scholarly journals Walking Cautiously Into the Collatz Wilderness: Algorithmically, Number Theoretically, Randomly

2006 ◽  
Vol DMTCS Proceedings vol. AG,... (Proceedings) ◽  
Author(s):  
Edward G. Belaga ◽  
Maurice Mignotte
Keyword(s):  
Experimental Data ◽  
Dynamical Systems ◽  
Discrete Dynamical Systems ◽  
Experimental Results ◽  
Diophantine Representation ◽  
Random Behavior ◽  
International Audience ◽  
Collatz Problem

International audience Building on theoretical insights and rich experimental data of our preprints, we present here new theoretical and experimental results in three interrelated approaches to the Collatz problem and its generalizations: \emphalgorithmic decidability, random behavior, and Diophantine representation of related discrete dynamical systems, and their \emphcyclic and divergent properties.

scholarly journals On the bialgebra of functional graphs and differential algebras

1997 ◽  
Vol Vol. 1 ◽  
Author(s):  
Maurice Ginocchio
Keyword(s):  
Dynamical Systems ◽  
Differential Operators ◽  
Discrete Dynamical Systems ◽  
Rooted Trees ◽  
Connected Components ◽  
Differential Algebras ◽  
Noncommutative Polynomials ◽  
International Audience

International audience We develop the bialgebraic structure based on the set of functional graphs, which generalize the case of the forests of rooted trees. We use noncommutative polynomials as generating monomials of the functional graphs, and we introduce circular and arborescent brackets in accordance with the decomposition in connected components of the graph of a mapping of \1, 2, \ldots, n\ in itself as in the frame of the discrete dynamical systems. We give applications fordifferential algebras and algebras of differential operators.

scholarly journals Sur le retard à la bifurcation

2008 ◽  
Vol Volume 9, 2007 Conference in... ◽  
Author(s):  
Augustin Fruchard ◽  
Reinhard Schäfke
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Discrete Dynamical Systems ◽  
International Audience ◽  
Bifurcation Delay

International audience We give a non-exhaustive overview of the problem of bifurcation delay from its appearance in France at the end of the 80ies to the most recent contributions. We present the bifurcation delay for differential equations as well as for discrete dynamical systems. Nous donnons un aperçu non exhaustif du problème du retard à la bifurcation, depuis son apparition en France à la fin des années 1980 jusqu’aux contributions les plus récentes. Le problème et les résultats sont présentés d’une part pour les équations différentielles et d’autre part pour les systèmes dynamiques discrets

scholarly journals Resonance in orbits of plane partitions

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Kevin Dilks ◽  
Oliver Pechenik ◽  
Jessica Striker
Keyword(s):  
Dynamical Systems ◽  
Discrete Dynamical Systems ◽  
Plane Partitions ◽  
Higher Dimensional ◽  
International Audience ◽  
K Promotion

International audience We introduce a new concept of resonance on discrete dynamical systems. Our main result is an equivariant bijection between plane partitions in a box under rowmotion and increasing tableaux under K-promotion, using a generalization of the equivariance of promotion and rowmotion [J. Striker–N. Williams '12] to higher dimensional lattices. This theorem implies new results for K-promotion and new proofs of previous results on plane partitions.

scholarly journals Hidden Attractors in Discrete Dynamical Systems

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 616
Author(s):  
Marek Berezowski ◽  
Marcin Lawnik
Keyword(s):  
Dynamical Systems ◽  
Chaos Theory ◽  
Scientific Literature ◽  
Discrete Systems ◽  
Discrete Dynamical Systems ◽  
Continuous Systems ◽  
Hidden Attractors ◽  
Negative Effects ◽  
Chemical Reactors ◽  
Points Of View

Research using chaos theory allows for a better understanding of many phenomena modeled by means of dynamical systems. The appearance of chaos in a given process can lead to very negative effects, e.g., in the construction of bridges or in systems based on chemical reactors. This problem is important, especially when in a given dynamic process there are so-called hidden attractors. In the scientific literature, we can find many works that deal with this issue from both the theoretical and practical points of view. The vast majority of these works concern multidimensional continuous systems. Our work shows these attractors in discrete systems. They can occur in Newton’s recursion and in numerical integration.

Convective Losses From Cavity Solar Receivers—Comparisons Between Analytical Predictions and Experimental Results

1983 ◽  
Vol 105 (1) ◽  
pp. 29-33 ◽  
Author(s):  
A. M. Clausing
Keyword(s):  
Experimental Data ◽  
Experimental Evidence ◽  
Analytical Model ◽  
Excellent Agreement ◽  
Experimental Results ◽  
Simple Analytical Model ◽  
Refined Model ◽  
Wall Area

Cavity solar receivers are generally believed to have higher thermal efficiencies than external receivers due to reduced losses. A simple analytical model was presented by the author which indicated that the ability to heat the air inside the cavity often controls the convective loss from cavity receivers. Thus, if the receiver contains a large amount of inactive hot wall area, it can experience a large convective loss. Excellent experimental data from a variety of cavity configurations and orientations have recently become available. These data provided a means of testing and refining the analytical model. In this manuscript, a brief description of the refined model is presented. Emphasis is placed on using available experimental evidence to substantiate the hypothesized mechanisms and assumptions. Detailed comparisons are given between analytical predictions and experimental results. Excellent agreement is obtained, and the important mechanisms are more clearly delineated.

