1,023 research outputs found
Stirring by swimmers in confined microenvironments
We consider the tracer diffusion that arises from the run-and-tumble
motion of low Reynolds number swimmers, such as bacteria. In unbounded dilute
suspensions, where the dipole swimmers move in uncorrelated runs of length
, an exact solution showed that is independent of .
Here we verify this result in numerical simulations for a particular model
swimmer, the spherical squirmer. We also note that in confined
microenvironments, such as microscopic droplets, microfluidic devices and
bacterial microzones in marine ecosystems, the size of the system can be
comparable to . We show that this effect alone reduces the value of
in comparison to its bulk value, and predict a scaling form for its
relative decrease.Comment: submitted to JSTA
Fluid mixing by curved trajectories of microswimmers
We consider the tracer diffusion that arises from the run-and-tumble
motion of low Reynolds number swimmers, such as bacteria. Assuming a dilute
suspension, where the bacteria move in uncorrelated runs of length ,
we obtain an exact expression for for dipolar swimmers in three
dimensions, hence explaining the surprising result that this is independent of
. We compare to the contribution to tracer diffusion from
entrainment.Comment: 5 pages, 2 figure
On correspondence between tensors and bispinors
It is known that in the four-dimensional Riemannian space the complex
bispinor generates a number of tensors: scalar, pseudo-scalar, vector,
pseudo-vector, antisymmetric tensor. This paper solves the inverse problem: the
above tensors are arbitrarily given, it is necessary to find a bispinor
(bispinors) reproducing the tensors. The algorithm for this mapping constitutes
construction of Hermitean matrix from the tensors and finding its
eigenvalue spectrum. A solution to the inverse problem exists only when is
nonnegatively definite. Under this condition a matrix satisfying equation
can be found. One and the same system of tensor values can be used
to construct the matrix accurate to an arbitrary factor on the left-hand
side, viz. unitary matrix in polar expansion . The matrix is
shown to be expandable to a set of bispinors, for which the unitary matrix
is responsible for the internal (gauge) degrees of freedom. Thus, a group of
gauge transformations depends only on the Riemannian space dimension,
signature, and the number field used. The constructed algorithm for mapping
tensors to bispinors admits extension to Riemannian spaces of a higher
dimension.Comment: 14 pages;LaTeX2e;to appear in the 9th Marcel Grossmann Meeting (MG9)
Proceedings,Rome, July, 200
Existence of Solutions to a Class of Nonlinear Convergent Chattering-free Sliding Mode Control Systems
Sliding mode control is a nonlinear control technique, which is robust against some classes of uncertainties and disturbances. However, this control produces chattering which can cause instability due to unmodeled dynamics and can also cause damage to actuators or the plant. There are essentially two ways to counter the chattering phenomenon. One way is to use higher order sliding mode, and the other way is to add a boundary layer around the switching surface and use continuous control inside the boundary. The problem with the first method is that the derivative of a certain state variable is not available for measurement, and therefore methods have to be used to observe that variable. In the second method, it is important that the trajectories inside the boundary layer do not try to come outside the boundary after entering the boundary layer. Control laws producing chattering-free sliding mode using a boundary layer have been proposed and the existence of solutions to the system using these control laws are presente
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