23,166 research outputs found
Generalized hydrodynamics of a dilute finite-sized particles suspension: Dynamic viscosity
We present a mesoscopic hydrodynamic description of the dynamics of colloidal
suspensions. We consider the system as a gas of Brownian particles suspended in
a Newtonian heat bath subjected to stationary non-equilibrium conditions
imposed by a velocity field. Using results already obtained in previous studies
in the field by means of a generalized Fokker-Planck equation, we obtain a set
of coupled differential equations for the local diffusion current and the
evolution of the total stress tensor. We find that the dynamic shear viscosity
of the system contains contributions arising from the finite size of the
particles.Comment: To appear in Physical Review
On piecewise isomorphism of some varieties
Two quasi-projective varieties are called piecewise isomorphic if they can be
stratified into pairwise isomorphic strata. We show that the m-th symmetric
power of the complex affine space is piecewise isomorphic to
and the m-th symmetric power of the infinite
dimensional complex projective space is piecewise isomorphic to the infinite
dimensional Grassmannian
Analytical study of coherence in seeded modulation instability
We derive analytical expressions for the coherence in the onset of modulation
instability, in excellent agreement with thorough numerical simulations. As
usual, we start by a linear perturbation analysis, where broadband noise is
added to a continuous wave (CW) pump; then, we investigate the effect of adding
a deterministic seed to the CW pump, a case of singular interest as it is
commonly encountered in parametric amplification schemes. Results for the
dependence of coherence on parameters such as fiber type, pump power,
propagated distance, seed signal-to-noise ratio are presented. Finally, we show
the importance of including higher-order linear and nonlinear dispersion when
dealing with generation in longer wavelength regions (mid IR). We believe these
results to be of relevance when applied to the analysis of the coherence
properties of supercontinua generated from CW pumps.Comment: 6 pages, 8 figure
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