A Technique for the Laboratory Determination of Recirculation in Single Needle Dialysis

1993 ◽  
Vol 16 (2) ◽  
pp. 63-70 ◽  
Author(s):  
N.A. Hoenich ◽  
P.T. Smirthwaite ◽  
C. Woffindin ◽  
P. Lancaster ◽  
T.H. Frost ◽  
...  
Keyword(s):  
Experimental Data ◽  
Flow Rate ◽  
Experimental Results ◽  
New Technique ◽  
Treatment Efficiency ◽  
Single Lumen ◽  
Theoretical Predictions ◽  
Lumen Catheter ◽  
A New Technique

Recirculation is an important factor in single needle dialysis and, if high, can compromise treatment efficiency. To provide information regarding recirculation characteristics of access devices used in single needle dialysis, we have developed a new technique to characterise recirculation and have used this to measure the recirculation of a Terumo 15G fistula needle and a VasCath SC2300 single lumen catheter. The experimentally obtained results agreed well with those established clinically (8.5 ± 2.4% and 18.4 ± 3.4%). The experimental results have also demonstrated a dependence on access type, pump speeds and fistula flow rate. A comparison of experimental data with theoretical predictions showed that the latter exceeded those measured with the largest contribution being due to the experimental fistula.

A STUDY OF BIFURCATIONS IN A CIRCULAR REAL CELLULAR AUTOMATON

1993 ◽  
Vol 03 (02) ◽  
pp. 293-321 ◽  
Author(s):  
JÜRGEN WEITKÄMPER
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Parallel Computers ◽  
Discrete Dynamical Systems ◽  
Two Dimensional ◽  
Bifurcation Structure ◽  
Logistic Mapping ◽  
Henon Mapping

Real cellular automata (RCA) are time-discrete dynamical systems on ℝN. Like cellular automata they can be obtained from discretizing partial differential equations. Due to their structure RCA are ideally suited to implementation on parallel computers with a large number of processors. In a way similar to the Hénon mapping, the system we consider here embeds the logistic mapping in a system on ℝN, N>1. But in contrast to the Hénon system an RCA in general is not invertible. We present some results about the bifurcation structure of such systems, mostly restricting ourselves, due to the complexity of the problem, to the two-dimensional case. Among others we observe cascades of cusp bifurcations forming generalized crossroad areas and crossroad areas with the flip curves replaced by Hopf bifurcation curves.

Validating Numerical CFD Simulations With Experimental Data for Turbulence Phenomena in Axial Flow Gas Turbine Diffusers

2009 ◽  
Author(s):  
Farrokh Zarifi-Rad ◽  
Hamid Vajihollahi ◽  
James O’Brien
Keyword(s):  
Experimental Data ◽  
Gas Turbine ◽  
Turbine Blades ◽  
Axial Flow ◽  
Experimental Results ◽  
Scale Model ◽  
Data Set ◽  
Pressure Profiles ◽  
Scale Models ◽  
Inlet Conditions

Scale models give engineers an excellent understanding of the aerodynamic behavior behind their design; nevertheless, scale models are time consuming and expensive. Therefore computer simulations such as Computational Fluid Dynamics (CFD) are an excellent alternative to scale models. One must ask the question, how close are the CFD results to the actual fluid behavior of the scale model? In order to answer this question the engineering team investigated the performance of a large industrial Gas Turbine (GT) exhaust diffuser scale model with performance predicted by commercially available CFD software. The experimental results were obtained from a 1:12 scale model of a GT exhaust diffuser with a fixed row of blades to simulate the swirl generated by the last row of turbine blades five blade configurations. This work is to validate the effect of the turbulent inlet conditions on an axial diffuser, both on the experimental front and on the numerical analysis approach. The object of this work is to bring forward a better understanding of velocity and static pressure profiles along the gas turbine diffusers and to provide an accurate experimental data set to validate the CFD prediction. For the CFD aspect, ANSYS CFX software was chosen as the solver. Two different types of mesh (hexagonal and tetrahedral) will be compared to the experimental results. It is understood that hexagonal (HEX) meshes are more time consuming and more computationally demanding, they are less prone to mesh sensitivity and have the tendancy to converge at a faster rate than the tetrahedral (TET) mesh. It was found that the HEX mesh was able to generate more consistent results and had less error than TET mesh.

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