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Louis Saddier

Publications and source records attributed to Louis Saddier.

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Breaking of a floating particle raft by water waves

When particles of a few tens of microns are spread on the surface of water, they aggregate under the action of capillary forces and form a thin floating membrane, a particle raft. In a tank with a raft made of graphite powder, we generate in the laboratory gravity surface waves, whose wavelength {about 17 cm} is very large compared to the thickness of the raft {of order 10 microns}. For a sufficiently strong wave amplitude, the raft breaks up progressively by developing cracks and producing fragments whose sizes decrease on a time scale long compared to the period of the wave. We characterize the breaking mechanisms. Then, we investigate the area distribution of the fragments produced during the fragmentation process. The visual appearance of the fragments distributed in size and surrounded by open water bears a {notable} resemblance to the floes produced by the fracturing of sea ice by waves in the polar oceans. Fragmentation concepts and morphological tools built for sea ice floes can be applied to our macroscopic analog, on which the entire dynamic evolution is accessible. {However, the mechanic of the two systems differ, as our particle raft breaks due to the viscous stresses, whereas the sea-ice fractures due its bending by the waves.

physics.flu-dyn

A Bayesian theory of market impact

The available liquidity at any time in financial markets falls largely short of the typical size of the orders that institutional investors would trade. In order to reduce the impact on prices due to the execution of large orders, traders in financial markets split large orders into a series of smaller ones, which are executed sequentially. The resulting sequence of trades is called a meta-order. Empirical studies have revealed a non-trivial set of statistical laws on how meta-orders affect prices, which include i) the square-root behaviour of the expected price variation with the total volume traded, ii) its crossover to a linear regime for small volumes, and iii) a reversion of average prices towards its initial value, after the sequence of trades is over. Here we recover this phenomenology within a minimal theoretical framework where the market sets prices by incorporating all information on the direction and speed of trade of the meta-order in a Bayesian manner. The simplicity of this derivation lends further support to the robustness and universality of market impact laws. In particular, it suggests that the square-root impact law originates from the over-estimation of order flows originating from meta-orders.

q-fin.TR