A Multi-Dimensional Lieb-Schultz-Mattis Theorem

For a large class of finite-range quantum spin models with half-integer spins, we prove that uniqueness of the ground state implies the existence of a low-lying excited state. For systems of linear size L, with arbitrary finite dimension, we obtain an upper bound on the excitation energy (i.e., the gap above the ground state) of the form (C log L)/L. This result can be regarded as a multi-dimensional Lieb-Schultz-Mattis theorem [14] and provides a rigorous proof of the main result in [8].     

Palladium-mediated fragmentation of meta photocycloadducts using carbon based electrophiles. Part 1

Substituted benzene derived meta photocycloadducts have been shown to undergo a fragmentation/arylation reaction under Heck reaction conditions to give bridged bicyclo[3.2.1] compounds in a highly atom-efficient manner. When an anisole derived meta photocycloadduct is used, a bridgehead ketone is generated. However, if an alkylbenzene derived meta photocycloadduct is used, a bridgehead alkene is formed. This strategy has been used to create novel enol ether and transient allyl silane compounds.     

Combined CI–HY studies of atomic states. II. Compact wave functions for the be ground state

Combined CI –HY method techniques have been employed in obtaining a 57-term CI –HY wave function with an energy of ?14.66632 a.u. A method due to Brown has been adopted for obtaining this wave function and various shorter expansions. A 44-term expansion with an energy of ?14.66606 a.u. is analyzed in terms of various pair effects, and qualitative arguments are presented for understanding these effects.     

High‐precision Hy–CI variational calculations for the ground state of neutral helium and helium‐like ions

Hylleraas–configuration interaction (Hy–CI) method variational calculations with up to 4648 expansion terms are reported for the ground ¹S state of neutral helium. Convergence arguments are presented to obtain estimates for the exact nonrelativistic energy of this state. The nonrelativistic energy is calculated to be ?2.9037 2437 7034 1195 9829 99 a.u. Comparisons with other calculations and an energy extrapolation give an estimated nonrelativistic energy of ?2.9037 2437 7034 1195 9830(2) a.u., which agrees well with the best previous variational energy, ?2.9037 2437 7034 1195 9829 55 a.u., of Korobov (Phys Rev A 2000, 61, 64503), obtained using the universal (exponential) variational expansion method with complex exponents (Frolov, A. M.; Smith, V. H. Jr. J Phys B Atom Mol Opt Phys 1995, 28, L449). In addition to He, results are also included for the ground ¹S states of H^?, Li⁺, Be⁺⁺, and B⁺³. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Fast-lysis cell traps for chemical cytometry

Electrically addressable cell traps were integrated with capillary electrophoresis for the analysis of the contents of single adherent cells. Electrodes composed of indium tin oxide were patterned on a glass surface followed by formation of topographical cell traps using 1002F photoresist. Single cells trapped in the holes could be lysed in less than 66 ms by applying a brief electric field (10 ms) across the electrode beneath the cell and the ground electrode placed in the aqueous media above the cell traps. The gas formed during cell lysis remained localized within the cavity formed by the 1002F photoresist. The retention of the gas in the cell trap enabled the cell traps to be coupled to an overlying capillary without blockage of the capillary. Single cells cultured in the traps were loaded with fluorescein and Oregon Green and then electrically lysed. By simultaneous application of an electric field to the capillary, the cell's contents were loaded into the capillary and electrophoretically separated. Orgeon Green and fluorescein from a single cell were fully resolved in less than two minutes. The use of a single patterned electrode beneath the 1002F cell trap yielded a simple easily fabricated design that was robust when immersed in aqueous solutions. Moreover, the design can easily be scaled up to create arrays of adherent cells for serial analyses using a single capillary or for parallel analysis by mating to an array of capillaries. Enhancing the rate of analysis of single adherent cells would enable a greater understanding of cellular physiology.     

Micropallet arrays with poly(ethylene glycol) walls

Arrays of releasable micropallets with surrounding walls of poly(ethylene glycol) (PEG) were fabricated for the patterning and sorting of adherent cells. PEG walls were fabricated between the SU-8 pallets using a simple, mask-free strategy. By utilizing the difference in UV-transmittance of glass and SU-8, PEG monomer was selectively photopolymerized in the space surrounding the pallets. Since the PEG walls are composed of a cross-linked structure, the stability of the walls is independent of the pallet array geometry and the properties of the overlying solution. Even though surrounded with PEG walls, the individual pallets were detached from the array by the mechanical force generated by a focused laser pulse, with a release threshold of 6 microJ. Since the PEG hydrogels are repellent to protein adsorption and cell attachment, the walls localized cell growth to the pallet top surface. Cells grown in the microwells formed by the PEG walls were released by detaching the underlying pallet. The released cells/pallets were collected, cultured and clonally expanded. The micropallet arrays with PEG walls provide a platform for performing single cell analysis and sorting on chip.     

Examination of laser microbeam cell lysis in a PDMS microfluidic channel using time-resolved imaging

We use time-resolved imaging to examine the lysis dynamics of non-adherent BAF-3 cells within a microfluidic channel produced by the delivery of single highly-focused 540 ps duration laser pulses at lambda = 532 nm. Time-resolved bright-field images reveal that the delivery of the pulsed laser microbeam results in the formation of a laser-induced plasma followed by shock wave emission and cavitation bubble formation. The confinement offered by the microfluidic channel constrains substantially the cavitation bubble expansion and results in significant deformation of the PDMS channel walls. To examine the cell lysis and dispersal of the cellular contents, we acquire time-resolved fluorescence images of the process in which the cells were loaded with a fluorescent dye. These fluorescence images reveal cell lysis to occur on the nanosecond to microsecond time scale by the plasma formation and cavitation bubble dynamics. Moreover, the time-resolved fluorescence images show that while the cellular contents are dispersed by the expansion of the laser-induced cavitation bubble, the flow associated with the bubble collapse subsequently re-localizes the cellular contents to a small region. This capacity of pulsed laser microbeam irradiation to achieve rapid cell lysis in microfluidic channels with minimal dilution of the cellular contents has important implications for their use in lab-on-a-chip applications.     

Localization in One Dimensional Random Media:¶A Scattering Theoretic Approach

We use scattering theoretic methods to prove exponential localization for random displacement models in one dimension. The operators we consider model both quantum and classical wave propagation. Our main tools are the reflection and transmission coefficients for compactly supported single site perturbations. We show that randomly displaced, non-reflectionless single sites lead to localization. Received: 23 September 1999 / Accepted: 13 March 2000