Search results for "Mathematical physics"
showing 10 items of 2687 documents
Hölder regularity for stochastic processes with bounded and measurable increments
2022
We obtain an asymptotic Hölder estimate for expectations of a quite general class of discrete stochastic processes. Such expectations can also be described as solutions to a dynamic programming principle or as solutions to discretized PDEs. The result, which is also generalized to functions satisfying Pucci-type inequalities for discrete extremal operators, is a counterpart to the Krylov-Safonov regularity result in PDEs. However, the discrete step size $\varepsilon$ has some crucial effects compared to the PDE setting. The proof combines analytic and probabilistic arguments.
Understanding tungsten erosion during inter/intra-ELM periods in He-dominated JET-ILW plasmas
2021
Tungsten erosion was quantified during inter/intra-ELM periods in He-dominated JET-ILW plasmas by optical emission spectroscopy. The intra-ELM tungsten sputtering in helium plasmas, which dominates the total W source, prevails by a factor of about 4 over inter-ELM sputtering in the investigated ELM frequency range from 90 Hz-120 Hz. He ions are mainly responsible for the W erosion during the ELMs in He plasmas. The strong in/out asymmetry of the ELM-induced W erosion is observed in He plasmas even at high ELM frequencies beyond 100 Hz. In Ohmic/L-mode plasmas and during the H-mode inter-ELM plasma phases both He2+ and Be2+ ionic species are major contributors to the W erosion. Their contrib…
Regularity for nonlinear stochastic games
2015
We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for the corresponding partial differential equations. peerReviewed
Remarks on regularity for p-Laplacian type equations in non-divergence form
2018
We study a singular or degenerate equation in non-divergence form modeled by the $p$-Laplacian, $$-|Du|^\gamma\left(\Delta u+(p-2)\Delta_\infty^N u\right)=f\ \ \ \ \text{in}\ \ \ \Omega.$$ We investigate local $C^{1,\alpha}$ regularity of viscosity solutions in the full range $\gamma>-1$ and $p>1$, and provide local $W^{2,2}$ estimates in the restricted cases where $p$ is close to 2 and $\gamma$ is close to 0.
The ALICE experiment at the CERN LHC
2008
Journal of Instrumentation 3(08), S08002 (2008). doi:10.1088/1748-0221/3/08/S08002
Deformation Quantization in White Noise Analysis
2007
We define and present an example of a deformation quantization product on a Hida space of test functions endowed with a Wick product.
First and second order rational solutions to the Johnson equation and rogue waves
2018
Rational solutions to the Johnson equation are constructed as a quotient of two polynomials in x, y and t depending on several real parameters. We obtain an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2N (N + 1) in x, and t, 4N (N + 1) in y, depending on 2N − 2 real parameters for each positive integer N. We construct explicit expressions of the solutions in the cases N = 1 and N = 2 which are given in the following. We study the evolution of the solutions by constructing the patterns of their modulus in the (x, y) plane, and this for different values of parameters.
The defocusing NLS equation : quasi-rational and rational solutions
2022
Quasi-rational solutions to the defocusing nonlinear Schrödinger equation (dNLS) in terms of wronskians and Fredholm determinants of order 2N depending on 2N − 2 real parameters are given. We get families of quasi-rational solutions to the dNLS equation expressed as a quotient of two polynomials of degree N (N + 1) in the variables x and t. We present also rational solutions as a quotient of determinants involving certain particular polynomials.
Solutions to the Gardner equation with multi-parameters and the rational case
2022
We construct solutions to the Gardner equation in terms of trigonometric and hyperbolic functions, depending on several real parameters. Using a passage to the limit when one of these parameters goes to 0, we get, for each positive integer N , rational solutions as a quotient of polynomials in x and t depending on 2N parameters. We construct explicit expressions of these rational solutions for orders N = 1 until N = 3. We easily deduce solutions to the mKdV equation in terms of wronskians as well as rational solutions depending on 2N real parameters.
Beam-induced and cosmic-ray backgrounds observed in the ATLAS detector during the LHC 2012 proton-proton running period
2016
This paper discusses various observations on beam-induced and cosmic-ray backgrounds in the ATLAS detector during the LHC 2012 proton-proton run. Building on published results based on 2011 data, the correlations between background and residual pressure of the beam vacuum are revisited. Ghost charge evolution over 2012 and its role for backgrounds are evaluated. New methods to monitor ghost charge with beam-gas rates are presented and observations of LHC abort gap population by ghost charge are discussed in detail. Fake jets from colliding bunches and from ghost charge are analysed with improved methods, showing that ghost charge in individual radio-frequency buckets of the LHC can be resol…