On a nonlinear autoregressive method applied to geophysical signals

Geophysics ◽  
1994 ◽  
Vol 59 (8) ◽  
pp. 1270-1277 ◽  
Author(s):  
Mauro Bracalari ◽  
Ettore Salusti
Keyword(s):  
Sea Level ◽  
Signal Amplitude ◽  
Sudden Increase ◽  
Algebraic Equations ◽  
Crustal Motion ◽  
Sea Level Fluctuations ◽  
Linear Algebraic Equations ◽  
Harmonic Tremors ◽  
Nonlinear Autoregressive ◽  
Autoregressive Analysis

A nonlinear second‐order autoregressive analysis of time varying signals leads to simple inhomogeneous linear algebraic equations. This method was applied to the analysis of three types of geophysical signals: the fluctuation of sea level at Venice (Italy), “harmonic tremors” at Stromboli (Eolian Islands), and the earth’s crustal motion at L’Aquila (Italy). For more regular motions (earth’s crustal motion), linear and nonlinear methods give essentially equivalent results. Compared to the customary linear autoregressive method, our method more accurately predicts nonlinearities whenever there is a sudden increase of the signal amplitude, such as sea level fluctuations and seismic tremors.

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

scholarly journals Spatial distribution of water level impact to back-barrier bays

2018 ◽  
Author(s):  
Alfredo L. Aretxabaleta ◽  
Neil K. Ganju ◽  
Zafer Defne ◽  
Richard P. Signell
Keyword(s):  
Water Level ◽  
Sea Level ◽  
Water Levels ◽  
Analytical Models ◽  
Barnegat Bay ◽  
Sea Level Fluctuations ◽  
Flooding Hazard ◽  
Short Period ◽  
Inlet Geometry ◽  
Spatial Estimates

Abstract. Water level in semi-enclosed bays, landward of barrier islands, is mainly driven by offshore sea level fluctuations that are modulated by bay geometry and bathymetry, causing spatial variability in the ensuing response (transfer). Local wind setup can have a secondary role that depends on wind speed, fetch, and relative orientation of the wind direction and the bay. Inlet geometry and bathymetry primarily regulate the magnitude of the transfer between open ocean and bay. Tides and short-period offshore oscillations are more damped in the bays than longer-lasting offshore fluctuations, such as storm surge and sea level rise. We compare observed and modeled water levels at stations in a mid-Atlantic bay (Barnegat Bay) with offshore water level proxies. Observed water levels in Barnegat Bay are compared and combined with model results from the Coupled Ocean–Atmosphere–Wave–Sediment Transport (COAWST) modeling system to evaluate the spatial structure of the water level transfer. Analytical models based on the dimensional characteristics of the bay are used to combine the observed data and the numerical model results in a physically consistent approach. Model water level transfers match observed values at locations inside the Bay in the storm frequency band (transfers ranging from 70–100 %) and tidal frequencies (10–55 %). The contribution of frequency-dependent local setup caused by wind acting along the bay is also considered. The approach provides transfer estimates for locations inside the Bay where observations were not available resulting in a complete spatial characterization. The approach allows for the study of the Bay response to alternative forcing scenarios (landscape changes, future storms, and rising sea level). Detailed spatial estimates of water level transfer can inform decisions on inlet management and contribute to the assessment of current and future flooding hazard in back-barrier bays and along mainland shorelines.

scholarly journals Exact statistical solution for the hopping transport of trapped charge via finite Markov jump processes

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Andrey A. Pil’nik ◽  
Andrey A. Chernov ◽  
Damir R. Islamov
Keyword(s):  
Charge Transport ◽  
Thin Layers ◽  
Jump Processes ◽  
Dielectric Films ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Statistical Solution ◽  
Linear Algebraic Equations ◽  
Special Cases ◽  
Thin Dielectric Films

AbstractIn this study, we developed a discrete theory of the charge transport in thin dielectric films by trapped electrons or holes, that is applicable both for the case of countable and a large number of traps. It was shown that Shockley–Read–Hall-like transport equations, which describe the 1D transport through dielectric layers, might incorrectly describe the charge flow through ultra-thin layers with a countable number of traps, taking into account the injection from and extraction to electrodes (contacts). A comparison with other theoretical models shows a good agreement. The developed model can be applied to one-, two- and three-dimensional systems. The model, formulated in a system of linear algebraic equations, can be implemented in the computational code using different optimized libraries. We demonstrated that analytical solutions can be found for stationary cases for any trap distribution and for the dynamics of system evolution for special cases. These solutions can be used to test the code and for studying the charge transport properties of thin dielectric films.

scholarly journals Two matrix methods for solution of nonlinear and linear Lane-Emden type equations with mixed condition by operational matrix

2015 ◽  
Vol 4 (3) ◽  
pp. 420 ◽  
Author(s):  
Behrooz Basirat ◽  
Mohammad Amin Shahdadi
Keyword(s):  
Bernstein Polynomials ◽  
Operational Matrix ◽  
Numerical Procedure ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Mixed Condition ◽  
Matrix Methods ◽  
Numerical Examples ◽  
Linear Algebraic Equations ◽  
The Given

<p>The aim of this article is to present an efficient numerical procedure for solving Lane-Emden type equations. We present two practical matrix method for solving Lane-Emden type equations with mixed conditions by Bernstein polynomials operational matrices (BPOMs) on interval [<em>a; b</em>]. This methods transforms Lane-Emden type equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equations. We also give some numerical examples to demonstrate the efficiency and validity of the operational matrices for solving Lane-Emden type equations (LEEs).</p>

scholarly journals Optimal Random Packing of Spheres and Extremal Effective Conductivity

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1063
Author(s):  
Vladimir Mityushev ◽  
Zhanat Zhunussova
Keyword(s):  
Effective Conductivity ◽  
Dimensional Space ◽  
Elementary Function ◽  
Voronoi Tessellation ◽  
Random Packing ◽  
Periodicity Cell ◽  
Algebraic Equations ◽  
Optimal Packing ◽  
Linear Algebraic Equations ◽  
Initial Location

A close relation between the optimal packing of spheres in Rd and minimal energy E (effective conductivity) of composites with ideally conducting spherical inclusions is established. The location of inclusions of the optimal-design problem yields the optimal packing of inclusions. The geometrical-packing and physical-conductivity problems are stated in a periodic toroidal d-dimensional space with an arbitrarily fixed number n of nonoverlapping spheres per periodicity cell. Energy E depends on Voronoi tessellation (Delaunay graph) associated with the centers of spheres ak (k=1,2,…,n). All Delaunay graphs are divided into classes of isomorphic periodic graphs. For any fixed n, the number of such classes is finite. Energy E is estimated in the framework of structural approximations and reduced to the study of an elementary function of n variables. The minimum of E over locations of spheres is attained at the optimal packing within a fixed class of graphs. The optimal-packing location is unique within a fixed class up to translations and can be found from linear algebraic equations. Such an approach is useful for random optimal packing where an initial location of balls is randomly chosen; hence, a class of graphs is fixed and can dynamically change following prescribed packing rules. A finite algorithm for any fixed n is constructed to determine the optimal random packing of spheres in Rd.

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