Velocity Correlations in Driven Two-Dimensional Granular Media

Simulations of volumetrically forced granular media in two dimensions produce s tates with nearly homogeneous density. In these states, long-range velocity correlations with a characteristic vortex structure develop; given sufficient time, the correlations fill the entire simulated area. These velocity correlations reduce the rate and violence of collisions, so that pressure is smaller for driven inelastic particles than for undriven elastic particles in the same thermodynamic state. As the simulation box size increases, the effects of veloc ity correlations on the pressure are enhanced rather than reduced.Comment: 12 pages, 6 figures, 21 reference

Fluctuations in granular gases

A driven granular material, e.g. a vibrated box full of sand, is a stationary system which may be very far from equilibrium. The standard equilibrium statistical mechanics is therefore inadequate to describe fluctuations in such a system. Here we present numerical and analytical results concerning energy and injected power fluctuations. In the first part we explain how the study of the probability density function (pdf) of the fluctuations of total energy is related to the characterization of velocity correlations. Two different regimes are addressed: the gas driven at the boundaries and the homogeneously driven gas. In a granular gas, due to non-Gaussianity of the velocity pdf or lack of homogeneity in hydrodynamics profiles, even in the absence of velocity correlations, the fluctuations of total energy are non-trivial and may lead to erroneous conclusions about the role of correlations. In the second part of the chapter we take into consideration the fluctuations of injected power in driven granular gas models. Recently, real and numerical experiments have been interpreted as evidence that the fluctuations of power injection seem to satisfy the Gallavotti-Cohen Fluctuation Relation. We will discuss an alternative interpretation of such results which invalidates the Gallavotti-Cohen symmetry. Moreover, starting from the Liouville equation and using techniques from large deviation theory, the general validity of a Fluctuation Relation for power injection in driven granular gases is questioned. Finally a functional is defined using the Lebowitz-Spohn approach for Markov processes applied to the linear inelastic Boltzmann equation relevant to describe the motion of a tracer particle. Such a functional results to be different from injected power and to satisfy a Fluctuation Relation.Comment: 40 pages, 18 figure

Velocity correlations in driven twodimensional granular media

Abstract. Simulations of volumetrically forced granular media in two dimensions produce states with nearly homogeneous density. In these states, long-range velocity correlations with a characteristic vortex structure develop; given sufficient time, the correlations fill the entire simulated area. These velocity correlations reduce the rate and violence of collisions, so that pressure is smaller for driven inelastic particles than for undriven elastic particles in the same thermodynamic state. As the simulation box size increases, the effects of velocity correlations on the pressure are enhanced rather than reduced. 1

SYNGAP1 encephalopathy A distinctive generalized developmental and epileptic encephalopathy

OBJECTIVE: To delineate the epileptology, a key part of the SYNGAP1 phenotypic spectrum, in a large patient cohort. METHODS: Patients were recruited via investigators' practices or social media. We included patients with (likely) pathogenic SYNGAP1 variants or chromosome 6p21.32 microdeletions incorporating SYNGAP1. We analyzed patients' phenotypes using a standardized epilepsy questionnaire, medical records, EEG, MRI, and seizure videos. RESULTS: We included 57 patients (53% male, median age 8 years) with SYNGAP1 mutations (n = 53) or microdeletions (n = 4). Of the 57 patients, 56 had epilepsy: generalized in 55, with focal seizures in 7 and infantile spasms in 1. Median seizure onset age was 2 years. A novel type of drop attack was identified comprising eyelid myoclonia evolving to a myoclonic-atonic (n = 5) or atonic (n = 8) seizure. Seizure types included eyelid myoclonia with absences (65%), myoclonic seizures (34%), atypical (20%) and typical (18%) absences, and atonic seizures (14%), triggered by eating in 25%. Developmental delay preceded seizure onset in 54 of 56 (96%) patients for whom early developmental history was available. Developmental plateauing or regression occurred with seizures in 56 in the context of a developmental and epileptic encephalopathy (DEE). Fifty-five of 57 patients had intellectual disability, which was moderate to severe in 50. Other common features included behavioral problems (73%); high pain threshold (72%); eating problems, including oral aversion (68%); hypotonia (67%); sleeping problems (62%); autism spectrum disorder (54%); and ataxia or gait abnormalities (51%). CONCLUSIONS: SYNGAP1 mutations cause a generalized DEE with a distinctive syndrome combining epilepsy with eyelid myoclonia with absences and myoclonic-atonic seizures, as well as a predilection to seizures triggered by eating