Correlation Structure and Time Scale of Simple Hydrologic Systems

1977 ◽  
Vol 8 (3) ◽  
pp. 129-140 ◽  
Author(s):  
Lars Gottschalk
Keyword(s):  
River Runoff ◽  
Groundwater Level ◽  
Correlation Functions ◽  
Time Scale ◽  
Equations Of Motion ◽  
Nonlinear Effects ◽  
Correlation Structure ◽  
Linearized Equations ◽  
Hydrologic Systems ◽  
Meteorological Input

Correlation structure of river runoff is a complicated set of different persistence phenomena in the watershed itself and in the meteorological input to the watershed. Correlation functions and time scale of isolated processes in a watershed (groundwater level and river runoff) are derived analytically from the linearized equations of motion for these processes. Nonlinear effects on the correlation functions are shown for river runoff and for the watershed as a whole.

scholarly journals Spatial Correlation of Hydrologic and Physiographic Elements

1978 ◽  
Vol 9 (5) ◽  
pp. 267-276 ◽  
Author(s):  
Lars Gottschalk
Keyword(s):  
Spatial Correlation ◽  
Correlation Functions ◽  
Equations Of Motion ◽  
Time Correlation ◽  
Space Correlation ◽  
Linearized Equations ◽  
Hydrologic Processes ◽  
Analytical Expressions

In an earlier paper (Gottschalk 1977) analytical expressions were given for the time correlation of hydrologic processes from the linearized equations of motion for these processes. In this paper space correlation is similarly treated. Comparison is made with empirical space correlation functions of hydrologic and physiographic elements.

scholarly journals Two point functions in defect CFTs

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Christopher P. Herzog ◽  
Abhay Shrestha
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Equations Of Motion ◽  
Physical Space ◽  
Arbitrary Spin ◽  
Momentum Tensor ◽  
Maxwell Theory ◽  
Conformal Field ◽  
Point Correlation

Abstract This paper is designed to be a practical tool for constructing and investigating two-point correlation functions in defect conformal field theory, directly in physical space, between any two bulk primaries or between a bulk primary and a defect primary, with arbitrary spin. Although geometrically elegant and ultimately a more powerful approach, the embedding space formalism gets rather cumbersome when dealing with mixed symmetry tensors, especially in the projection to physical space. The results in this paper provide an alternative method for studying two-point correlation functions for a generic d-dimensional conformal field theory with a flat p-dimensional defect and d − p = q co-dimensions. We tabulate some examples of correlation functions involving a conserved current, an energy momentum tensor and a Maxwell field strength, while analysing the constraints arising from conservation and the equations of motion. A method for obtaining bulk-to-defect correlators is also explained. Some explicit examples are considered: free scalar theory on ℝp× (ℝq/ℤ2) and a free four dimensional Maxwell theory on a wedge.

Some Nonlinear Effects of Magnetic Bearings

1999 ◽  
Author(s):  
Norbert Steinschaden ◽  
Helmut Springer
Keyword(s):  
Equations Of Motion ◽  
Period Doubling ◽  
Path Following ◽  
Nonlinear Effects ◽  
Magnetic Bearing ◽  
Operating Conditions ◽  
Active Magnetic Bearing ◽  
Nonlinear Phenomena ◽  
Amb System ◽  
Large Rotor

Abstract In order to get a better understanding of the dynamics of active magnetic bearing (AMB) systems under extreme operating conditions a simple, nonlinear model for a radial AMB system is investigated. Instead of the common way of linearizing the magnetic forces at the center position of the rotor with respect to rotor displacement and coil current, the fully nonlinear force to displacement and the force to current characteristics are used. The AMB system is excited by unbalance forces of the rotor. Especially for the case of large rotor eccentricities, causing large rotor displacements, the behaviour of the system is discussed. A path-following analysis of the equations of motion shows that for some combinations of parameters well-known nonlinear phenomena may occur, as, for example, symmetry breaking, period doubling and even regions of global instability can be observed.

scholarly journals Nonlinear Effects and the Limitation of Electron Streaming Instabilities in Astrophysics

1985 ◽  
Vol 107 ◽  
pp. 355-359
Author(s):  
Steven R. Spangler ◽  
James P. Sheerin
Keyword(s):  
Charged Particle ◽  
Time Scales ◽  
Time Scale ◽  
Pitch Angle ◽  
Radio Galaxy ◽  
Linear Time ◽  
Nonlinear Effects ◽  
Particle Beam ◽  
Charged Particle Beam ◽  
Hydromagnetic Waves

