scholarly journals Topology Structure Implied in β-Hilbert Space, Heisenberg Uncertainty Quantum Characteristics and Numerical Simulation of the DE Algorithm

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 330 ◽  
Author(s):  
Kaiguang Wang ◽  
Yuelin Gao
Keyword(s):  
Numerical Simulation ◽  
Hilbert Space ◽  
Topological Structure ◽  
Single Point ◽  
Inverse Correlation ◽  
Quantum States ◽  
Iterative Sequence ◽  
Optimal Point ◽  
Global Optimal ◽  
Changing Rate

The differential evolutionary ( D E ) algorithm is a global optimization algorithm. To explore the convergence implied in the H i l b e r t space with the parameter β of the D E algorithm and the quantum properties of the optimal point in the space, we establish a control convergent iterative form of a higher-order differential equation under the conditions of P - ε and analyze the control convergent properties of its iterative sequence; analyze the three topological structures implied in H i l b e r t space of the single-point topological structure, branch topological structure, and discrete topological structure; and establish and analyze the association between the H e i s e n b e r g uncertainty quantum characteristics depending on quantum physics and its topological structure implied in the β -Hilbert space of the D E algorithm as follows: The speed resolution Δ v 2 of the iterative sequence convergent speed and the position resolution Δ x β ε of the global optimal point with the swinging range are a pair of conjugate variables of the quantum states in β -Hilbert space about eigenvalues λ i ∈ R , corresponding to the uncertainty characteristics on quantum states, and they cannot simultaneously achieve bidirectional efficiency between convergent speed and the best point precision with any procedural improvements. Where λ i ∈ R is a constant in the β -Hilbert space. Finally, the conclusion is verified by the quantum numerical simulation of high-dimensional data. We get the following important quantitative conclusions by numerical simulation: except for several dead points and invalid points, under the condition of spatial dimension, the number of the population, mutated operator, crossover operator, and selected operator are generally decreasing or increasing with a variance deviation rate + 0 . 50 and the error of less than ± 0 . 5 ; correspondingly, speed changing rate of the individual iterative points and position changing rate of global optimal point β exhibit a inverse correlation in β -Hilbert space in the statistical perspectives, which illustrates the association between the H e i s e n b e r g uncertainty quantum characteristics and its topological structure implied in the β -Hilbert space of the D E algorithm.

Numerical simulation of squeezing Cu–Water nanofluid flow by a kernel-based method

2021 ◽  
pp. 2250005
Author(s):  
Mojtaba Fardi ◽  
Yasir Khan
Keyword(s):  
Numerical Simulation ◽  
Hilbert Space ◽  
Linear System ◽  
Numerical Simulations ◽  
Numerical Results ◽  
Kernel Matrix ◽  
Nanofluid Flow ◽  
Parallel Disks ◽  
Engineering Problems ◽  
Well Conditioning

The main aim of this paper is to propose a kernel-based method for solving the problem of squeezing Cu–Water nanofluid flow between parallel disks. Our method is based on Gaussian Hilbert–Schmidt SVD (HS-SVD), which gives an alternate basis for the data-dependent subspace of “native” Hilbert space without ever forming kernel matrix. The well-conditioning linear system is one of the critical advantages of using the alternate basis obtained from HS-SVD. Numerical simulations are performed to illustrate the efficiency and applicability of the proposed method in the sense of accuracy. Numerical results obtained by the proposed method are assessed by comparing available results in references. The results demonstrate that the proposed method can be recommended as a good option to study the squeezing nanofluid flow in engineering problems.

scholarly journals The Spatio-Temporal Evolution of River Island Based on Landsat Satellite Imagery, Hydrodynamic Numerical Simulation and Observed Data

2018 ◽  
Vol 10 (12) ◽  
pp. 2046 ◽  
Author(s):  
Haiyun Shi ◽  
Yuhan Cao ◽  
Changming Dong ◽  
Changshui Xia ◽  
Chunhui Li
Keyword(s):  
Numerical Simulation ◽  
Temporal Evolution ◽  
Thematic Mapper ◽  
Sediment Discharge ◽  
Natural Factor ◽  
River Islands ◽  
Island Evolution ◽  
Spatio Temporal ◽  
Landsat Satellite ◽  
Changing Rate

