1,116,616 research outputs found

    Momentum Regularity and Stability of the Relativistic Vlasov-Maxwell-Boltzmann System

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    In the study of solutions to the relativistic Boltzmann equation, their regularity with respect to the momentum variables has been an outstanding question, even local in time, due to the initially unexpected growth in the post-collisional momentum variables which was discovered in 1991 by Glassey & Strauss \cite{MR1105532}. We establish momentum regularity within energy spaces via a new splitting technique and interplay between the Glassey-Strauss frame and the center of mass frame of the relativistic collision operator. In a periodic box, these new momentum regularity estimates lead to a proof of global existence of classical solutions to the two-species relativistic Vlasov-Boltzmann-Maxwell system for charged particles near Maxwellian with hard ball interaction.Comment: 23 pages; made revisions which were suggested by the referee; to appear in Comm. Math. Phy

    The Vlasov-Poisson-Landau System in Rx3\R^3_x

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    For the Landau-Poisson system with Coulomb interaction in Rx3\R^3_x, we prove the global existence, uniqueness, and large time convergence rates to the Maxwellian equilibrium for solutions which start out sufficiently close.Comment: 50 page

    Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff

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    In this paper we prove new constructive coercivity estimates for the Boltzmann collision operator without cutoff, that is for long-range interactions. In particular we give a generalized sufficient condition for the existence of a spectral gap which involves both the growth behavior of the collision kernel at large relative velocities and its singular behavior at grazing and frontal collisions. It provides in particular existence of a spectral gap and estimates on it for interactions deriving from the hard potentials \phi(r) = r^{-(s−1)}, s≄5s \ge 5 or the so-called moderately soft potentials \phi(r) = r^{−(s−1)}, 3<s<53 < s < 5, (without angular cutoff). In particular this paper recovers (by constructive means), improves and extends previous results of Pao [46]. We also obtain constructive coercivity estimates for the Landau collision operator for the optimal coercivity norm pointed out in [34] and we formulate a conjecture about a unified necessary and sufficient condition for the existence of a spectral gap for Boltzmann and Landau linearized collision operators.Comment: 29 page

    Assumed-strain finite element technique for accurate modelling of plasticity problems

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    In this work a linear hexahedral element based on an assumed-strain ïŹnite element technique is presented for the solution of plasticity problems. The element stems from the NICE formulation and its extensions. Assumed gradient operators are derived via nodal integration from the kinematic-weighted residual; the degrees of freedom are only the displacements at the nodes. The adopted constitutive model is the classical associative von-Mises plasticity model with isotropic and kinematic hardening; in particular a double- step midpoint integration algorithm is adopted for the integration and solution of the relevant nonlinear evolution equations. EïŹƒciency of the proposed method is assessed through simple benchmark problem and comparison with reference solutions

    Ultrashort Q-switched pulses from a passively mode-locked distributed Bragg reflector semiconductor laser

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    A compact semiconductor mode-locked laser (MLL) is presented that demonstrates strong passive Q-switched mode-locking over a wide range of drive conditions. The Q-switched frequency is tunable between 1 and 4 GHz for mode-locked pulses widths around 3.5 ps. The maximum ratio of peak to average power of the pulse-train is &gt;120, greatly exceeding that of similarly sized passively MLLs