Evolution of the mean instantaneous intensity in fibers affected by polarization mode dispersion

It is shown that the mean instantaneous intensity (MII) of a pulse propagating in an optical fiber affected by polarization mode dispersion is related to the frequency autocorrelation of the fiber's Jones matrix through a Fourier transform. A simple derivation of the diffusion equation satisfied by the MII and the autocorrelation function of a Jones matrix is described.     

Determinants in Triangulated Categories

For a small triangulated category , Bass's K ₁ group is described, and the theorem of the heart is proved. We define the determinant map from to Neeman's , and we compute this map when is the derived category of an Abelian category .     

Tunable nonlinear viscoelastic "focusing" in a microfluidic device

In this Letter we describe a novel method for tunable viscoelastic focusing of particles flowing in a microchannel. It is proposed that some elasticity, inherently present in dilute polymer solutions, may be responsible for highly nonuniform spatial distribution of flowing particles across the channel cross section, yielding their "focusing" in the midplane of the channel. A theory based on scaling arguments is presented to explain the lateral migration and is found to be in a very good agreement with the experimental observations. It was found that, in agreement with the theoretical prediction, the particles would have different spatial distribution depending on their size and rheology of the suspending medium. We demonstrate how the viscoelastic focusing can be precisely controlled by proper rheological design of the carrier solution.     

Polymeric actuators for biological applications.

To shed light on the role of cell rheology and mechanotransduction in various physiological and disease states, different techniques of force application, such as optical tweezers and deformable substrates, are employed. In this present paper we describe a new approach for the deformation of cells based on the temperature-sensitive polymer poly(N-isopropylacrylamide), PNIPAM. In response to temperature changes, PNIPAM gels undergo extensive and reversible changes in volume that allow them to be used as actuators for stretching and compressing cells and tissues. Herein we focus mainly on our experience with the deformation of red blood cells as proof of principle, and demonstrate the wealth of possibilities such stimuli-responsive materials may offer as actuators.     

The asymptotic core,nucleolus and Shapley value of smooth market games with symmetric large players

We examine the asymptotic nucleolus of a smooth and symmetric oligopoly with an atomless sector in a transferable utility (TU) market game. We provide sufficient conditions for the asymptotic core and the nucleolus to coincide with the unique TU competitive payoff distribution. This equivalence results from nucleolus of a finite TU market game belonging to its core, the core equivalence in a symmetric oligopoly with identical atoms and single-valuedness of the core in the limiting smooth game. In some cases (but not always), the asymptotic Shapley value is more favourable for the large traders than the nucleolus, in contrast to the monopoly case (Einy et al. in J Econ Theory 89(2):186–206, 1999), where the nucleolus allocation is larger than the Shapley value for the atom.     

Nanoscale memory provided by thermoreversible stochastically structured polymer aggregates on mica

Stimuli-responsive polymers are used in a large variety of applications due to the controlled manner in which their physical properties can be reversibly altered. In this study, we demonstrate the thermoreversible structuring of poly(N-isopropylacrylamide)-based polymer. By temperature-controlled atomic force microscopy, we demonstrate that polymer aggregates form on mica above the polymer lower critical solution temperature and disperse below it, and in so doing, display positional "memory" in that the nanodomains are retained in the same positions and with the same shapes during repeated cooling/heating cycles. Such positional "memory" may be useful for multiple applications in nano-microscale devices.     

Coalescence-assisted generation of single nanoliter droplets with predefined composition

We demonstrate the generation of highly accurate nanoliter droplets with a predefined composition. This composition control over a single droplet is achieved by merging two droplets with known concentrations and defined volumes. A forced coalescence is accomplished by synchronizing two piezoelectric-based active droplet generators. A microscope-mounted CCD camera is used to record, quantify and monitor the process to assure its high fidelity. The device is disposable, surfactant free, simple to operate and does not require microelectrode fabrication. It delivers a single on-demand droplet with adjustable high resolution mixing ratios up to 9 at a volume range of 1-10 nanoliters. The presented platform offers, for the first time, a means to perform droplet-based high-throughput screening in the nanoliter range.     

On the minimal fourier degree of symmetric Boolean functions

In this paper we give a new upper bound on the minimal degree of a nonzero Fourier coefficient in any non-linear symmetric Boolean function. Specifically, we prove that for every non-linear and symmetric f: {0, 1} ^k → {0, 1} there exists a set; \(\not 0 \ne S \subset [k]\) such that ¦S¦ = O(Γ(k)+√k, and \(\hat f(S) \ne 0\) where Γ(m)≤m ^0.525 is the largest gap between consecutive prime numbers in {1,..., m}. As an application we obtain a new analysis of the PAC learning algorithm for symmetric juntas, under the uniform distribution, of Mossel et al. [10]. Our bound on the degree is a significant improvement over the previous result of Kolountzakis et al. [8] who proved that ¦S¦=O(k=log k). We also show a connection between lower-bounding the degree of non-constant functions that take values in {0,1,2} and the question that we study here.     

The rheologic properties of erythrocytes: a study using an automated rheoscope

Red blood cells (RBCs) suspended in a high-viscosity medium were filmed while flowing through a microchannel using an automated rheoscope. Under these conditions, erythrocytes take different orientations and undergo varying deformation according to their location in the velocity profile. Measurements of the mean deformation at several distances from the center of the microchannel at a constant flow rate were acquired for normal and thalassemia erythrocytes. The measurements demonstrate how diagnosis can be made based on a single flow rate in contrast to conventional methods where shear is mechanically controlled. The spatial distribution and velocity of RBCs and rigid microspheres (1 μm) were measured. The maximum slip velocity was found to be linearly correlated to the flow rate for both cells and microspheres. RBCs showed enhanced inward lateral migration compared to the rigid spheres, which is attributed to RBC deformation. The results demonstrate the coupling between RBC mechanical properties and their motion in microvessels. This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27-29, 2006.