We show a strict hierarchy among various edge and vertex expansion properties of Markov chains. This gives easy proofs of a range of bounds, both classical and new, on chi-square distance, spectral gap and mixing time. The 2-gradient is then used to give an isoperimetric proof that a random walk on the grid [k] mixes in time O∗(k2 n).

We developed a new passive-type micromixer based on the baker's transformation and realized a fast mixing of a protein solution, which has lower diffusion constant. The baker's transformation is an ideal mixing method, but there is no report on the microfluidic baker's transformation (MBT), since it is required to fabricate the complicated three-dimensional (3D) structure to realize the MBT dev...

This paper presents the results of fluidic switching and mixing, performed in microfluidic channels, integrated with micromachined acoustic transducers. The transducers operate at 400 MHz while the microfluidic channels are made by casting polydimethylsiloxane (PDMS) on silicon moulds. Rapid switching is incorporated by applying pressure waves in one of the two outlet channels to get preferenti...

A novel concept of simultaneous injection-effective mixing analysis (SIEMA) is proposed, and a SIEMA method applied to the spectrophotometric determination of palladium using a water-soluble chromogenic reagent has been demonstrated. The flow configuration of SIEMA is a hybrid format of flow injection analysis (FIA), sequential injection analysis (SIA) and multicommutation in flow-based analysi...

We introduce a Markov chain for sampling from the uniform distribution on a Riemannian manifoldM, which we call the geodesic walk. We prove that the mixing time of this walk on any manifold with positive sectional curvature Cx(u, v) bounded both above and below by 0 < m2 ≤ Cx(u, v) ≤ M2 < ∞ is O∗ ( M2 m2 ) . In particular, this bound on the mixing time does not depend explicitly on the dimensio...

2.1. Turbulent Mixing 1838 2.2. Stopped-Flow Methods 1838 2.3. Continuous-Flow Techniques 1839 3. Detection Methods 1841 3.1. Tryptophan Fluorescence 1841 3.2. ANS Fluorescence 1842 3.3. Fluorescence Energy Transfer 1842 3.4. Continuous-Flow Absorbance 1843 3.5. Probes of Secondary Structure Formation 1844 3.6. Small-Angle X-ray Scattering 1844 3.7. Other Detection Methods 1844 4. Quenched-Flow...

We report for the first time a laminar high-performance continuous micromixing process of two fluids over a length of 200 microns in under 10 milliseconds achieved by an optimization of the control parameters amplitude and frequency in the mixing device denoted as 'Shear Superposition Micromixer'. We improve mixing time by approximately 5 orders of magnitude over diffusion-limited mixing. The d...

The aim of microfluidic mixing is to achieve a thorough and rapid mixing of multiple samples in microscale devices. In such devices, sample mixing is essentially achieved by enhancing the diffusion effect between the different species flows. Broadly speaking, microfluidic mixing schemes can be categorized as either "active", where an external energy force is applied to perturb the sample specie...

In this paper a Markov chain for contingency tables with two rows is deened. The chain is shown to be rapidly mixing using the path coupling method. The mixing time of the chain is quadratic in the number of columns and linear in the logarithm of the table sum. Two extensions of the new chain are discussed: one for three-rowed contingency tables and one for m-rowed contingency tables. We show t...

47 The interpretation of the Cretaceous-Paleogene (K-Pg) iridium anomaly – and other 48 impact ejecta – as the result of a single, large asteroid impact has been the subject of much 49 debate, in part due to the distribution of impact markers beyond the narrow confines of the K-Pg 50 boundary sedimentary layer. Here, we revisit the hypothesized processes leading to the shape of 51 K-Pg iridium ...