Search results for "Theory"
showing 10 items of 24627 documents
Constant inner potential DFT for modelling electrochemical systems under constant potential and bias
2021
Electrochemical interfaces and reactions play a decisive role in e.g. clean energy conversion but understanding their complex chemistry remains an outstanding challenge. Constant potential or grand canonical ensemble (GCE) simulations are indispensable for unraveling the properties of electrochemical processes as a function of the electrode potential. Currently, constant electrode potential calculations at the density functional theory (DFT) level are carried out by fixing the Fermi level of the simulation cell. However, the Fermi level from DFT calculations does does not always reflect the experimentally controlled electrode potential or describe the thermodynamic independent variable in G…
Jacobi Fields, Conjugate Points
2001
Let us go back to the action principle as realized by Jacobi, i.e., time is eliminated, so we are dealing with the space trajectory of a particle. In particular, we want to investigate the conditions under which a path is a minimum of the action and those under which it is merely an extremum. For illustrative purposes we consider a particle in two-dimensional real space.
Arm Space Decomposition as a Strategy for Tackling Large Scale Multi-armed Bandit Problems
2013
Recent multi-armed bandit based optimization schemes provide near-optimal balancing of arm exploration against arm exploitation, allowing the optimal arm to be identified with probability arbitrarily close to unity. However, the convergence speed drops dramatically as the number of bandit arms grows large, simply because singling out the optimal arm requires experimentation with all of the available arms. Furthermore, effective exploration and exploitation typically demands computational resources that grow linearly with the number of arms. Although the former problem can be remedied to some degree when prior knowledge about arm correlation is available, the latter problem persists. In this…
Predictive control of networked systems with communication delays
2012
This paper studies the problem of predictive output feedback control for networked control systems with random communication delays. A networked predictive control scheme is employed to compensate for random communication delays, which mainly consists of the control prediction generator and network delay compensator. Furthermore, a new strategy of designing the time-varying predictive controller with mixed random delays for networked systems is proposed. Then the system can be formulated as a Markovian jump system. New techniques are presented to deal with the distributed delay in the discrete-time domain. Based on analysis of closed-loop networked predictive control systems, the designed p…
Non Linear Systems Under Complex α-Stable Le´vy White Noise
2003
The problem of predicting the response of linear and nonlinear systems under Levy white noises is examined. A method of analysis is proposed based on the observation that these processes have impulsive character, so that the methods already used for Poisson white noise or normal white noise may be also recast for Levy white noises. Since both the input and output processes have no moments of order two and higher, the response is here evaluated in terms of characteristic function.Copyright © 2003 by ASME
Sliding mode exponential H<inf>&#x221E;</inf> synchronization of Markovian jumping master-slave systems with time-delays and nonlinea…
2011
This paper investigates the problem of exponential H ∞ synchronization for a class of master-slave systems with both discrete and distributed time-delays, norm-bounded nonlinear uncertainties and Markovian switching parameters. Using an appropriate Lyapunov-Krasovskii functional, some delay-dependent sufficient conditions and a synchronization law which include the master-slave parameters are established for designing a delay-dependent mode-dependent sliding mode exponential H ∞ synchronization control law in terms of linear matrix inequalities. The controller guarantees the H ∞ synchronization of the two coupled master and slave systems regardless of their initial states. A numerical examp…
Non-linear systems under parametric alpha-stable LÉVY WHITE NOISES
2005
In this study stochastic analysis of nonlinear dynamical systems under a-stable, multiplicative white noise has been performed. Analysis has been conducted by means of the Ito rule extended to the case of α-stable noises. In this context the order of increments of Levy process has been evaluated and differential equations ruling the evolutions of statistical moments of either parametrically and external dynamical systems have been obtained. The extended Ito rule has also been used to yield the differential equation ruling the evolution of the characteristic function for parametrically excited dynamical systems. The Fourier transform of the characteristic function, namely the probability den…
A novel approach to nonlinear variable-order fractional viscoelasticity.
2020
This paper addresses nonlinear viscoelastic behaviour of fractional systems with variable time-dependent fractional order. In this case, the main challenge is that the Boltzmann linear superposition principle, i.e. the theoretical basis on which linear viscoelastic fractional operators are formulated, does not apply in standard form because the fractional order is not constant with time. Moving from this consideration, the paper proposes a novel approach where the system response is derived by a consistent application of the Boltzmann principle to an equivalent system, built at every time instant based on the fractional order at that instant and the response at all the previous ones. The ap…
Self-regulation mechanism of an ecosystem in a non-Gaussian fluctuation regime
1996
We study a dynamical model for an ecological network of many interacting species. We consider a Malthus-Verhulst type of self-regulation mechanism. In the framework of the mean field theory we study the nonlinear relaxation in three different cases: (a) towards the equilibrium state, (b) towards the absorbing barrier, (c) at the critical point. We obtain asymptotic behavior in all different cases for the time average of the process. The dynamical behavior of the system, in the limit of infinitely many interacting species, is investigated in the stability and instability conditions and theoretical results are compared with numerical simulations. \textcopyright{} 1996 The American Physical So…
Modal analysis for random response of MDOF systems
1990
The usefulness of the mode-superposition method of multidegrees of freedom systems excited by stochastic vector processes is here presented. The differential equations of moments of every order are written in compact form by means of the Kronecker algebra; then the method for integration of these equations is presented for both classically and non-classically damped systems, showing that the fundamental operator available for evaluating the response in the deterministic analysis is also useful for evaluating the response in the stochastic analysis.