3,528 research outputs found
Covariant Magnetic Connection Hypersurfaces
In the single fluid, nonrelativistic, ideal-Magnetohydrodynamic (MHD) plasma
description magnetic field lines play a fundamental role by defining
dynamically preserved "magnetic connections" between plasma elements. Here we
show how the concept of magnetic connection needs to be generalized in the case
of a relativistic MHD description where we require covariance under arbitrary
Lorentz transformations. This is performed by defining 2-D {\it magnetic
connection hypersurfaces} in the 4-D Minkowski space. This generalization
accounts for the loss of simultaneity between spatially separated events in
different frames and is expected to provide a powerful insight into the 4-D
geometry of electromagnetic fields when .Comment: 10 pages no figure
Generalised relativistic Ohm's laws, extended gauge transformations and magnetic linking
Generalisations of the relativistic ideal Ohm's law are presented that
include specific dynamical features of the current carrying particles in a
plasma. Cases of interest for space and laboratory plasmas are identified where
these generalisations allow for the definition of generalised electromagnetic
fields that transform under a Lorentz boost in the same way as the real
electromagnetic fields and that obey the same set of homogeneous Maxwell's
equations
Expansion of a finite size plasma in vacuum
The expansion dynamics of a finite size plasma is examined from an analytical
perspective. Results regarding the charge distribution as well as the
electrostatic potential are presented. The acceleration of the ions and the
associated cooling of the electrons that takes place during the plasma
expansion is described. An extensive analysis of the transition between the
semi infinite and the finite size plasma behaviour is carried out. Finally, a
test of the analytical results, performed through numerical simulations, is
presented.Comment: 4 pages with 5 figure
Multi-Lag Term Structure Models with Stochastic Risk Premia.
The purpose of this paper is to propose discrete-time term structure models where the historical dynamics of the factor (xt) is given, in the univariate case, by a Gaussian AR(p) process, and, in the multivariate case, by a Gaussian n-dimensional VAR(p) process. The factor (xt) is considered as a latent or an observable variable and, in the second case, (xt) is given by the short rate (in the scalar setting) or by a vector of several yields (in the multivariate setting). We consider an exponential-affine stochastic discount factor (SDF) with a stochastic factor risk correction coefficient defined, at time t, as an affine function of Xt = (xt, . . . , xt?p+1)0 and, consequently, the yield-to-maturity formula at time t is an affine function of the p most recent lagged values of xt+1. We study the Gaussian AR(p) and the Gaussian VAR(p) Factor-Based Term Structure Models. We investigate, under the risk-neutral and the S-forward probability, the Moving Average (or discrete-time Heath, Jarrow and Morton) representation of the yield and short-term forward rate processes. This representation gives the possibility to exactly replicate the currently-observed yield curve. We also study the problem of matching the theoretical and currently-observed market term structure by means of the Extended AR(p) approach.Discrete-time Affine Term Structure Models ; Stochastic Discount Factor, Gaussian VAR(p) processes ; Stochastic risk premia ; Moving Average or discrete-time HJM representations ; Exact Fitting of the currently-observed yield curve.
Switching VARMA Term Structure Models - Extended Version.
The purpose of the paper is to propose a global discrete-time modeling of the term structure of interest rates able to capture simultaneously the following important features : (i) an historical dynamics of the factor driving term structure shapes involving several lagged values, and switching regimes; (ii) a specification of the stochastic discount factor (SDF) with time-varying and regime dependent risk-premia; (iii) explicit or quasi explicit formulas for zero-coupon bond and interest rate derivative prices; (iv) the positivity of the yields at each maturity. The first family of models we develop is given by the Switching Autoregressive Normal (SARN) and the Switching Vector Autoregressive Normal (SVARN) Factor-Based Term Structure Models of order p. The second family of models we study is given by the Switching Autoregressive Gamma (SARG) and the Switching Vector Autoregressive Gamma (SVARG) Factor-Based Term Structure Models of order p. Regime shifts are described by a Markov chain with (historical) non-homogeneous transition probabilities.Affine Term Structure Models ; Stochastic Discount Factor ; Car processes ; Switching Regimes ; VARMA processes ; Lags ; Positivity ; Derivative Pricing.
Nonlinear Kinetic Dynamics of Magnetized Weibel Instability
Kinetic numerical simulations of the evolution of the Weibel instability
during the full nonlinear regime are presented. The formation of strong
distortions in the electron distribution function resulting in formation of
strong peaks in it and their influence on the resulting electrostatic waves are
shown.Comment: 6 pages, 4 figure
Theory and applications of the Vlasov equation
Forty articles have been recently published in EPJD as contributions to the
topical issue "Theory and applications of the Vlasov equation". The aim of this
topical issue was to provide a forum for the presentation of a broad variety of
scientific results involving the Vlasov equation. In this editorial, after some
introductory notes, a brief account is given of the main points addressed in
these papers and of the perspectives they open.Comment: Editoria
Pricing and Inference with Mixtures of Conditionally Normal Processes.
We consider the problems of derivative pricing and inference when the stochastic discount factor has an exponential-affine form and the geometric return of the underlying asset has a dynamics characterized by a mixture of conditionally Normal processes. We consider both the static case in which the underlying process is a white noise distributed as a mixture of Gaussian distributions (including extreme risks and jump diffusions) and the dynamic case in which the underlying process is conditionally distributed as a mixture of Gaussian laws. Semi-parametric, non parametric and Switching Regime situations are also considered. In all cases, the risk-neutral processes and explicit pricing formulas are obtained.Derivative Pricing ; Stochastic Discount Factor ; Implied Volatility, Mixture of Normal Distributions ; Mixture of Conditionally Normal Processes ; Nonparametric Kernel Estimation ; Mixed-Normal GARCH Processes ; Switching Regime Models.
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