scholarly journals COVARIANT FEATURE OF THE MIXMASTER MODEL INVARIANT MEASURE

2002 ◽  
Vol 11 (08) ◽  
pp. 1321-1330 ◽  
Author(s):  
GIOVANNI IMPONENTE ◽  
GIOVANNI MONTANI
Keyword(s):  
Invariant Measure ◽  
Arbitrary Function ◽  
Chaotic Behavior ◽  
Time Variable ◽  
Cosmological Singularity ◽  
Constant Of Motion ◽  
Set Up ◽  
Lapse Function ◽  
Mixmaster Model ◽  
Hamiltonian Analysis

We provide a Hamiltonian analysis of the Mixmaster Universe dynamics showing the covariant nature of its chaotic behavior with respect to any choice of time variable. Asymptotically to the cosmological singularity, we construct the appropriate invariant measure for the system (which relies on the appearance of an "energy-like" constant of motion) in such a way that its existence is independent of fixing the time gauge, i.e. the corresponding lapse function. The key point in our analysis consists of introducing generic Misner–Chitré-like variables containing an arbitrary function, whose specification allows us to set up the same statistical scheme in any time gauge.

scholarly journals MIXMASTER CHAOTICITY AS SEMICLASSICAL LIMIT OF THE CANONICAL QUANTUM DYNAMICS

2003 ◽  
Vol 12 (06) ◽  
pp. 977-984 ◽  
Author(s):  
GIOVANNI IMPONENTE ◽  
GIOVANNI MONTANI
Keyword(s):  
Probability Distribution ◽  
Quantum Dynamics ◽  
Chaotic Behavior ◽  
Semiclassical Limit ◽  
Canonical Quantization ◽  
Cosmological Singularity ◽  
Canonical Quantum ◽  
Hamiltonian Analysis

Within a cosmological framework, we provide a Hamiltonian analysis of the Mixmaster Universe dynamics on the base of a standard Arnowitt–Deser–Misner approach, showing how the chaotic behavior characterizing the evolution of the system near the cosmological singularity can be obtained as the semiclassical limit of the canonical quantization of the model in the same dynamical representation. The relation between this intrinsic chaotic behavior and the indeterministic quantum dynamics is inferred through the coincidence between the microcanonical probability distribution and the semiclassical quantum one.

Research on Chaotic Behavior of Concrete under External Load Based on Discontinuous Medium Mechanical Model

2009 ◽  
Vol 79-82 ◽  
pp. 1145-1148
Author(s):  
Hao Qin ◽  
Shu Cai Li
Keyword(s):  
External Load ◽  
Mechanical Model ◽  
Dynamical Equation ◽  
Chaotic Behavior ◽  
Concrete Material ◽  
Nonlinear Dynamical ◽  
Load Change ◽  
Nonlinear Science ◽  
Set Up ◽  
Discontinuous Medium

Outburst and random are typical characters of concrete when under external load. Traditional mechanics methods are difficult to be applied in. Depend on nonlinear science to set up the nonlinear dynamical equation that is fit for its characteristics. The subsystem dynamical equation of concrete is set up based on discontinuous medium mechanical model, and find that the concrete dynamical equation under external load is a Duffin equation. Then analyze and discuss the effect of external load on concrete by math analysis soft of maple. Results show that the concrete material take on complicated response to external load change.

CHAOTIC BEHAVIOR OF HIGHER DIMENSIONAL TRANSFORMATIONS DEFINED ON COUNTABLE PARTITIONS

1993 ◽  
Vol 03 (04) ◽  
pp. 1045-1049
Author(s):  
A. BOYARSKY ◽  
Y. S. LOU
Keyword(s):  
Invariant Measure ◽  
Additional Condition ◽  
Invariant Measures ◽  
Chaotic Behavior ◽  
Finite Collection ◽  
Continuous Invariant Measure ◽  
Absolutely Continuous ◽  
Higher Dimensional ◽  
Absolutely Continuous Invariant Measure ◽  
Absolutely Continuous Invariant

Jablonski maps are higher dimensional maps defined on rectangular partitions with each component a function of only one variable. It is well known that expanding Jablonski maps have absolutely continuous invariant measures. In this note we consider Jablonski maps defined on countable partitions. Such maps occur, for example, in multivariable number theoretic problems. The main result establishes the existence of an absolutely continuous invariant measure for Jablonski maps on a countable partition with the additional condition that the images of all the partition elements form a finite collection. An example is given.

scholarly journals Optimal transport and dynamics of expanding circle maps acting on measures

2012 ◽  
Vol 33 (2) ◽  
pp. 529-548 ◽  
Author(s):  
BENOÎT KLOECKNER
Keyword(s):  
Invariant Measure ◽  
Optimal Transport ◽  
Continuous Invariant Measure ◽  
Absolutely Continuous ◽  
Absolutely Continuous Invariant Measure ◽  
Expanding Circle ◽  
Rigorous Framework ◽  
Infinite Multiplicity ◽  
Set Up ◽  
Absolutely Continuous Invariant

AbstractIn this paper we compute the derivative of the action on probability measures of an expanding circle map at its absolutely continuous invariant measure. The derivative is defined using optimal transport: we use the rigorous framework set up by Gigli to endow the space of measures with a kind of differential structure. It turns out that 1 is an eigenvalue of infinite multiplicity of this derivative, and we deduce that the absolutely continuous invariant measure can be deformed in many ways into atomless, nearly invariant measures. We also show that the action of standard self-covering maps on measures has positive metric mean dimension.

scholarly journals A Generalized 2D-Dynamical Mean-Field Ising Model with a Rich Set of Bifurcations (Inspired and Applied to Financial Crises)

