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Improving the multi-objective evolutionary optimization algorithm for hydropower reservoir operations in the California Oroville-Thermalito complex
This study demonstrates the application of an improved Evolutionary optimization Algorithm (EA), titled Multi-Objective Complex Evolution Global Optimization Method with Principal Component Analysis and Crowding Distance Operator (MOSPD), for the hydropower reservoir operation of the Oroville-Thermalito Complex (OTC) - a crucial head-water resource for the California State Water Project (SWP). In the OTC's water-hydropower joint management study, the nonlinearity of hydropower generation and the reservoir's water elevation-storage relationship are explicitly formulated by polynomial function in order to closely match realistic situations and reduce linearization approximation errors. Comparison among different curve-fitting methods is conducted to understand the impact of the simplification of reservoir topography. In the optimization algorithm development, techniques of crowding distance and principal component analysis are implemented to improve the diversity and convergence of the optimal solutions towards and along the Pareto optimal set in the objective space. A comparative evaluation among the new algorithm MOSPD, the original Multi-Objective Complex Evolution Global Optimization Method (MOCOM), the Multi-Objective Differential Evolution method (MODE), the Multi-Objective Genetic Algorithm (MOGA), the Multi-Objective Simulated Annealing approach (MOSA), and the Multi-Objective Particle Swarm Optimization scheme (MOPSO) is conducted using the benchmark functions. The results show that best the MOSPD algorithm demonstrated the best and most consistent performance when compared with other algorithms on the test problems. The newly developed algorithm (MOSPD) is further applied to the OTC reservoir releasing problem during the snow melting season in 1998 (wet year), 2000 (normal year) and 2001 (dry year), in which the more spreading and converged non-dominated solutions of MOSPD provide decision makers with better operational alternatives for effectively and efficiently managing the OTC reservoirs in response to the different climates, especially drought, which has become more and more severe and frequent in California
Dissipative Bose-Einstein condensation in contact with a thermal reservoir
We investigate the real-time dynamics of open quantum spin- or hardcore
boson systems on a spatial lattice, which are governed by a Markovian quantum
master equation. We derive general conditions under which the hierarchy of
correlation functions closes such that their time evolution can be computed
semi-analytically. Expanding our previous work [Phys. Rev. A 93, 021602 (2016)]
we demonstrate the universality of a purely dissipative quantum Markov process
that drives the system of spin- particles into a totally symmetric
superposition state, corresponding to a Bose-Einstein condensate of hardcore
bosons. In particular, we show that the finite-size scaling behavior of the
dissipative gap is independent of the chosen boundary conditions and the
underlying lattice structure. In addition, we consider the effect of a uniform
magnetic field as well as a coupling to a thermal bath to investigate the
susceptibility of the engineered dissipative process to unitary and nonunitary
perturbations. We establish the nonequilibrium steady-state phase diagram as a
function of temperature and dissipative coupling strength. For a small number
of particles , we identify a parameter region in which the engineered
symmetrizing dissipative process performs robustly, while in the thermodynamic
limit , the coupling to the thermal bath destroys any
long-range order.Comment: 30 pages, 8 figures; Revised version: Minor changes and references
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Dynamical generation of the constituent mass in expanding plasma
We investigate dynamics of the chiral transition in expanding quark-antiquark
plasma produced in an ultra-relativistic heavy ion collision. The chiral
symmetry break-down and dynamical generation of the constituent quark mass are
studied within the linear sigma model and Nambu-Jona-Lasinio model. Time
dependence of the quark and antiquark densities is obtained from the scaling
solution of the relativistic Vlasov equation. Fast initial growth and strong
oscillations of the constituent quark mass are found in the linear sigma model
as well as in the NJL model, when derivative terms are taken into account.Comment: 7 pages, Latex. To appear in Physics Letters
A numerical method with properties of consistency in the energy domain for a class of dissipative nonlinear wave equations with applications to a Dirichlet boundary-value problem
In this work, we present a conditionally stable finite-difference scheme that
consistently approximates the solution of a general class of (3+1)-dimensional
nonlinear equations that generalizes in various ways the quantitative model
governing discrete arrays consisting of coupled harmonic oscillators.
Associated with this method, there exists a discrete scheme of energy that
consistently approximates its continuous counterpart. The method has the
properties that the associated rate of change of the discrete energy
consistently approximates its continuous counterpart, and it approximates both
a fully continuous medium and a spatially discretized system. Conditional
stability of the numerical technique is established, and applications are
provided to the existence of the process of nonlinear supratransmission in
generalized Klein-Gordon systems and the propagation of binary signals in
semi-unbounded, three-dimensional arrays of harmonic oscillators coupled
through springs and perturbed harmonically at the boundaries, where the basic
model is a modified sine-Gordon equation; our results show that a perfect
transmission is achieved via the modulation of the driving amplitude at the
boundary. Additionally, we present an example of a nonlinear system with a
forbidden band-gap which does not present supratransmission, thus establishing
that the existence of a forbidden band-gap in the linear dispersion relation of
a nonlinear system is not a sufficient condition for the system to present
supratransmission
Unified Approach to KdV Modulations
We develop a unified approach to integrating the Whitham modulation
equations. Our approach is based on the formulation of the initial value
problem for the zero dispersion KdV as the steepest descent for the scalar
Riemann-Hilbert problem, developed by Deift, Venakides, and Zhou, 1997, and on
the method of generating differentials for the KdV-Whitham hierarchy proposed
by El, 1996. By assuming the hyperbolicity of the zero-dispersion limit for the
KdV with general initial data, we bypass the inverse scattering transform and
produce the symmetric system of algebraic equations describing motion of the
modulation parameters plus the system of inequalities determining the number
the oscillating phases at any fixed point on the - plane. The resulting
system effectively solves the zero dispersion KdV with an arbitrary initial
data.Comment: 27 pages, Latex, 5 Postscript figures, to be submitted to Comm. Pure.
Appl. Mat
Analytic model for a frictional shallow-water undular bore
We use the integrable Kaup-Boussinesq shallow water system, modified by a
small viscous term, to model the formation of an undular bore with a steady
profile. The description is made in terms of the corresponding integrable
Whitham system, also appropriately modified by friction. This is derived in
Riemann variables using a modified finite-gap integration technique for the
AKNS scheme. The Whitham system is then reduced to a simple first-order
differential equation which is integrated numerically to obtain an asymptotic
profile of the undular bore, with the local oscillatory structure described by
the periodic solution of the unperturbed Kaup-Boussinesq system. This solution
of the Whitham equations is shown to be consistent with certain jump conditions
following directly from conservation laws for the original system. A comparison
is made with the recently studied dissipationless case for the same system,
where the undular bore is unsteady.Comment: 24 page
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