Modeling of turbulent mixing in opposed jet configuration: One-dimensional Monte Carlo probability density function simulation

2000 ◽  
Vol 28 (1) ◽  
pp. 141-148 ◽  
Author(s):  
J. Eckstein ◽  
J.-Y. Chen ◽  
C.-P. Chou ◽  
J. Janicka
Keyword(s):  
Monte Carlo ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Turbulent Mixing ◽  
One Dimensional ◽  
Opposed Jet

scholarly journals A fractional generalization of the dirichlet distribution and related distributions

2021 ◽  
Vol 24 (1) ◽  
pp. 112-136
Author(s):  
Elvira Di Nardo ◽  
Federico Polito ◽  
Enrico Scalas
Keyword(s):  
Monte Carlo ◽  
Probability Density Function ◽  
Monte Carlo Simulations ◽  
Probability Density ◽  
Dirichlet Distribution ◽  
One Dimensional ◽  
Reasonable Approximation ◽  
Generalized Dirichlet Distribution ◽  
The One ◽  
Generalized Dirichlet

Abstract This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the n partitions of the interval [0, Wn ] are independent and identically distributed random variables following the generalized Mittag-Leffler distribution. The expected value and variance of the one-dimensional marginal are derived as well as the form of its probability density function. A related generalized Dirichlet distribution is studied that provides a reasonable approximation for some values of the parameters. The relation between this distribution and other generalizations of the Dirichlet distribution is discussed. Monte Carlo simulations of the one-dimensional marginals for both distributions are presented.

Monte Carlo Probability Density Function Method for Gas Turbine Combustor Flowfield Predictions

1997 ◽  
Vol 13 (2) ◽  
pp. 218-225 ◽  
Author(s):  
Anil K. Tolpadi ◽  
Sanjay M. Correa ◽  
David L. Burrus ◽  
Hukam C. Mongia
Keyword(s):  
Monte Carlo ◽  
Probability Density Function ◽  
Probability Density ◽  
Gas Turbine ◽  
Density Function ◽  
Function Method ◽  
Gas Turbine Combustor

The nature of the electronic states in disordered one-dimensional systems

1963 ◽  
Vol 274 (1359) ◽  
pp. 529-545 ◽  
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Analytical Calculation ◽  
Homogeneous Boundary Condition ◽  
High Electron ◽  
One Dimensional ◽  
Computer Calculations ◽  
A Chain ◽  
Zero Potential

We consider an electron moving in the field of a one-dimensional infinite chain of identical potentials separated by regions of zero potential, the lengths s of these regions being distributed according to a probability density function p(8) . If we define the reduced phase of a real solution of the wave equation as the principal value of arctan ( — ψ'/kψ ) and є i as the reduced phase at the point x i immediately to the left of the i th atomic potential, it is shown for all bounded p(s) and sufficiently high electron energies that the є i are distributed according to a probability density function which depends on the direction of integration from a specified homogeneous boundary condition. This result is shown to imply that the eigenfunctions for such systems are localized in the sense that the envelope of such a function decays on average in an exponential manner on either side of some region. An analytical calculation for a random chain of δ-functions gives the decay of the nodes explicitly for high energies, and numerical calculations of the decay for a liquid model are presented. Further support for the theory is provided by computer calculations of some of the eigenfunctions of a chain of 1000 randomly placed δ-functions.

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.

scholarly journals Mobile/Wireless Robot Navigation

Robotics ◽  
2013 ◽  
pp. 366-374
Author(s):  
Amina Waqar
Keyword(s):  
Monte Carlo ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Efficient Method ◽  
Feedback Loop ◽  
Loop Filter ◽  
Mobile Wireless ◽  
External Loop ◽  
Monte Carlo Localization

Sensor-based localization has been found to be one of the most preliminary issues in the world of Mobile/Wireless Robotics. One can easily track a mobile robot using a Kalman Filter, which uses a Phase Locked Loop for tracing via averaging the values. Tracking has now become very easy, but one wants to proceed to navigation. The reason behind this is that tracking does not help one determine where one is going. One would like to use a more precise “Navigation” like Monte Carlo Localization. It is a more efficient and precise way than a feedback loop because the feedback loops are more sensitive to noise, making one modify the external loop filter according to the variation in the processing. In this case, the robot updates its belief in the form of a probability density function (pdf). The supposition is considered to be one meter square. This probability density function expands over the entire supposition. A door in a wall can be identified as peak/rise in the probability function or the belief of the robot. The mobile updates a window of 1 meter square (area depends on the sensors) as its belief. One starts with a uniform probability density function, and then the sensors update it. The authors use Monte Carlo Localization for updating the belief, which is an efficient method and requires less space. It is an efficient method because it can be applied to continuous data input, unlike the feedback loop. It requires less space. The robot does not need to store the map and, hence, can delete the previous belief without any hesitation.