Nonlinear effects, such as soliton collapse, will result in evolution of hydromagnetic waves excited by a field-aligned charged particle beam. If the time scale for such evolution is comparable to, or shorter than, linear time scales such as those for wave growth or pitch angle isotropization, then nonlinear effects may limit the instability. For conditions appropriate to relativistic electron streaming in a radio galaxy, the nonlinear time scale may be comparable to the linear time scales.

scholarly journals Nonlinear gas oscillations in pipes. Part 1. Theory

1973 ◽  
Vol 59 (1) ◽  
pp. 23-46 ◽  
Author(s):  
J. Jimenez
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Nonlinear Effects ◽  
Wave Form ◽  
Cube Root ◽  
Acoustic Oscillations ◽  
Open Mouth ◽  
Near Resonance ◽  
Reflexion Coefficient ◽  
Two Parameters

The problem of forced acoustic oscillations in a pipe is studied theoretically. The oscillations are produced by a moving piston in one end of the pipe, while a variety of boundary conditions ranging from a completely closed to a completely open mouth at the other end are considered. All these boundary conditions are modelled by two parameters: a length correction and a reflexion coefficient equivalent to the acoustic impedance.The linear theory predicts large amplitudes near resonance and nonlinear effects become crucially important. By expanding the equations of motion in a series in the Mach number, both the amplitude and wave form of the oscillation are predicted there.In both the open- and closed-end cases the need for shock waves in some range of parameters is found. The amplitude of the oscillation is different for the two cases, however, being proportional to the square root of the piston amplitude in the closed-end case and to the cube root for the open end.

Order-Tuned Vibration Absorbers for Cyclic Rotating Flexible Structures

2005 ◽  
Author(s):  
Brian J. Olson ◽  
Steve W. Shaw ◽  
Christophe Pierre
Keyword(s):  
Equations Of Motion ◽  
Flexible Structures ◽  
Closed Form Solution ◽  
Nonlinear Effects ◽  
Form Solution ◽  
Vibration Absorbers ◽  
Bladed Disk ◽  
Tuned Vibration Absorbers ◽  
Engine Order ◽  
Bladed Disk Assembly

This paper investigates the use of order-tuned absorbers to attenuate vibrations of flexible blades in a bladed disk assembly subjected to engine order excitation. The blades are modeled by a cyclic chain of N oscillators, and a single vibration absorber is fitted to each blade. These absorbers exploit the centrifugal field arising from rotation so that they are tuned to a given order of rotation, rather than to a fixed frequency. A standard change of coordinates based on the cyclic symmetry of the system essentially decouples the governing equations of motion, yielding a closed form solution for the steady-state response of the overall system. These results show that optimal reduction of blade vibrations is achieved by tuning the absorbers to the excitation order n, but that the resulting system is highly sensitive to small perturbations. Intentional detuning (meaning that the absorbers are slightly over- or under-tuned relative to n) can be implemented to improve the robustness of the design. It is shown that by slightly undertuning the absorbers there are no system resonances near the excitation order of interest and that the resulting system is robust to mistuning (i.e., small random uncertainties in the system parameters) of the absorbers and/or blades. These results offer a basic understanding of the dynamics of a bladed disk assembly fitted with order-tuned vibration absorbers, and serve as a first step to the investigation of more realistic models, where, for example, imperfections and nonlinear effects are considered, and multi-DOF and general-path absorbers are employed.

scholarly journals LONG-TIME RELAXATION ON SPIN LATTICE AS A MANIFESTATION OF CHAOTIC DYNAMICS

2004 ◽  
Vol 18 (08) ◽  
pp. 1119-1159 ◽  
Author(s):  
BORIS V. FINE
Keyword(s):  
Correlation Functions ◽  
Time Scale ◽  
Inelastic Neutron Scattering ◽  
Spin Correlation ◽  
Inelastic Neutron ◽  
Theoretical Explanation ◽  
Characteristic Time Scale ◽  
Time Behavior ◽  
Intermediate Structure ◽  
Long Time

The long-time behavior of the infinite temperature spin correlation functions describing the free induction decay in nuclear magnetic resonance and intermediate structure factors in inelastic neutron scattering is considered. These correlation functions are defined for one-, two- and three-dimensional infinite lattices of interacting spins, both classical and quantum. It is shown that, even though the characteristic time-scale of the long-time decay of the correlation functions considered is non-Markovian, the generic functional form of this decay is either simple exponential or exponential multiplied by cosine. This work contains (i) the summary of the existing experimental and numerical evidence of the above asymptotic behavior; (ii) theoretical explanation of this behavior; and (iii) semi-empirical analysis of various factors discriminating between the monotonic and the oscillatory long-time decays. The theory is based on a fairly strong conjecture that, as a result of chaos generated by spin dynamics, a Brownian-like Markovian description can be applied to the long-time properties of ensemble average quantities on a non-Markovian time-scale. The formalism resulting from that conjecture can be described as "correlated diffusion in finite volumes."

