell of revolution to very low values, and good agreement is seen between the results of the present method and the exact solution for spinning disks and the approximate solution for a deep paraboloid.

Nonlinear Analysis of a Coaxial Microhelicopter with a Bell Stabilizer Bar

2014 ◽  
Vol 59 (1) ◽  
pp. 1-14
Author(s):  
Basile Graf ◽  
Philippe Müllhaupt
Keyword(s):  
Nonlinear Analysis ◽  
State Space ◽  
Numerical Integration ◽  
Physical Meaning ◽  
Nonlinear Modeling ◽  
Control Design ◽  
Black Box ◽  
Coordinate Transformations ◽  
Time Simulation ◽  
System Equations

Nonlinear modeling of coaxial microhelicopters is studied. All equations are derived using a Lagrangian approach and simplified aerodynamics assumptions so that all parameters have a physical meaning; there is no “black box.” The model is constructed with a view toward control design and real-time simulation. The state-space size is kept minimal, and the numerical conditioning of the resulting differential equations is critical. A set of coordinate transformations is proposed that allows averaging and reducing the number of system equations, effectively suppressing stiffness and tremendously accelerating numerical integration.

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