A river island is a shaped sediment accumulation body with its top above the water’s surface in crooked or branching streams. In this paper, four river islands in Yangzhong City in the lower reaches of the Yangtze River were studied. The spatio-temporal evolution information of the islands was quantitatively extracted using the threshold value method, binarization model, and cluster analysis, based on Thematic Mapper (TM) and Enhanced Thematic Mapper+ (ETM+) images of the Landsat satellite series from 1985 to 2015. The variation mechanism and influencing factors were analyzed using an unstructured-grid, Finite-Volume Coastal Ocean Model (FVCOM) hydrodynamic numerical simulation, as well as the water-sediment data measured by hydrological stations. The annual average total area of these islands was 251,224.46 m2 during 1985–2015, and the total area first increased during 1985–2000 and decreased later during 2000–2015. Generally, the total area increased during these 30 years. Taipingzhou island had the largest area and the biggest changing rate, Xishadao island had the smallest area, and Zhongxinsha island had the smallest changing rate. The river islands’ area change was influenced by river runoff, sediment discharge, and precipitation, and sediment discharge proved to be the most significant natural factor in island evolution. River island evolution was also found to be affected by both runoff and oceanic tide. The difference in flow-field caused silting up in the Leigongdao Island and the head of Taipingzhou Island, and a serious reduction in the middle and tail of Taipingzhou Island. The method used in this paper has good applicability to river islands in other rivers around the world.

Optimal ambiguous discrimination between states given by two projections

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Krzysztof Kaniowski
Keyword(s):  
Hilbert Space ◽  
Quantum States ◽  
Prior Probabilities ◽  
Optimal Measurements

AbstractLet P 0 and P 1 be projections in a Hilbert space H. We shall construct a class of optimal measurements for the problem of discrimination between quantum states $$\rho _i = \tfrac{1} {{\dim P_i }}P_i$$, with prior probabilities π 0 and π 1. The probabilities of failure for such measurements will also be derived.

Quantumness, generalized spherical 2-design, and symmetric informationally complete POVM

2007 ◽  
Vol 7 (8) ◽  
pp. 730-737
Author(s):  
I.H. Kim
Keyword(s):  
Hilbert Space ◽  
Lower Bound ◽  
Equivalence Relation ◽  
Open Problem ◽  
Natural Generalization ◽  
Quantum States ◽  
Minimal Set ◽  
Dimensional Hilbert Space

Fuchs and Sasaki defined the quantumness of a set of quantum states in \cite{Quantumness}, which is related to the fidelity loss in transmission of the quantum states through a classical channel. In \cite{Fuchs}, Fuchs showed that in $d$-dimensional Hilbert space, minimum quantumness is $\frac{2}{d+1}$, and this can be achieved by all rays in the space. He left an open problem, asking whether fewer than $d^2$ states can achieve this bound. Recently, in a different context, Scott introduced a concept of generalized $t$-design in \cite{GenSphet}, which is a natural generalization of spherical $t$-design. In this paper, we show that the lower bound on the quantumness can be achieved if and only if the states form a generalized 2-design. As a corollary, we show that this bound can be only achieved if the number of states are larger or equal to $d^2$, answering the open problem. Furthermore, we also show that the minimal set of such ensemble is Symmetric Informationally Complete POVM(SIC-POVM). This leads to an equivalence relation between SIC-POVM and minimal set of ensemble achieving minimal quantumness.

Research on Flow Characteristics of Aerostatic Circular Thrust Bearing with a Cone Cavity

2011 ◽  
Vol 308-310 ◽  
pp. 189-192
Author(s):  
Long Xing Chen ◽  
Wen Qi Ma ◽  
He Chun Yu ◽  
Hai Yan Liu ◽  
Hong Wang Du
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Thrust Bearing ◽  
Single Point ◽  
Flow Characteristics ◽  
Simulation Method ◽  
Flow Passage ◽  
Testing Method ◽  
Measurement Results ◽  
Simulation And Experiment

The aerostatic circular thrust bearing was taken as a study subject. The numerical simulation method was used to calculate the flow passage. Meanwhile, the single-point testing method was used to test the pressure distribution. The simulation and experiment measurement results were compared and analyzed. The results show that: The single-point testing method is effective to capture the change of flow characteristics. The overall results of simulation and testing coincide with each other well. In the range of cone cavity, the flow pattern for the gas is turbulent flow, and the flow field should be divided into different zones for simulation.

