Dynamics
 2024
DOI: 10.3390/dynamics4010003
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Multiplicative Renormalization of Stochastic Differential Equations for the Abelian Sandpile Model

Dimitri Volchenkov
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Abstract: The long-term, large-scale behavior in a problem of stochastic nonlinear dynamics corresponding to the Abelian sandpile model is studied with the use of the quantum-field theory renormalization group approach. We prove the multiplicative renormalization of the model including an infinite number of coupling parameters, calculate an infinite number of renormalization constants, identify a plane of fixed points in the infinite dimensional space of coupling parameters, discuss their stability and critical scaling … Show more

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“…This model is widely used in fields such as physics, economics, mathematics, and theoretical computer science [ 21 , 22 , 23 , 24 , 25 ]. Its applications range from cellular automata and information systems to earthquake calculations [ 26 ], studies of river sediments [ 27 ], the spread of forest fires [ 28 , 29 , 30 , 31 ], investigations of the Earth’s magnetosphere [ 32 ], studies of precipitation distribution [ 20 ], diffusion problems (such as those involving lattice gas and lattice Boltzmann models) [ 33 ], social sciences [ 34 ], neuroscience [ 35 ], and the study of consciousness [ 36 ], as well as theoretical mathematical investigations on the application of renormalization group methods [ 37 , 38 ].…”
Section: Characteristics Of the Sandpile Modelmentioning
confidence: 99%
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
show abstract
“…This model is widely used in fields such as physics, economics, mathematics, and theoretical computer science [ 21 , 22 , 23 , 24 , 25 ]. Its applications range from cellular automata and information systems to earthquake calculations [ 26 ], studies of river sediments [ 27 ], the spread of forest fires [ 28 , 29 , 30 , 31 ], investigations of the Earth’s magnetosphere [ 32 ], studies of precipitation distribution [ 20 ], diffusion problems (such as those involving lattice gas and lattice Boltzmann models) [ 33 ], social sciences [ 34 ], neuroscience [ 35 ], and the study of consciousness [ 36 ], as well as theoretical mathematical investigations on the application of renormalization group methods [ 37 , 38 ].…”
Section: Characteristics Of the Sandpile Modelmentioning
confidence: 99%
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
show abstract
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
show abstract
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
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