scholarly journals Controlling the Shannon Entropy of Quantum Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yifan Xing ◽  
Jun Wu
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Shannon Entropy ◽  
Quantum Control ◽  
Control Method ◽  
Controller Design ◽  
Three Dimensional ◽  
Quantum Systems ◽  
Discretization Method

This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.

PROBABILITY DENSITY FUNCTION CONTROL OF QUANTUM SYSTEMS

2011 ◽  
Vol 25 (17) ◽  
pp. 2289-2297 ◽  
Author(s):  
YI-FAN XING ◽  
JUN WU
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Quantum Control ◽  
Quantum Systems ◽  
Quantum Model ◽  
Control Engineering ◽  
Control Of Quantum Systems ◽  
Probability Density Function Pdf ◽  
Specific Control

This paper proposes a new method of controlling quantum systems via probability density function (PDF) control. Based on the quantum model from the PDF perspective, two specific control algorithms are proposed for the general case and limited input energy, respectively. Unlike traditional quantum control methods, this method directly controls the probability distribution of the quantum state. It provides an alternative method for quantum control engineering.

scholarly journals Derivation of Equations for a Size Distribution of Spherical Particles in Non-Transparent Materials

2021 ◽  
Vol 5 (4) ◽  
pp. 53-60
Author(s):  
Daniel Gurgul ◽  
Andriy Burbelko ◽  
Tomasz Wiktor
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Size Distribution ◽  
Density Function ◽  
Cross Section ◽  
Three Dimensional ◽  
Spherical Particles ◽  
Two Dimensional ◽  
Mathematical Formulas ◽  
Transparent Materials

This paper presents a new proposition on how to derive mathematical formulas that describe an unknown Probability Density Function (PDF3) of the spherical radii (r3) of particles randomly placed in non-transparent materials. We have presented two attempts here, both of which are based on data collected from a random planar cross-section passed through space containing three-dimensional nodules. The first attempt uses a Probability Density Function (PDF2) the form of which is experimentally obtained on the basis of a set containing two-dimensional radii (r2). These radii are produced by an intersection of the space by a random plane. In turn, the second solution also uses an experimentally obtained Probability Density Function (PDF1). But the form of PDF1 has been created on the basis of a set containing chord lengths collected from a cross-section.The most important finding presented in this paper is the conclusion that if the PDF1 has proportional scopes, the PDF3 must have a constant value in these scopes. This fact allows stating that there are no nodules in the sample space that have particular radii belonging to the proportional ranges the PDF1.

scholarly journals Assessment of a three-dimensional line-of-response probability density function system matrix for PET

2012 ◽  
Vol 57 (21) ◽  
pp. 6827-6848 ◽  
Author(s):  
Rutao Yao ◽  
Ranjith M Ramachandra ◽  
Neeraj Mahajan ◽  
Vinay Rathod ◽  
Noel Gunasekar ◽  
...  
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Three Dimensional ◽  
Response Probability ◽  
Function System ◽  
System Matrix

A probability density function method for turbulent mixing and combustion on three-dimensional unstructured deforming meshes

2000 ◽  
Vol 1 (2) ◽  
pp. 171-190 ◽  
Author(s):  
S Subramaniam ◽  
D. C. Haworth
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Turbulent Mixing ◽  
Three Dimensional ◽  
Quantitative Agreement ◽  
Particle Number Density ◽  
Time Dependent ◽  
Ic Engine ◽  
Density Control

A hybrid Lagrangian-Eulerian methodology is developed for numerical simulation of turbulent mixing and combustion in arbitrary three-dimensional time-dependent geometric configurations. The context is a probability density function (PDF) based approach intended for modelling in cylinder processes in reciprocating piston internal combustion (IC) engines. Issues addressed include mean estimation, particle tracking and particle number-density control on three-dimensional unstructured deforming meshes. The suitability of the methodology for statistically time-dependent three-dimensional turbulent flow with large density variations is demonstrated via simulations of turbulent freon vapour/air mixing on an unstructured deforming mesh representing an idealized IC engine [13]. Computed profiles of mean and r.m.s. freon mole fractions show good quantitative agreement with measurements. Moreover, inherent advantages of the Lagrangian-Eulerian PDF approach are demonstrated, compared to Eulerian finite volume solutions of an (approximately) equivalent set of moment equations. The new approach is, by design, compatible with existing computational fluid dynamics codes that are used for multidimensional modelling of in-cylinder thermal fluids processes. This work broadens the accessibility of PDF methods for practical turbulent combustion systems.

Development and Application of a Transported Probability Density Function Method on Unstructured Three-Dimensional Grids for the Prediction of Nitric Oxides

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
Andreas Fiolitakis ◽  
Peter Ess ◽  
Peter Gerlinger ◽  
Manfred Aigner
Keyword(s):  
Nitric Oxide ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Flame Structure ◽  
Hybrid Approach ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Nitric Oxides ◽  
German Aerospace

The present work explores the capability of the transported probability density function (PDF) method to predict nitric oxide (NO) formation in turbulent combustion. To this end a hybrid finite-volume/Lagrangian Monte Carlo method is implemented into the THETA code of the German Aerospace Center (DLR). In this hybrid approach the transported PDF method governs the evolution of the thermochemical variables, whereas the flow field evolution is computed with a Reynolds-averaged Navier–Stokes (RANS) method. The method is used to compute a turbulent hydrogen-air flame and a methane-air flame and computational results are compared to experimental data. In order to assess the advantages of the transported PDF method, the flame computations are repeated with the “laminar chemistry” approach as well as with an “assumed PDF” method, which are both computationally less expensive. The present study reveals that the transported PDF method provides the highest accuracy in predicting the overall flame structure and nitric oxide formation.

scholarly journals Shannon Entropy Estimation for Linear Processes

2020 ◽  
Vol 13 (9) ◽  
pp. 205
Author(s):  
Timothy Fortune ◽  
Hailin Sang
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Shannon Entropy ◽  
Kernel Density ◽  
Linear Process ◽  
Kernel Density Estimator ◽  
Density Estimator ◽  
Linear Processes ◽  
Entropy Estimation

In this paper, we estimate the Shannon entropy S(f)=−E[log(f(x))] of a one-sided linear process with probability density function f(x). We employ the integral estimator Sn(f), which utilizes the standard kernel density estimator fn(x) of f(x). We show that Sn(f) converges to S(f) almost surely and in Ł2 under reasonable conditions.

scholarly journals On the velocity distribution in homogeneous isotropic turbulence: correlations and deviations from Gaussianity

2011 ◽  
Vol 676 ◽  
pp. 191-217 ◽  
Author(s):  
MICHAEL WILCZEK ◽  
ANTON DAITCHE ◽  
RUDOLF FRIEDRICH
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Isotropic Turbulence ◽  
Single Point ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Homogeneous Isotropic Turbulence ◽  
Navier Stokes Equation ◽  
Conditional Averaging

We investigate the single-point probability density function of the velocity in three-dimensional stationary and decaying homogeneous isotropic turbulence. To this end, we apply the statistical framework of the Lundgren–Monin–Novikov hierarchy combined with conditional averaging, identifying the quantities that determine the shape of the probability density function. In this framework, the conditional averages of the rate of energy dissipation, the velocity diffusion and the pressure gradient with respect to velocity play a key role. Direct numerical simulations of the Navier–Stokes equation are used to complement the theoretical results and assess deviations from Gaussianity.

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