Itô's formula is the chain rule with wick ordering

Non-commutative stochastic integrals are defined using exponential vectors in Fock space. It is shown that the generalisation of Itô's formula is essentially the ordinary chain rule, combined with Wick ordering.     

Magneto-controlled illumination with opto-fluidics

Imaging of micro- and nanofluidics is a challenge since the size of the channels is so small that the installment of additional optical and mechanical switches is very difficult. The size of the device and associated increase in viscous dissipation constitute another constraint. In response to these limitations, this work proposes and demonstrates the manipulation of light by adding a functional lens to control the light on demand. In the present work, this lens is realized by filling a hollow fiber with a colloid of superparamagnetic Fe₃O₄ nanoparticles. When the propagation of light is perpendicular to the magnetic field, this lens stretches the circular beam into a ribbon yielding a larger visible area. Potentially, one can apply a rotating magnetic field thus illuminating a larger spot size or creating other beam geometries. Such composite fibers might also be of value for Faraday isolation and other magneto-optic effects in optical fibers.     

Hamilton-Jacobi theory for continuation of magnetic field across a toroidal surface supporting a plasma pressure discontinuity

The vanishing of the divergence of the total stress tensor (magnetic plus kinetic) in a neighborhood of an equilibrium plasma containing a toroidal surface of discontinuity gives boundary and jump conditions that strongly constrain allowable continuations of the magnetic field across the surface. The boundary conditions allow the magnetic fields on either side of the discontinuity surface to be described by surface magnetic potentials, reducing the continuation problem to that of solving a Hamilton-Jacobi equation. The characteristics of this equation obey Hamiltonian equations of motion, and a necessary condition for the existence of a continued field across a general toroidal surface is that there exist invariant tori in the phase space of this Hamiltonian system. It is argued from the Birkhoff theorem that existence of such an invariant torus is also, in general, sufficient for continuation to be possible. An important corollary is that the rotational transform of the continued field on a surface of discontinuity must, generically, be irrational.     

Coating single-walled carbon nanotubes with phospholipids

Single-walled carbon nanotubes (SWNTs), being hydrophobic by nature, aggregate in water to form large bundles. However, isolated SWNTs possess unique physical and chemical properties that are desirable for sensing and biological applications. Conventionally isolated SWNTs can be obtained by wrapping the tubes with biopolymers or surfactants. The binding modes proposed for these solubilization schemes, however, are less than comprehensive. Here we characterize the efficacies of solubilizing SWNTs through various types of phospholipids and other amphiphilic surfactants. Specifically, we demonstrate that lysophospholipids, or single-chained phospholipids offer unprecedented solubility for SWNTs, while double-chained phospholipids are ineffective in rendering SWNTs soluble. Using transmission electron microscopy (TEM) we show that lysophospholipids wrap SWNTs as striations whose size and regularity are affected by the polarity of the lysophospholipids. We further show that wrapping is only observed when SWNTs are in the lipid phase and not the vacuum phase, suggesting that the environment has a pertinent role in the binding process. Our findings shed light on the debate over the binding mechanism of amphiphilic polymers and cylindrical nanostructures and have implications on the design of novel supramolecular complexes and nanodevices.     

Occupied and Unoccupied Orbitals of C60 and C70

Abstract

The full spectrum of occupied and unoccupied σ and π orbitals is presented for solid C₆₀, C₇₀, and graphite, using Cls emission and absorption spectroscopy. There are significant diffcrences between C₆₀ and C₇₀, and even larger changes relative to their infinite analog graphite (C∝). A comparison is made with photocmission and inverse photoemission results, along with first principles quasiparticle calculations.     

Synchronization engineering: theoretical framework and application to dynamical clustering

A method for engineering the global behavior of populations of rhythmic elements is presented. The framework, which is based on phase models, allows a nonlinear time-delayed global feedback signal to be constructed which produces an interaction function corresponding to the desired behavior of the system. It is shown theoretically and confirmed in numerical simulations that a polynomial, delayed feedback is a versatile tool to tune synchronization patterns. Dynamical states consisting of one to four clusters were engineered to demonstrate the application of synchronization engineering in an experimental electrochemical system.     

Mitigation of loss within a molecular Stark decelerator

The transverse motion inside a Stark decelerator plays a large role in the total efficiency of deceleration. We differentiate between two separate regimes of molecule loss during the slowing process. The first mechanism involves distributed loss due to coupling of transverse and longitudinal motion, while the second is a result of the rapid decrease of the molecular velocity within the final few stages. In this work, we describe these effects and present means for overcoming them. Solutions based on modified switching time sequences with the existing decelerator geometry lead to a large gain of stable molecules in the intermediate velocity regime, but fail to address the loss at very low final velocities. We propose a new decelerator design, the quadrupole-guiding decelerator, which eliminates distributed loss due to transverse/longitudinal couplings throughout the slowing process and also exhibits gain over normal deceleration to the lowest velocities.