2018 ◽  
Vol 28 (04) ◽  
pp. 1830010 ◽  
Author(s):  
Damian Smug ◽  
Didier Sornette ◽  
Peter Ashwin
Keyword(s):  
Ising Model ◽  
Chaotic Behavior ◽  
Moving Average ◽  
Mean Field ◽  
Opinion Dynamics ◽  
State Variable ◽  
Physical Representation ◽  
Social Opinions ◽  
Set Up ◽  
Two Parameters

We analyze an extended version of the dynamical mean-field Ising model. Instead of classical physical representation of spins and external magnetic field, the model describes traders' opinion dynamics. The external field is endogenized to represent a smoothed moving average of the past state variable. This model captures in a simple set-up the interplay between instantaneous social imitation and past trends in social coordinations. We show the existence of a rich set of bifurcations as a function of the two parameters quantifying the relative importance of instantaneous versus past social opinions on the formation of the next value of the state variable. Moreover, we present a thorough analysis of chaotic behavior, which is exhibited in certain parameter regimes. Finally, we examine several transitions through bifurcation curves and study how they could be understood as specific market scenarios. We find that the amplitude of the corrections needed to recover from a crisis and to push the system back to “normal” is often significantly larger than the strength of the causes that led to the crisis itself.

Modeling and Simulation of Freshwater Generator Subsystem of Low Speed Engine Room Simulator Based on Visual

2012 ◽  
Vol 557-559 ◽  
pp. 2324-2328
Author(s):  
Qian Ming Shang
Keyword(s):  
3D Models ◽  
Time Variable ◽  
Practical Situation ◽  
Generator System ◽  
System A ◽  
Working Principle ◽  
Network Communications ◽  
Sustainable System ◽  
Set Up ◽  
Speed Engine

3d models of the equipments of freshwater generator system are built according to the real ship. In support of a simulative sustainable system, a real-time variable database and mathematical models of the subsystem are set up. Then the precision of the models are proved to meet the demands by comparing the simulation results with the practical situation. The interfaces are available by making use of VC++6.0. Finally, the data connections between the math models and interfaces are established by means of the technology of network communications. The purpose of developing this simulation system is training, which offers students a chance to make a good knowledge of the structure and working principle of the freshwater generator subsystem.

Exact Solutions of Simple Nonlinear Difference Equation Systems that show Chaotic Behavior

1983 ◽  
Vol 38 (9) ◽  
pp. 1035-1039 ◽  
Author(s):  
Taskashi Tsuchiya ◽  
Attila Szabo ◽  
Nobuhiko Saitô
Keyword(s):  
Exact Solution ◽  
Correlation Function ◽  
Invariant Measure ◽  
Difference Equation ◽  
Exact Solutions ◽  
Extreme Values ◽  
Chaotic Behavior ◽  
Nonlinear Difference Equation ◽  
Initial Value ◽  
Simple Difference

Abstract Exact solutions are given for May's simple difference equation and the broken linear model, both for extreme values of the parameters, and the relation between these two systems for the solvable cases is clarified. The invariant measure and the correlation function for each case are calculated using the exact solutions. The initial-value dependence of the behavior of the solutions, choatic or periodic, is completely determined. By using the exact solution, encounters of any two nonperiodic orbits can be precisely analyzed.

scholarly journals CLASSICAL AND QUANTUM FEATURES OF THE MIXMASTER SINGULARITY

2008 ◽  
Vol 23 (16n17) ◽  
pp. 2353-2503 ◽  
Author(s):  
GIOVANNI MONTANI ◽  
MARCO VALERIO BATTISTI ◽  
RICCARDO BENINI ◽  
GIOVANNI IMPONENTE
Keyword(s):  
Review Paper ◽  
Cosmological Singularity ◽  
Mixmaster Model ◽  
Classical Picture

This review paper is devoted to analyzing the main properties of the cosmological singularity associated with the homogeneous and inhomogeneous Mixmaster model. After the introduction of the main tools required to treat the cosmological issue, we review in detail the main results obtained over the last forty years on the Mixmaster topic. We first assess the classical picture of the homogeneous chaotic cosmologies and, after a presentation of the canonical method for the quantization, we develop the quantum Mixmaster behavior. Finally, we extend both the classical and the quantum features to the fully inhomogeneous case. Our survey analyzes the fundamental framework of the Mixmaster picture and completes it by accounting for recent and peculiar outstanding results.

scholarly journals A SCENARIO FOR THE DIMENSIONAL COMPACTIFICATION IN ELEVEN-DIMENSIONAL SPACE–TIME

2004 ◽  
Vol 13 (06) ◽  
pp. 1029-1036 ◽  
Author(s):  
GIOVANNI MONTANI
Keyword(s):  
Power Law ◽  
Dimensional Space ◽  
Conformal Factor ◽  
Space Time ◽  
Geometrical Theory ◽  
Cosmological Singularity ◽  
3 Dimensional ◽  
Dimensional Space Time ◽  
Mixmaster Model

We discuss the inhomogeneous multidimensional mixmaster model in view of the appearing, near the cosmological singularity, of a scenario for the dimensional compactification in correspondence to an 11-dimensional space–time. Our analysis candidates such a collapsing picture toward the singularity to describe the actual expanding 3-dimensional Universe and an associated collapsed 7-dimensional space. To this end, a conformal factor is determined in front of the 4-dimensional metric to remove the 4-curvature divergences and the resulting Universe expands with a power-law inflation. Thus we provide an additional peculiarity of the eleven space-time dimensions in view of implementing a geometrical theory of unification.

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