scholarly journals Minimizing movements for oscillating energies: the critical regime

2018 ◽  
Vol 149 (03) ◽  
pp. 719-737 ◽  
Author(s):  
Nadia Ansini ◽  
Andrea Braides ◽  
Johannes Zimmer
Keyword(s):  
Initial Data ◽  
Time Scales ◽  
Fast Time ◽  
Convex Functional ◽  
Slow Time ◽  
Time Step ◽  
Small Oscillations ◽  
Spatial Parameter ◽  
Minimizing Movements

AbstractMinimizing movements are investigated for an energy which is the superposition of a convex functional and fast small oscillations. Thus a minimizing movement scheme involves a temporal parameter τ and a spatial parameter ε, with τ describing the time step and the frequency of the oscillations being proportional to 1/ε. The extreme cases of fast time scales τ ≪ ε and slow time scales ε ≪ τ have been investigated in [4]. In this paper, the intermediate (critical) case of finite ratio ε/τ > 0 is studied. It is shown that a pinning threshold exists, with initial data below the threshold being a fixed point of the dynamics. A characterization of the pinning threshold is given. For initial data above the pinning threshold, the equation and velocity describing the homogenized motion are determined.

scholarly journals Slow and Fast Time Scales in Cardiomyocyte Beating

2019 ◽  
Vol 116 (3) ◽  
pp. 162a
Author(s):  
Ohad Cohen ◽  
Samuel Safran
Keyword(s):  
Time Scales ◽  
Fast Time

GLOBAL EXISTENCE FOR PHASE TRANSITION PROBLEMS VIA A VARIATIONAL SCHEME

2004 ◽  
Vol 01 (04) ◽  
pp. 747-768
Author(s):  
CHRISTIAN ROHDE ◽  
MAI DUC THANH
Keyword(s):  
Phase Transition ◽  
Surface Tension ◽  
Initial Data ◽  
Time Discretization ◽  
Approximate Solutions ◽  
Implicit Time ◽  
Time Step ◽  
Dynamical Phase Transition ◽  
Transition Dynamics ◽  
Variational Scheme

We construct approximate solutions of the initial value problem for dynamical phase transition problems via a variational scheme in one space dimension. First, we deal with a local model of phase transition dynamics which contains second and third order spatial derivatives modeling the effects of viscosity and surface tension. Assuming that the initial data are periodic, we prove the convergence of approximate solutions to a weak solution which satisfies the natural dissipation inequality. We note that this result still holds for non-periodic initial data. Second, we consider a model of phase transition dynamics with only Lipschitz continuous stress–strain function which contains a non-local convolution term to take account of surface tension. We also establish the existence of weak solutions. In both cases the proof relies on implicit time discretization and the analysis of a minimization problem at each time step.

A New Model for Long-Term Stochastic Analysis and Prediction—Part I: Theoretical Background

1992 ◽  
Vol 36 (01) ◽  
pp. 1-16
Author(s):  
G. A. Athanassoulis ◽  
P. B. Vranas ◽  
T. H. Soukissian
Keyword(s):  
Time Scale ◽  
Random Function ◽  
Spectral Characteristics ◽  
Time History ◽  
Time Variable ◽  
Sea Surface ◽  
Surface Elevation ◽  
Fast Time ◽  
Slow Time

A new approach for calculating the long-term statistics of sea waves is proposed. A rational long-term stochastic model is introduced which recognizes that the wave climate at a given site in the ocean consists of a random succession of individual sea states, each sea state possessing its own duration and intensity. This model treats the sea-surface elevation as a random function of a "fast" time variable, and the time history of the spectral characteristics of the successive sea states as a random function of a "slow" time variable. By developing an appropriate conceptual framework, it becomes possible to express various probabilistic characteristics of the sea-surface elevation, which are sensible only in the fast-time scale, in terms of the statistics of sea-states duration and intensity, which is meaningful only in the slow-time scale. As an example, we study the random quantity MU(T) = "number of maxima of the sea-surface elevation lying above the level u and occurring during a long-term time period [0,T]." Exploiting the proposed framework, it is shown that, under certain clearly defined assumptions, Mu(T) can be given the structure of a renewal-reward (cumulative) process, whose interarrival times correspond to the duration of successive sea states. Thus, using renewal theory, the complete characterization of the probability structure of MU(T) is obtained. As a consequence, the long-term probability distribution function of the individual wave height is rigorously defined and calculated. The relation of the present results with corresponding ones previously obtained is thoroughly discussed. The proposed model can be extended twofold: either by replacing some of the simplifying assumptions by more realistic ones, or by extending the model for treating the corresponding problems for ship and structures responses.

