The Effect of Stochastic Noise on Predictability

2000 ◽  
Author(s):  
Prashant Sardeshmukh ◽  
Cecile Penland ◽  
Matthew Newman
Keyword(s):  
Stochastic Noise

scholarly journals A Stochastic Kinetic Type Reactions Model for COVID-19

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1221
Author(s):  
Giorgio Sonnino ◽  
Fernando Mora ◽  
Pasquale Nardone
Keyword(s):  
Real Data ◽  
Stochastic Noise ◽  
Mathematical Basis ◽  
Sis Model ◽  
Theoretical Predictions ◽  
Coronavirus Infection ◽  
Massive Distribution ◽  
Second Wave ◽  
Stochastic Sis Model

We propose two stochastic models for the Coronavirus pandemic. The statistical properties of the models, in particular the correlation functions and the probability density functions, were duly computed. Our models take into account the adoption of lockdown measures as well as the crucial role of hospitals and health care institutes. To accomplish this work we adopt a kinetic-type reaction approach where the modelling of the lockdown measures is obtained by introducing a new mathematical basis and the intensity of the stochastic noise is derived by statistical mechanics. We analysed two scenarios: the stochastic SIS-model (Susceptible ⇒ Infectious ⇒ Susceptible) and the stochastic SIS-model integrated with the action of the hospitals; both models take into account the lockdown measures. We show that, for the case of the stochastic SIS-model, once the lockdown measures are removed, the Coronavirus infection will start growing again. However, the combined contributions of lockdown measures with the action of hospitals and health institutes is able to contain and even to dampen the spread of the SARS-CoV-2 epidemic. This result may be used during a period of time when the massive distribution of vaccines in a given population is not yet feasible. We analysed data for USA and France. In the case of USA, we analysed the following situations: USA is subjected to the first wave of infection by Coronavirus and USA is in the second wave of SARS-CoV-2 infection. The agreement between theoretical predictions and real data confirms the validity of our approach.

The Role of Stochastic Noise on the Glass Transition

1995 ◽  
Vol 407 ◽  
Author(s):  
Fernando C. Perez-Cardenas ◽  
Hao Gan
Keyword(s):  
Relaxation Time ◽  
Glass Transition ◽  
Time Spectrum ◽  
Structure Evolution ◽  
Stochastic Noise ◽  
Relaxation Time Spectrum ◽  
Glass Transition Region ◽  
Type Differential Equation ◽  
Glass Relaxation

ABSTRACTGlasses are amorphous solids that exhibit an intricate structural relaxation. A broad relaxation time spectrum always emerges when these systems are perturbed. By using a Langevin-type differential equation to describe the structure dynamicsof these materials, it is depicted how the broad relaxation time spectrum arises due to the stochastic noise and how this affects the system's structure evolution as it is cooled down into the glass transition region. This stochastic model provides a macroscopic as well a microscopic view of the glass relaxation process.

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