scholarly journals Συνεισφορά της οπτικής τoμογραφίας OCT (optical computed tomography) στην μονοφωτονική τομοσπινθηρογραφία

2019 ◽  
Author(s):  
Αριστοτέλης-Νικόλαος Ραψομανίκης
Keyword(s):  
Computed Tomography ◽  
Monte Carlo ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Ray Tracing ◽  
Optical Tomography ◽  
Time Resolved ◽  
Optical Computed Tomography ◽  
Pet Ct

Η ανατομική πληροφορία στις καθιερωμένες συνδυαστικές μοριακές απεικονίσεις γίνεται συνήθως με ιοντίζουσες ακτινοβολίες (ακτίνες-Χ, SPECT/CT, PET/CT), οι οποίες επιβαρύνουν κατά κανόνα τον ασθενή με επιπρόσθετη ακτινοβόληση. Η σύγχρονη έρευνα εστιάζεται στη χρήση οπτικών μεθόδων για την υλοποίηση της ζητούμενης μορφολογικής εικόνας, όπου σκεδαζόμενο φως από την υπό εξέταση περιοχή ανακατασκευάζεται κατάλληλα για να αποδώσει τη ζητούμενη ανατομική πληροφορία. Σκοπός της Διδακτορικής αυτής Διατριβής είναι η μελέτη μιας καινοτόμου μεθόδου οπτικής απεικόνισης, όπου, παρά την υψηλή σκεδαστικότητα του μέσου, η χρονικά αξιοποιημένη λαμβανόμενη πληροφορία να δύναται να χρησιμοποιηθεί επιτυχώς για την μορφολογική ανασύσταση του σκεδαζόμενου μέσου σε τομογραφικό επίπεδο. Απώτερος στόχος της μελέτης αυτής είναι η ανάπτυξη ενός υβριδικού τομογραφικού συστήματος αποτελούμενου από μία γ-Camera (SPECT) και ενός συστήματος τηλεκεντρικού φωτισμού με υπέρυθρη παλμική ακτινοβολία και σύστημα οπτικής ανάλυσης με χρονική πληροφορία (Time Resolved Optical Tomography - TROT). Βασικός αρωγός στην κατανόηση των φυσικών διεργασιών στο στάδιο αυτό, πέραν του πειραματικού ελέγχου της εφαρμοσιμότητας συμβατικών μαθηματικών αλγορίθμων για την ανακατασκευή της τομογραφικής εικόνας με υπέρυθρη και οπτική ακτινοβολία, αποτέλεσε η ανάπτυξη ενός εκτεταμένου εργαλείου προσομοίωσης με τεχνικές Monte-Carlo, το οποίο, πέραν από τη λεπτομερή παρακολούθηση της τροχιάς ενός φωτονίου (ray-tracing) σε ισχυρά σκεδαστικό μέσο, καινοτομεί σε δύο βασικά σημεία: Εισάγει με στοχαστικό τρόπο, υπό τη μορφή συνάρτησης πυκνότητας πιθανότητας (probability density function), την μακροσκοπική προσομοίωση της κυριαρχούσης στο μέσο σκέδασης Mie, αποφεύγοντας τοιουτοτρόπως μεγάλους υπολογιστικούς χρόνους. Παράλληλα, υπολογίζει το χρόνο πτήσης (Time-of-Flight) για κάθε προσομοιούμενο φωτόνιο, παρακολουθώντας όλες τις γνωστές φυσικές αλληλεπιδράσεις στις οποίες αυτό υπεισέρχεται. Το λογισμικό αυτό (PhoSim) με την μορφή ενός ολοκληρωμένου πακέτου εφαρμογής αποτελεί τον πυρήνα της μελέτης του εξεταζόμενου θέματος στην Διδακτορική αυτή Διατριβή.

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