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River intakes
Published in Arved J. Raudkivi, Sedimentation, 2020
The major variables are flow rate (Q −QD), flow depth and to a lesser extent flow width. The aim of the design is to cause as little change in the river slope as possible. By knowing (or predicting) the river flow as a function of time, Q = f(time), and the demand QD =f(time), one can determine downstream flow rate as a function of time (Q − QD) =f(t). At any instant the basic equations of continuity of sediment and water transport and the equations of motion must be satisfied. Thus, for water (see Section 2.3) Q−QD=Q1Q=BCyo32S12orQ=Bnyo53S12
Introduction: The optical nature of a charged particle beam
Published in Timothy R. Groves, Charged Particle Optics Theory, 2017
Quantum mechanics teaches that the absolute square of the wave amplitude is equal to the probability that a single measurement finds the particle at a given position at any given instant in time. Because this probability is described by a propagating wave, it is not possible to know the position and momentum simultaneously with perfect precision. This is known as the Heisenberg uncertainty principle, after the physicist who first elucidated it in the 1920s. A remarkable consequence of quantum mechanics, and one which may appear counterintuitive at first, is that a single particle can be described by two or more waves which interfere constructively or destructively with one another. Each wave corresponds to a particular alternative path of motion of the particle, where the actual path of motion is fundamentally unknowable. For example, it is impossible to know which path in Figure 1.4 is the actual path taken by the charged particle. Each possible path can be described by a separate wave, where all of the waves corresponding to the different paths propagate coherently, with a particular phase relationship to one another. They all interfere at the image plane to cause a blurred spot (not depicted in the figure).
Rigid Body Motion
Published in Richard M. Murray, Zexiang Li, S. Shankar Sastry, A Mathematical Introduction to Robotic Manipulation, 2017
Richard M. Murray, Zexiang Li, S. Shankar Sastry
The motion of a particle moving in Euclidean space is described by giving the location of the particle at each instant of time, relative to an inertial Cartesian coordinate frame. Specifically, we choose a set of three orthonormal axes and specify the particle’s location using the triple (x, y, z) ∈ ℝ3, where each coordinate gives the projection of the particle’s location onto the corresponding axis. A trajectory of the particle is represented by the parameterized curve p(t) = (x(t), y(t), z(t)) ∈ ℝ3.
Self-triggered model predictive control of discrete-time Markov jump linear systems
Published in International Journal of Control, 2023
Peng He, Jiwei Wen, Xiaoli Luan, Fei Liu
Self-triggered scheme, as an aperiodic sampling scheme, is proposed for computational and communicational resources saving with the increasing popularity of wired and wireless networks in control systems (Heemels et al., 2012). In some systems, control tasks share communication networks, and communication resources can be scarce. In this case, it might not be necessary to perform control actions at all time-triggered periods to guarantee the closed-loop performance (Gommans et al., 2014). Therefore, aperiodic sampling schemes, mainly event-triggered scheme and self-triggered scheme, are proposed to reduce unnecessary sampling. In event-triggered scheme, the triggering time instant is determined by continuously monitoring the current measurements. In self-triggered scheme, the next triggering time instant when the control action has to be updated is computed based on current system dynamics. In recent years, aperiodic sampling control is of growing interest, such as in the study of network control frameworks (Fei et al., 2017; Henriksson et al., 2015), switched systems (Fei et al., 2019; Qi et al., 2018) and Markov jump systems (Guan et al., 2020; Wan et al., 2020).
Analyzing the role of the Inf-Sup condition for parameter identification in saddle point problems with application in elasticity imaging
Published in Optimization, 2020
Baasansuren Jadamba, Akhtar A. Khan, Michael Richards, Miguel Sama, Christiane Tammer
Saddle point problem (3) leads to a non-invertible system after discretization, requiring specialized solution strategies. A commonly used technique is to regularize (3), an instant advantage being that the regularized saddle point problem leads to an invertible system. Let be a continuous and elliptic bilinear form. That is, there are constants and with Given the regularized saddle point problem seeks with The regularized saddle point problem (10) possesses some crucial computational advantages over (3), and it has been studied extensively, see [23,25,26].
Energy management in solar microgrid via reinforcement learning using fuzzy reward
Published in Advances in Building Energy Research, 2018
Panagiotis Kofinas, George Vouros, Anastasios I. Dounis
We assume that the time interval between two consecutive instants is 50 s. At any time instant the agent performs one action for the battery and one action for the desalination unit. The actions which can take place in the battery are two: charging (‘C’) and discharging (‘D’). If there is an energy surplus and the battery is in charging mode, then it absorbs the remaining power. If there is surplus in energy and the battery is in discharging mode then the battery does not charge or discharge. If there is deficit in energy and the battery is in charging mode, the battery does not charge or discharge too. If there is energy deficit and the battery is in discharging mode, the battery offers the power that is needed. The actions that can take place in the desalination unit are two. Stop (‘S’) and operate at maximum power of 550 W (‘P’). If the desalination unit is in operation, the desalination unit consumes 550 W and potable water is added into the tank with a rate of about 100 lt/h. If the desalination unit is in no operation mode the desalination unit consumes 0 W and no water is added in the tank. Thus, the agent at any time instant may decide any combination of two actions.