48,021 research outputs found
Large-eddy simulation of large-scale structures in long channel flow
We investigate statistics of large-scale structures from large-eddy simulation (LES) of turbulent channel flow at friction Reynolds numbers Re_τ = 2K and 200K (where K denotes 1000). In order to capture the behaviour of large-scale structures properly, the channel length is chosen to be 96 times the channel half-height. In agreement with experiments, these large-scale structures are found to give rise to an apparent amplitude modulation of the underlying small-scale fluctuations. This effect is explained in terms of the phase relationship between the large- and small-scale activity. The shape of the dominant large-scale structure is investigated by conditional averages based on the large-scale velocity, determined using a filter width equal to the channel half-height. The conditioned field demonstrates coherence on a scale of several times the filter width, and the small-scale–large-scale relative phase difference increases away from the wall, passing through π/2 in the overlap region of the mean velocity before approaching π further from the wall. We also found that, near the wall, the convection velocity of the large scales departs slightly, but unequivocally, from the mean velocity
On Inefficiency of Markowitz-Style Investment Strategies When Drawdown is Important
The focal point of this paper is the issue of "drawdown" which arises in
recursive betting scenarios and related applications in the stock market.
Roughly speaking, drawdown is understood to mean drops in wealth over time from
peaks to subsequent lows. Motivated by the fact that this issue is of paramount
concern to conservative investors, we dispense with the classical variance as
the risk metric and work with drawdown and mean return as the risk-reward pair.
In this setting, the main results in this paper address the so-called
"efficiency" of linear time-invariant (LTI) investment feedback strategies
which correspond to Markowitz-style schemes in the finance literature. Our
analysis begins with the following principle which is widely used in finance:
Given two investment opportunities, if one of them has higher risk and lower
return, it will be deemed to be inefficient or strictly dominated and generally
rejected in the marketplace. In this framework, with risk-reward pair as
described above, our main result is that classical Markowitz-style strategies
are inefficient. To establish this, we use a new investment strategy which
involves a time-varying linear feedback block K(k), called the drawdown
modulator. Using this instead of the original LTI feedback block K in the
Markowitz scheme, the desired domination is obtained. As a bonus, it is also
seen that the modulator assures a worst-case level of drawdown protection with
probability one.Comment: This paper has been published in Proceedings of 56th IEEE Conference
on Decision and Control (CDC) 201
Hamiltonian formulation of SL(3) Ur-KdV equation
We give a unified view of the relation between the KdV, the mKdV, and
the Ur-KdV equations through the Fr\'{e}chet derivatives and their inverses.
For this we introduce a new procedure of obtaining the Ur-KdV equation, where
we require that it has no non-local operators. We extend this method to the
KdV equation, i.e., Boussinesq(Bsq) equation and obtain the hamiltonian
structure of Ur-Bsq equationin a simple form. In particular, we explicitly
construct the hamiltonian operator of the Ur-Bsq system which defines the
poisson structure of the system, through the Fr\'{e}chet derivative and its
inverse.Comment: 12 pages, KHTP-93-03 SNUTP-93-2
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