22,130 research outputs found
A Fractional Variational Approach for Modelling Dissipative Mechanical Systems: Continuous and Discrete Settings
Employing a phase space which includes the (Riemann-Liouville) fractional
derivative of curves evolving on real space, we develop a restricted
variational principle for Lagrangian systems yielding the so-called restricted
fractional Euler-Lagrange equations (both in the continuous and discrete
settings), which, as we show, are invariant under linear change of variables.
This principle relies on a particular restriction upon the admissible variation
of the curves. In the case of the half-derivative and mechanical Lagrangians,
i.e. kinetic minus potential energy, the restricted fractional Euler-Lagrange
equations model a dissipative system in both directions of time, summing up to
a set of equations that is invariant under time reversal. Finally, we show that
the discrete equations are a meaningful discretisation of the continuous ones.Comment: Key words: Variational analysis, Mechanical systems, Lagrangian
mechanics, Damping, Fractional derivatives, Discretisation, Variational
integrators. 13 pages, no figures. Contributed paper to 6th IFAC Workshop on
Lagrangian and Hamiltonian Methods for Nonlinear Contro
A reduced-order strategy for 4D-Var data assimilation
This paper presents a reduced-order approach for four-dimensional variational
data assimilation, based on a prior EO F analysis of a model trajectory. This
method implies two main advantages: a natural model-based definition of a mul
tivariate background error covariance matrix , and an important
decrease of the computational burden o f the method, due to the drastic
reduction of the dimension of the control space. % An illustration of the
feasibility and the effectiveness of this method is given in the academic
framework of twin experiments for a model of the equatorial Pacific ocean. It
is shown that the multivariate aspect of brings additional
information which substantially improves the identification procedure. Moreover
the computational cost can be decreased by one order of magnitude with regard
to the full-space 4D-Var method
Ensemble prediction for nowcasting with a convection-permitting model - II: forecast error statistics
A 24-member ensemble of 1-h high-resolution forecasts over the Southern United Kingdom is used to study short-range forecast error statistics. The initial conditions are found from perturbations from an ensemble transform Kalman filter. Forecasts from this system are assumed to lie within the bounds of forecast error of an operational forecast system. Although noisy, this system is capable of producing physically reasonable statistics which are analysed and compared to statistics implied from a variational assimilation system. The variances for temperature errors for instance show structures that reflect convective activity. Some variables, notably potential temperature and specific humidity perturbations, have autocorrelation functions that deviate from 3-D isotropy at the convective-scale (horizontal scales less than 10 km). Other variables, notably the velocity potential for horizontal divergence perturbations, maintain 3-D isotropy at all scales. Geostrophic and hydrostatic balances are studied by examining correlations between terms in the divergence and vertical momentum equations respectively. Both balances are found to decay as the horizontal scale decreases. It is estimated that geostrophic balance becomes less important at scales smaller than 75 km, and hydrostatic balance becomes less important at scales smaller than 35 km, although more work is required to validate these findings. The implications of these results for high-resolution data assimilation are discussed
From Lagrangian mechanics to nonequilibrium thermodynamics: a variational perspective
In this paper, we survey our recent results on the variational formulation of
nonequilibrium thermodynamics for the finite dimensional case of discrete
systems as well as for the infinite dimensional case of continuum systems.
Starting with the fundamental variational principle of classical mechanics,
namely, Hamilton's principle, we show, with the help of thermodynamic systems
with gradually increasing level complexity, how to systematically extend it to
include irreversible processes. In the finite dimensional cases, we treat
systems experiencing the irreversible processes of mechanical friction, heat
and mass transfer, both in the adiabatically closed and in the open cases. On
the continuum side, we illustrate our theory with the example of multicomponent
Navier-Stokes-Fourier systems.Comment: 7 figure
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