Investigation of tokamak turbulent avalanches using wave-kinetic formulation in toroidal geometry

The interplay between toroidal drift-wave turbulence and tokamak profiles is investigated using a wave-kinetic description. The coupled system is used to investigate the interplay between marginally stable toroidal drift-wave turbulence and geodesic acoustic modes (GAMs). The coupled system is found to be unstable. Notably, the most unstable mode corresponds to the resonance between the turbulent wave radial group velocity and the GAM phase velocity. For a low-field-side ballooned drift-wave growth, a background flow shear breaks the symmetry between inwards- and outwards-travelling instabilities. Although this turbulence–GAM coupling may not be the primary driver for avalanches in standard core ion temperature gradient simulations, this mechanism is generic and displays many of the expected features, and should be of interest in several other regimes, which include towards the edge or in the presence of energetic particles.

A vanishing dynamic capillarity limit equation with discontinuous flux

We prove existence and uniqueness of a solution to the Cauchy problem corresponding to the dynamics capillarity equation $$\begin{aligned} {\left\{ \begin{array}{ll} \partial _t u_{\varepsilon ,\delta } +\mathrm {div} {\mathfrak f}_{\varepsilon ,\delta }(\mathbf{x}, u_{\varepsilon ,\delta })=\varepsilon \Delta u_{\varepsilon ,\delta }+\delta (\varepsilon ) \partial _t \Delta u_{\varepsilon ,\delta }, \ \ \mathbf{x} \in M, \ \ t\ge 0\\ u|_{t=0}=u_0(\mathbf{x}). \end{array}\right. } \end{aligned}$$ ∂ t u ε , δ + div f ε , δ ( x , u ε , δ ) = ε Δ u ε , δ + δ ( ε ) ∂ t Δ u ε , δ , x ∈ M , t ≥ 0 u | t = 0 = u 0 ( x ) . Here, $${{\mathfrak {f}}}_{\varepsilon ,\delta }$$ f ε , δ and $$u_0$$ u 0 are smooth functions while $$\varepsilon $$ ε and $$\delta =\delta (\varepsilon )$$ δ = δ ( ε ) are fixed constants. Assuming $${{\mathfrak {f}}}_{\varepsilon ,\delta } \rightarrow {{\mathfrak {f}}}\in L^p( {\mathbb {R}}^d\times {\mathbb {R}};{\mathbb {R}}^d)$$ f ε , δ → f ∈ L p ( R d × R ; R d ) for some $$1<p<\infty $$ 1 < p < ∞ , strongly as $$\varepsilon \rightarrow 0$$ ε → 0 , we prove that, under an appropriate relationship between $$\varepsilon $$ ε and $$\delta (\varepsilon )$$ δ ( ε ) depending on the regularity of the flux $${{\mathfrak {f}}}$$ f , the sequence of solutions $$(u_{\varepsilon ,\delta })$$ ( u ε , δ ) strongly converges in $$L^1_{loc}({\mathbb {R}}^+\times {\mathbb {R}}^d)$$ L loc 1 ( R + × R d ) toward a solution to the conservation law $$\begin{aligned} \partial _t u +\mathrm {div} {{\mathfrak {f}}}(\mathbf{x}, u)=0. \end{aligned}$$ ∂ t u + div f ( x , u ) = 0 . The main tools employed in the proof are the Leray–Schauder fixed point theorem for the first part and reduction to the kinetic formulation combined with recent results in the velocity averaging theory for the second. These results have the potential to generate a stable semigroup of solutions to the underlying scalar conservation laws different from the Kruzhkov entropy solutions concept.

Stochastic Entropy Solutions for Stochastic Scalar Balance Laws

We are concerned with the initial value problem for a multidimensional balance law with multiplicative stochastic perturbations of Brownian type. Using the stochastic kinetic formulation and the Bhatnagar-Gross-Krook approximation, we prove the uniqueness and existence of stochastic entropy solutions. Furthermore, as applications, we derive the uniqueness and existence of the stochastic entropy solution for stochastic Buckley-Leverett equations and generalized stochastic Burgers type equations.

The Field Limit Between Neurophysiology and Psychopathology Oro-Facial Apraxia

Praxia represents the totality of the gestures and movements necessary to perform complex voluntary actions in order to accomplish a goal. Praxia has two aspects: on the one hand, intentional activity and on the other hand a mnestic activity based on memorizing the succession over time and space of the various movements to be performed in order to accomplish the intentional action. Programming the fulfillment of a voluntary action in order to achieve a well-defined purpose proceeds gradually, at different successive levels. The first level is the conceptual one. The person aims to achieve a certain purpose, sets the purpose of the voluntary motor action. The second level is that of the kinetic formulation of action, gesture. The individual disintegrates from the mnesic stock of all kinetic formulas he has learned during his ontogenetic development those formulas that are most appropriate to achieve the proposed action. The third level includes central and peripheral motor innervation, pyramidal, extrapyramidal, cerebellar and medullary motoring ways, which are the peripheral performers of the voluntary action. At this level the harmonious interactions between the different muscles involved in the movements are established, as well as the harmonious innervation of the synergic muscles, fixators, agonists and antagonists. The study comprises 5 patients admitted in the clinic of psychiatry in Constan�a, who presented oro-facial-lingual apraxia, apraxic dysphasia and aphasia, appeared in various evolutionary phases of intracranial neoformative processes. Apraxia was due to the increase of the kinetic engraving threshold, to the laughter they are sequenced by the logic of gesture efficiency; the often repeated, deeply fixed, kinetic engraves are automated in time.The co-ordination needed to perform a gestional motor task in order to accomplish a determined action has significant psychological implications.

Regularity estimates for scalar conservation laws in one space dimension

We deal with the regularizing effect that, in scalar conservation laws in one space dimension, the nonlinearity of the flux function [Formula: see text] has on the entropy solution. More precisely, if the set [Formula: see text] is dense, the regularity of the solution can be expressed in terms of [Formula: see text] spaces, where [Formula: see text] depends on the nonlinearity of [Formula: see text]. If moreover the set [Formula: see text] is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that [Formula: see text] for every [Formula: see text] and that this can be improved to [Formula: see text] regularity except an at most countable set of singular times. Finally, we present some examples that show the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces.