Related Experiment Video
Updated: May 13, 2026
09:25
NMR 15N Relaxation Experiments for the Investigation of Picosecond to Nanoseconds Structural Dynamics of Proteins
Published on: November 1, 2024
Anomalous statistics of random relaxations in random environments
1Holon Institute of Technology, P.O. Box 305, Holon 58102, Israel. eliazar@post.tau.ac.il
Summary
This study analyzes the random relaxation (RARE) model, revealing conditions for anomalous statistics in relaxation times and ranges. We provide analytic results for heavy tails, indicating frequent small and large outliers.
Area of Science:
- Statistical Physics
- Complex Systems Modeling
Background:
- The random relaxation (RARE) model describes systems with random excitations and reactions.
- Understanding anomalous statistics is crucial for complex system behavior.
Purpose of the Study:
- To analyze the emergence of anomalous statistics in the RARE model.
- To determine conditions leading to heavy tails in relaxation time and range.
Main Methods:
- Comprehensive analysis of the RARE model.
- Derivation of closed-form analytic results.
Main Results:
- Identified conditions for anomalous statistics in relaxation time and range.
- Demonstrated emergence of heavy tails at zero and infinity.
Conclusions:
- The RARE model can exhibit anomalous statistical behaviors.
- Analytic results precisely define the emergence of heavy-tailed distributions.
More Related Videos
Related Concept Videos
01:04Random Error
Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
01:16Unusual Results
Unusual results are those that have a very low chance of occurring. Unusual results can be identified using probabilities and the range rule of thumb. In problems involving probability, unusual results can be observed in 2 instances – an unusually high number of successes or an unusually low number of successes.
According to the range rule of thumb, any value above or below two standard deviations, 2σ from the mean, μ is considered unusual.
Maximum unusual value = μ + 2σ
Minimum unusual value...
According to the range rule of thumb, any value above or below two standard deviations, 2σ from the mean, μ is considered unusual.
Maximum unusual value = μ + 2σ
Minimum unusual value...
01:28Atomic Nuclei: Types of Nuclear Relaxation
Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers energy to a nearby...
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers energy to a nearby...
01:23Atomic Nuclei: Nuclear Relaxation Processes
In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis, the precessing magnetic moments are randomly oriented around the z-axis. This...
02:49Second Law of Thermodynamics
In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
01:17Wald-Wolfowitz Runs Test II
The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and 0s. In...
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and 0s. In...