Coherent manipulations of atoms using laser light

2008 ◽  
Vol 58 (3) ◽  
Author(s):  
Bruce Shore
Keyword(s):  
Hilbert Space ◽  
Pulse Propagation ◽  
Laser Light ◽  
Equations Of Motion ◽  
Pulse Sequences ◽  
Three Dimensional ◽  
Analytic Solutions ◽  
Quantum States ◽  
Excitation Energies ◽  
Mathematical Concepts

Coherent manipulations of atoms using laser lightThe internal structure of a particle - an atom or other quantum system in which the excitation energies are discrete - undergoes change when exposed to pulses of near-resonant laser light. This tutorial review presents basic concepts of quantum states, of laser radiation and of the Hilbert-space statevector that provides the theoretical portrait of probability amplitudes - the tools for quantifying quantum properties not only of individual atoms and molecules but also of artificial atoms and other quantum systems. It discusses the equations of motion that describe the laser-induced changes (coherent excitation), and gives examples of laser-pulse effects, with particular emphasis on two-state and three-state adiabatic time evolution within the rotating-wave approximation. It provides pictorial descriptions of excitation based on the Bloch equations that allow visualization of two-state excitation as motion of a three-dimensional vector (the Bloch vector). Other visualization techniques allow portrayal of more elaborate systems, particularly the Hilbert-space motion of adiabatic states subject to various pulse sequences. Various more general multilevel systems receive treatment that includes degeneracies, chains and loop linkages. The concluding sections discuss techniques for creating arbitrary pre-assigned quantum states, for manipulating them into alternative coherent superpositions and for analyzing an unknown superposition. Appendices review some basic mathematical concepts and provide further details of the theoretical formalism, including photons, pulse propagation, statistical averages, analytic solutions to the equations of motion, exact solutions of periodic Hamiltonians, and population-trapping "dark" states.

scholarly journals Numerical simulation of a conical shape made by single point incremental

2013 ◽  
Author(s):  
J. I. V. de Sena ◽  
C. F. Guzman ◽  
L. Duchene ◽  
A. M. Habraken ◽  
R. A. F. Valente ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Single Point ◽  
Conical Shape

A Multi-Point Tire Model for Studying Bridge–Vehicle Coupled Vibration

2016 ◽  
Vol 16 (08) ◽  
pp. 1550047 ◽  
Author(s):  
Lu Deng ◽  
Ran Cao ◽  
Wei Wang ◽  
Xinfeng Yin
Keyword(s):  
Numerical Simulation ◽  
Single Point ◽  
Point Contact ◽  
Road Surface ◽  
Dynamic Responses ◽  
Tire Model ◽  
Point Model ◽  
Disk Model ◽  
The Road ◽  
Dynamic Amplification

The contact between a vehicle tire and the road surface has been usually assumed as a single-point contact in the numerical simulation of vehicle–bridge interacted vibrations. In reality, the tire contacts the road surface through a patch instead of a single point. According to some recent studies, the single-point tire model may overestimate the dynamic amplification of bridge responses due to vehicle loadings. A new tire model, namely, the multi-point tire model, is therefore proposed in this paper with the purpose of improving the accuracy of numerical simulation results over the single-point model, while maintaining a certain level of simplicity for applications. A series of numerical simulations are carried out to compare the effect of the proposed tire model with those of the existing single-point model and disk model on the bridge dynamic responses. The proposed tire model is also verified against the field test results. The results show that the proposed multi-point tire model can predict the bridge dynamic responses with better accuracy than the single-point model, especially under distressed bridge deck conditions, and is computationally more efficient and simpler for application than the disk model.

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