Parameter Estimation in a Nonlinear Vibrating System Using an Observer for an Extended System

1999 ◽  
Author(s):  
Anindya Chatterjee ◽  
Joseph P. Cusumano
Keyword(s):  
Parameter Estimation ◽  
Time Scale ◽  
Asymptotic Methods ◽  
System Response ◽  
Parameter Estimates ◽  
Fast Time ◽  
State Variables ◽  
Slow Time ◽  
Unknown Parameters ◽  
Lipschitz Continuous

Abstract We present a new observer-based method for parameter estimation for nonlinear oscillatory mechanical systems where the unknown parameters appear linearly (they may each be multiplied by bounded and Lipschitz continuous but otherwise arbitrary, possibly nonlinear, functions of the oscillatory state variables and time). The oscillations in the system may be periodic, quasiperiodic or chaotic. The method is also applicable to systems where the parameters appear nonlinearly, provided a good initial estimate of the parameter is available. The observer requires measurements of displacements. It estimates velocities on a fast time scale, and the unknown parameters on a slow time scale. The fast and slow time scales are governed by a single small parameter ϵ. Using asymptotic methods including the method of averaging, it is shown that the observer’s estimates of the unknown parameters converge like e−ϵt where t is time, provided the system response is such that the coefficient-functions of the unknown parameters are not close to being linearly dependent. It is also shown that the method is robust in that small errors in the model cause small errors in the parameter estimates. A numerical example is provided to demonstrate the effectiveness of the method.

Characterization of Microbial Fuel Cells at Microbially and Electrochemically Meaningful Time scales

2011 ◽  
Vol 45 (6) ◽  
pp. 2435-2441 ◽  
Author(s):  
Zhiyong Ren ◽  
Hengjing Yan ◽  
Wei Wang ◽  
Matthew M. Mench ◽  
John M. Regan
Keyword(s):  
Fuel Cells ◽  
Time Scales ◽  
Microbial Fuel Cells

Comparative effects of vasodilator drugs on flow distribution and venous return

1985 ◽  
Vol 63 (11) ◽  
pp. 1345-1355 ◽  
Author(s):  
R. I. Ogilvie
Keyword(s):  
Blood Flow ◽  
Blood Volume ◽  
Time Constant ◽  
Venous Return ◽  
Flow Distribution ◽  
Fast Time ◽  
Central Blood Volume ◽  
Slow Time ◽  
Arterial Resistance ◽  
Slow Time Constant

Systemic vascular effects of hydralazine, prazosin, captopril, and nifedipine were studied in 115 anesthetized dogs. Blood flow [Formula: see text] and right atrial pressure (Pra) were independently controlled by a right heart bypass. Transient changes in central blood volume after an acute reduction in Pra at a constant [Formula: see text] showed that blood was draining from two vascular compartments with different time constants, one fast and the other slow. At three dose levels producing comparable reductions in systemic arterial pressure (30–40% at the highest dose), these drugs had different effects on flow distribution and venous return. Hydralazine and prazosin had parallel and balanced effects on arterial resistance of the two vascular compartments, and flow distribution was unaltered. Captopril preferentially reduced arterial resistance of the compartment with a slow time constant for venous return (−26 ± 6%, −30 ± 6%, −50 ± 5% at 0.02, 0.10, and 0.50 mg∙kg−1∙h−1, respectively; [Formula: see text]) without altering arterial resistance of the fast time-constant compartment. Blood flow to the slow time-constant compartment was increased 43 ± 14% at the highest dose, and central blood volume was reduced 108 ± 15 mL. In contrast, nifedipine had a balanced effect on arterial resistance with the lowest dose (0.025 mg/kg) but caused a preferential reduction in arterial resistance of the fast time-constant compartment at higher doses (−38 ± 4% and −55 ± 2% at 0.05 and 0.10 mg/kg, respectively). Blood flow to the slow time-constant compartment was reduced 36 ± 5% at the highest dose of nifedipine, and central blood volume was increased 66 ± 12 mL. Total systemic venous compliance was unaltered or slightly reduced by each of the four drugs. These results add further evidence to the hypothesis that peripheral blood flow distribution is a major determinant of venous return to the heart.

Nonlinear acoustic forces acting on inhomogeneous fluids at slow time-scales

2016 ◽  
Vol 139 (4) ◽  
pp. 2152-2152 ◽  
Author(s):  
Jonas T. Karlsen ◽  
Per Augustsson ◽  
Henrik Bruus
Keyword(s):  
Time Scales ◽  
Slow Time ◽  
Inhomogeneous Fluids ◽  
Nonlinear Acoustic

scholarly journals Composite Stackelberg Strategy for Singularly Perturbed Bilinear Quadratic Systems

2015 ◽  
Vol 3 (2) ◽  
pp. 154-163
Author(s):  
Ning Bin ◽  
Chengke Zhang ◽  
Huainian Zhu ◽  
Zan Mo
Keyword(s):  
Singularly Perturbed ◽  
Stackelberg Equilibrium ◽  
Order System ◽  
Fast Time ◽  
Slow Time ◽  
Stackelberg Strategy ◽  
Fast Time Scale ◽  
Equilibrium Strategies ◽  
Numerical Result ◽  
Coupled Algebraic Riccati Equations

AbstractBased on singularly perturbed bilinear quadratic problems, this paper proposes to decompose the full-order system into two subsystems of a slow-time and fast-time scale. Utilizing the fixed point iterative algorithm to solve cross-coupled algebraic Riccati equations, equilibrium strategies of the two subsystems can be obtained, and further the composite strategy of the original full-order system. It was proved that such a composite strategy formed ano(ε) (near) Stackelberg equilibrium, and a numerical result of the algorithm was presented in the end.

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