Search results for "Mathematical Physics"
showing 10 items of 2687 documents
A first-order phase transition for pulsar surface
2012
In this paper, we explain the existence of a possible first-order phase transition that may occur over the external solid crust of a pulsar, by means of an interpretation of a particular formal model (drawn from Theoretical Astrophysics) whose thermodynamical phenomenology shows a possible first-order phase transition (according to Landau’s Phenomenological Theory).
Study of scintillation light collection, production and propagation in a 4 tonne dual-phase LArTPC
2020
The $3 \times 1 \times 1$ m$^3$ demonstrator is a dual phase liquid argon time projection chamber that has recorded cosmic rays events in 2017 at CERN. The light signal in these detectors is crucial to provide precise timing capabilities. The performances of the photon detection system, composed of five PMTs, are discussed. The collected scintillation and electroluminescence light created by passing particles has been studied in various detector conditions. In particular, the scintillation light production and propagation processes have been analyzed and compared to simulations, improving the understanding of some liquid argon properties.
Highly occupied gauge theories in 2 + 1 dimensions : a self-similar attractor
2019
Motivated by the boost-invariant Glasma state in the initial stages in heavy-ion collisions, we perform classical-statistical simulations of SU(2) gauge theory in 2+1 dimensional space-time both with and without a scalar field in the adjoint representation. We show that irrespective of the details of the initial condition, the far-from-equilibrium evolution of these highly occupied systems approaches a unique universal attractor at high momenta that is the same for the gauge and scalar sectors. We extract the scaling exponents and the form of the distribution function close to this non-thermal fixed point. We find that the dynamics are governed by an energy cascade to higher momenta with sc…
Topological canal foliations
2019
Regular canal surfaces of $\mathbb{R}^3$ or $\mathbb{S}^3$ admit foliations by circles: the characteristic circles of the envelope. In order to build a foliation of $\mathbb{S}^3$ with leaves being canal surfaces, one has to relax the condition “canal” a little (“weak canal condition”) in order to accept isolated umbilics. Here, we define a topological condition which generalizes this “weak canal” condition imposed on leaves, and classify the foliations of compact orientable 3-manifolds we can obtain this way.
Regularity and modulus of continuity of space-filling curves
2019
We study critical regularity assumptions on space-filling curves that possess certain modulus of continuity. The bounds we obtain are essentially sharp, as demonstrated by an example. peerReviewed
Dynamics of hydrofracturing and permeability evolution in layered reservoirs
2015
International audience; A coupled hydro-mechanical model is presented to model fluid driven fracturing in layered porous rocks. In the model the solid elastic continuum is described by a discrete element approach coupled with a fluid continuum grid that is used to solve Darcy based pressure diffusion. The model assumes poro-elasto-plastic effects and yields real time dynamic aspects of the fracturing and effective stress evolution under the influence of excess fluid pressure gradients. We show that the formation and propagation of hydrofractures are sensitive to mechanical and tectonic conditions of the system. In cases where elevated fluid pressure is the sole driving agent in a stable tec…
Residual a posteriori error estimation for frictional contact with Nitsche method
2023
We consider frictional contact problems in small strain elasticity discretized with finite elements and Nitsche method. Both bilateral and unilateral contact problems are taken into account, as well as both Tresca and Coulomb models for the friction. We derive residual a posteriori error estimates for each friction model, following [Chouly et al, IMA J. Numer. Anal. (38) 2018, pp. 921-954]. For the incomplete variant of Nitsche, we prove an upper bound for the dual norm of the residual, for Tresca and Coulomb friction, without any extra regularity and without a saturation assumption. Numerical experiments allow to assess the accuracy of the estimates and their interest for adaptive meshing …
8-parameter solutions of fifth order to the Johnson equation
2019
We give different representations of the solutions of the Johnson equation with parameters. First, an expression in terms of Fredholm determinants is given; we give also a representation of the solutions written as a quotient of wronskians of order 2N. These solutions of order N depend on 2N − 1 parameters. When one of these parameters tends to zero, we obtain N order rational solutions expressed as a quotient of two polyno-mials of degree 2N (N +1) in x, t and 4N (N +1) in y depending on 2N −2 parameters. Here, we explicitly construct the expressions of the rational solutions of order 5 depending on 8 real parameters and we study the patterns of their modulus in the plane (x, y) and their …
From first to fourth order rational solutions to the Boussinesq equation
2020
Rational solutions to the Boussinesq equation are constructed as a quotient of two polynomials in x and t. For each positive integer N , the numerator is a polynomial of degree N (N + 1) − 2 in x and t, while the denominator is a polynomial of degree N (N + 1) in x and t. So we obtain a hierarchy of rational solutions depending on an integer N called the order of the solution. We construct explicit expressions of these rational solutions for N = 1 to 4.
FORMATION OF MOLECULES IN ULTRACOLD ATOMIC GASES VIA QUASI-RESONANT FIELDS
2010
we study the nonlinear mean-field dynamics of diatomic molecule formation at coherent photo- and magneto-association of ultracold atoms focusing on the case when the system is initially in the all-atomic state. We show that in the limit of strongly nonlinear interaction between an ultra-cold atomic-molecular system and a quasi-resonant electromagnetic field, the molecule formation process, depending on the characteristics of the associating field, may evolve according two different scenarios, namely, weak- and strong-oscillatory regimes. In the first case the number of molecules increases without pronounced oscillations of atom-molecule populations, while in the second case high-amplitude R…