Concurrent Multiple-Time-Scale Simulations With Improved Numerical Dissipation for Structural Dynamics

2013 ◽  
Author(s):  
Tejas Ruparel ◽  
Azim Eskandarian ◽  
James Lee
Keyword(s):  
Time Scale ◽  
Equations Of Motion ◽  
Time Integration ◽  
Nonholonomic Constraints ◽  
Numerical Dissipation ◽  
Multiple Time ◽  
Multiple Time Scale ◽  
Constraint Forces ◽  
Conservation Of Energy ◽  
Coupled Equations

Work presented in this paper describes the formulation for implementation of a concurrent multiple-time-scale integration method with improved numerical dissipation capabilities. This approach generalizes the previous Multiple Grid and Multiple Time-Scale (MGMT) Method [1] implemented for the Newmark family of algorithms. The framework is largely based upon the fundamental principles of Lagrange multipliers used to enforce workless nonholonomic constraints and Domain Decomposition Methods (DDM) to obtain coupled equations of motion for distinct regions of a continuous domain. These methods when combined together systematically yield constraint forces that not only ensure conservation of energy but also enforce continuity of velocities across the interfaces. Multiple grid connections between (non-conforming) sub-domains are handled using Mortar elements whereas coupled multiple-time-scale equations are derived for the Generalized-α Method [2]. We show that MGMT Method can be easily extended to incorporate the Generalized-α family of time integration algorithms, hence allowing selective discretization in space and time along with controlled numerical dissipation for distinct grids. We also show that interface energy across connecting sub-domains is identically zero, further assuring global energy balance and continuity of velocities across connecting sub-domains.

Direct Linearization of Continuous and Hybrid Dynamical Systems

2009 ◽  
Vol 4 (3) ◽  
Author(s):  
Julie J. Parish ◽  
John E. Hurtado ◽  
Andrew J. Sinclair
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Equations ◽  
Equilibrium Configuration ◽  
Equations Of Motion ◽  
Hybrid Dynamical Systems ◽  
Linearized Equations ◽  
Direct Linearization ◽  
Taylor Series Expansions ◽  
Nonlinear Equations Of Motion ◽  
And Control

Nonlinear equations of motion are often linearized, especially for stability analysis and control design applications. Traditionally, the full nonlinear equations are formed and then linearized about the desired equilibrium configuration using methods such as Taylor series expansions. However, it has been shown that the quadratic form of the Lagrangian function can be used to directly linearize the equations of motion for discrete dynamical systems. This procedure is extended to directly generate linearized equations of motion for both continuous and hybrid dynamical systems. The results presented require only velocity-level kinematics to form the Lagrangian and find equilibrium configuration(s) for the system. A set of selected partial derivatives of the Lagrangian are then computed and used to directly construct the linearized equations of motion about the equilibrium configuration of interest, without first generating the entire nonlinear equations of motion. Given an equilibrium configuration of interest, the directly constructed linearized equations of motion allow one to bypass first forming the full nonlinear governing equations for the system. Examples are presented to illustrate the method for both continuous and hybrid systems.

Elementary derivation of the kinetic equation for the two-dimensional guiding centre plasma

1978 ◽  
Vol 19 (1) ◽  
pp. 121-133 ◽  
Author(s):  
Michael Mond ◽  
Georg Knorr
Keyword(s):  
Kinetic Equation ◽  
Langevin Equation ◽  
Time Scale ◽  
Equations Of Motion ◽  
Planck Equation ◽  
Stochastic Equations ◽  
Iteration Scheme ◽  
Two Dimensional ◽  
Hopf Equation ◽  
Rigorous Solution

A kinetic equation for a two-dimensional inviscid hydrodynamic fluid is derived in two ways. First, the equations of motion for the modes of the fluid are interpreted as stochastic equations resembling the Langevin equation. To lowest order a Fokker–Planck equation can be derived which is the kinetic equation for one mode. Secondly, a suitable iteration scheme is applied to the Hopf equation which results in the same kinetic equation. A parameter describing the time scale is arbitrary and cannot be determined by the applied methods alone. It is shown that the kinetic equation satisfies the conservation requirements and relaxes to an equilibrium which is a rigorous solution of the Hopf equation.

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