ergodicity sentence in Hindi
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- When implementing the algorithm, we must ensure that " g " ( ?, ? ) is selected such that ergodicity is met.
- The properties of ergodicity, weak mixing and strong mixing of a measure-preserving dynamical system can also be characterized by the average of observables.
- These assumptions of ergodicity are well-motivated in classical mechanics as a result of dynamical hard sphere gas has been rigorously proven to be ergodic.
- Under the assumption of point process ergodicity ( satisfied when using homogeneous Poisson processes ), the results for the typical user correspond to user averages.
- This shows that some sort of mixing of energies, formally called " ergodicity ", is important for the law of equipartition to hold.
- In a series of two papers ( one co-authored with Jean Bourgain ) he made major progress on Peter Sarnak's Arithmetic Quantum Unique Ergodicity conjecture.
- Anantharaman was included for her work in " quantum chaos, dynamical systems and Schr�dinger equation, including a remarkable advance in the problem of quantum unique ergodicity ".
- The validity of the continuum assumption may be verified by a theoretical analysis, in which either some clear periodicity is identified or statistical homogeneity and ergodicity of the microstructure exists.
- If sufficiently strong nonlinear terms are present in the energy function, energy may be transferred between the normal modes, leading to ergodicity and rendering the law of equipartition valid.
- Assuming that a particular system approaches all possible states over very long times ( quasi-ergodicity ), the resulting Monte Carlo dynamics realistically sample microscopic states that correspond to the given energy value.
- Given the restrictions noted above ( ergodicity, linearity ) the coherence function estimates the extent to which y ( t ) may be predicted from x ( t ) by an optimum linear least squares function.
- The averaging brackets \ left \ langle \ ldots \ right \ rangle is assumed to be an ensemble average over phase space or, under an assumption of ergodicity, a time average of a single system.
- Any time-invariant operations also preserves AEP, stationarity and ergodicity and we may easily turn a stationary process to non-stationary without losing AEP by nulling out a finite number of time samples in the process.
- However, complex disordered systems such as a spin glass show an even more complicated form of ergodicity breaking where the properties of the thermodynamic equilibrium state seen in practice are much more difficult to predict purely by symmetry arguments.
- Furthermore, weak mixing ( and thus also strong mixing ) implies ergodicity : that is, every system that is weakly mixing is also ergodic ( and so one says that mixing is a " stronger " notion than ergodicity ).
- Furthermore, weak mixing ( and thus also strong mixing ) implies ergodicity : that is, every system that is weakly mixing is also ergodic ( and so one says that mixing is a " stronger " notion than ergodicity ).
- "' Umbrella sampling "'is a technique in computational physics and chemistry, used to improve sampling of a system ( or different systems ) where ergodicity is hindered by the form of the system's energy landscape.
- Holowinsky was awarded the SASTRA Ramanujan Prize in 2011 for his contributions to " areas of mathematics influenced by the genius Srinivasa Ramanujan ", for proving, with Kannan Soundararajan, an important case of the quantum unique ergodicity ( QUE ) conjecture.
- The subsequent work of interpretation of the Parisi solution by M . Mezard, G . Parisi, M . A . Virasoro and many others revealed the complex nature of a glassy low temperature phase characterized by ergodicity breaking, ultrametricity and non-selfaverageness.
- Ratner's theorems provide a major generalization of ergodicity for unipotent flows on the homogeneous spaces of the form ? \ " G ", where " G " is a Lie group and ? is a lattice in " G ".
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