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The linear filtering, prediction and smoothing problems as well as the linear quadratic control problems can very generally be formulated as operator equations using basic linear algebra.The equations are of Fredholm type II, and they are difficult to solve directly.It is shown how the operator can be factorized into two Volterra operators using a matrix Riccati equation. Recursive solution of the
The 1-locus incompatibility system that is usually assumed to be present in the red clover is investigated. The allele fluctuations from one generation to the other are demonstrated. A mathematical state model is deduced for arbitrary numbers of alleles in the population, and its steady-state behaviour and stability are discussed. The eigenvalues of the linearized models as well as simulations sho
The random effects in tracer kinetics and cell cycle kinetics are usually described by the particle residence time. An analytical framework is developed, and the importance of the statistical independence of the residence times is emphasized.
The Grodsky packet storage model describes many features of insulin release, but at present more or less arbitrary simplifications are necessary. The consequences of various simplifications are discussed, especially with regard to identification of parameters thought to be of importance for glucose tolerance. In particular, the insulin release dynamics of the ordinary intravenous glucose tolerance
The overdamped dynamics of particles dragged by a parallel flow in a straight micro-channel in the presence of a transverse acoustophoretic force is investigated. Analytical solutions are presented in the case of plug, shear, or Poiseuille flow velocity profile. Two regimes of particle dynamics are observed, namely an early regime dominated by the local stream-wise velocity and a later regime gove
Deterministic lateral displacement provides a novel and efficient technique for sorting micrometer-sized particles based on particle size. It is grounded on the principle that the paths associated with particles of different diameters, entrained in flow streaming through a periodic lattice of obstacles, are characterized by different deflection angles with respect to the average direction of the c
We investigate the mixing layer thickness, δ(ξ), along the streamwise coordinate ξ of a straight channel fed with alternating streams of segregated solutes. We show the occurence of convection-enhanced mixing regimes downsteram the channel: i) an early-mixing regime, δ(ξ) ∼ξ 1/3 resembling the classical Lèvêque scaling of the thermal boundary layer, ii) an intermediate anomalous regime δ(ξ)∼ξ 3/5,
This article develops the theory of laminar dispersion in finite-length channel flows at high Péclet numbers, completing the classical Taylor-Aris theory which applies for long-term, long-distance properties. It is shown, by means of scaling analysis and invariant reformulation of the moment equations, that solute dispersion in finite length channels is characterized by the occurrence of a new reg
This article develops the theoretical analysis of transport and dispersion phenomena in wide-bore chromatography at values of the Peclet number Pe beyond the upper bound of validity of the Taylor-Aris theory. It is shown that for Poiseuille flows in cylindrical capillaries the average residence time grows logarithmically with the Peclet number, while the variance of the outlet chromatogram scales
This article analyses stationary scalar mixing downstream an open flow Couette device operating in the creeping flow regime. The device consists of two coaxial cylinders of finite length Lz, and radii κR and R (<1), which can rotate independently. At relatively large values of the aspect ratioα = Lz/R 1, and of the Pclet number Pe, the stationary response of the system can be accurately described
We develop a quantitative analysis of mixing regimes in an annular MHD-driven micromixer recently proposed by Gleeson et al. as a prototype for biomolecular applications. The analysis is based on the spectral properties of the advection - diffusion operator, with specific focus on the dependence of the dominant eigenvalue - eigenfunction on the Peclet number and on the system geometry. A theoretic
We study the spectral properties of the advection-diffusion operator associated with a non-chaotic 3d Stokes flow defined in the annular region between counter-rotating cylinders of finite length. The focus is on the dependence of the eigenvalue-eigenfunction spectrum on the Peclet number Pe. Several convection-enhanced mixing regimes are identified, each characterized by a power law scaling, -μd∼
We investigate the steady-state performance of a planar micromixer composed of several S-shaped units. Mixing efficiency is quantified by the decay of the scalar variance downstream the device for generic feeding conditions. We discuss how this decay is controlled by the spectral properties of the advection-diffusion Floquet operator, F, that maps a generic scalar profile at the inlet of a single
Spectral properties of the weighted Laplace operator in the presence of fractal boundaries are numerically investigated for both Neumann and Dirichlet boundary conditions. This corresponds to the characterization of heat and mass transport in microchannels with irregular and rough surfaces induced by the microfabrication process. The axial velocity field with no-slip boundary conditions, represent
