Spin Tunneling in Magnetic Molecules: Quasisingular Perturbations and Discontinuous SU(2) Instantons

Spin coherent state path integrals with discontinuous semiclassical paths are investigated with special reference to a realistic model for the magnetic degrees of freedom in the Fe8 molecular solid. It is shown that such paths are essential to a proper understanding of the phenomenon of quenched spin tunneling in these molecules. In the Fe8 problem, such paths are shown to arise as soon as a fourth order anisotropy term in the energy is turned on, making this term a singular perturbation from the semiclassical point of view. The instanton approximation is shown to quantitatively explain the magnetic field dependence of the tunnel splitting, as well as agree with general rules for the number of quenching points allowed for a given value of spin. An accurate approximate formula for the spacing between quenching points is derived

A two-step approach to achieve secondary amide transamidation enabled by nickel catalysis.

A long-standing challenge in synthetic chemistry is the development of the transamidation reaction. This process, which involves the conversion of one amide to another, is typically plagued by unfavourable kinetic and thermodynamic factors. Although some advances have been made with regard to the transamidation of primary amide substrates, secondary amide transamidation has remained elusive. Here we present a simple two-step approach that allows for the elusive overall transformation to take place using non-precious metal catalysis. The methodology proceeds under exceptionally mild reaction conditions and is tolerant of amino-acid-derived nucleophiles. In addition to overcoming the classic problem of secondary amide transamidation, our studies expand the growing repertoire of new transformations mediated by base metal catalysis

Motion of falling object

A simple setup was assembled to study the motion of an object while it falls. The setup was used to determine the instantaneous velocity, terminal velocity and acceleration due to gravity. Also, since the whole project was done within $20 it can easily be popularized.Comment: 11 pages, 4 figur

Whole-blood sorting, enrichment and in situ immunolabeling of cellular subsets using acoustic microstreaming

Analyzing undiluted whole human blood is a challenge due to its complex composition of hematopoietic cellular populations, nucleic acids, metabolites, and proteins. We present a novel multi-functional microfluidic acoustic streaming platform that enables sorting, enrichment and in situ identification of cellular subsets from whole blood. This single device platform, based on lateral cavity acoustic transducers (LCAT), enables (1) the sorting of undiluted donor whole blood into its cellular subsets (platelets, RBCs, and WBCs), (2) the enrichment and retrieval of breast cancer cells (MCF-7) spiked in donor whole blood at rare cell relevant concentrations (10 mL− 1), and (3) on-chip immunofluorescent labeling for the detection of specific target cellular populations by their known marker expression patterns. Our approach thus demonstrates a compact system that integrates upstream sample processing with downstream separation/enrichment, to carry out multi-parametric cell analysis for blood-based diagnosis and liquid biopsy blood sampling

Macroscopic Quantum Coherence in a Magnetic Nanoparticle Above the Surface of a Superconductor

We study macroscopic quantum tunneling of the magnetic moment in a single-domain particle placed above the surface of a superconductor. Such a setup allows one to manipulate the height of the energy barrier, preserving the degeneracy of the ground state. The tunneling amplitude and the effect of the dissipation in the superconductor are computed.Comment: RevTeX, 4 pages, 1 figure. Submitted to Phys. Rev. Let

Space Efficient Breadth-First and Level Traversals of Consistent Global States of Parallel Programs

Enumerating consistent global states of a computation is a fundamental problem in parallel computing with applications to debug- ging, testing and runtime verification of parallel programs. Breadth-first search (BFS) enumeration is especially useful for these applications as it finds an erroneous consistent global state with the least number of events possible. The total number of executed events in a global state is called its rank. BFS also allows enumeration of all global states of a given rank or within a range of ranks. If a computation on n processes has m events per process on average, then the traditional BFS (Cooper-Marzullo and its variants) requires $\mathcal{O}(\frac{m^{n-1}}{n})$ space in the worst case, whereas ou r algorithm performs the BFS requires $\mathcal{O}(m^2n^2)$ space. Thus, we reduce the space complexity for BFS enumeration of consistent global states exponentially. and give the first polynomial space algorithm for this task. In our experimental evaluation of seven benchmarks, traditional BFS fails in many cases by exhausting the 2 GB heap space allowed to the JVM. In contrast, our implementation uses less than 60 MB memory and is also faster in many cases

Spin tunnelling in mesoscopic systems

We study spin tunnelling in molecular magnets as an instance of a mesoscopic phenomenon, with special emphasis on the molecule Fe8. We show that the tunnel splitting between various pairs of Zeeman levels in this molecule oscillates as a function of applied magnetic field, vanishing completely at special points in the space of magnetic fields, known as diabolical points. This phenomena is explained in terms of two approaches, one based on spin-coherent-state path integrals, and the other on a generalization of the phase integral (or WKB) method to difference equations. Explicit formulas for the diabolical points are obtained for a model Hamiltonian.Comment: 13 pages, 5 figures, uses Pramana style files; conference proceedings articl

Bell's inequality for n spin-s particles

The Mermin-Klyshko inequality for n spin-1/2 particles and two dichotomic observables is generalized to n spin-s particles and two maximal observables. It is shown that some multiparty multilevel Greenberger-Horne-Zeilinger states [A. Cabello, Phys. Rev. A 63, 022104 (2001)] maximally violate this inequality for any s. For a fixed n, the magnitude of the violation is constant for any s, which provides a simple demonstration and generalizes the conclusion reached by Gisin and Peres for two spin-s particles in the singlet state [Phys. Lett. A 162, 15 (1992)]. For a fixed s, the violation grows exponentially with n, which provides a generalization to any s of Mermin's conclusion for n spin-1/2 particles [Phys. Rev. Lett. 65, 1838 (1990)].Comment: REVTeX4, 4 page

Fisheye Consistency: Keeping Data in Synch in a Georeplicated World

Over the last thirty years, numerous consistency conditions for replicated data have been proposed and implemented. Popular examples of such conditions include linearizability (or atomicity), sequential consistency, causal consistency, and eventual consistency. These consistency conditions are usually defined independently from the computing entities (nodes) that manipulate the replicated data; i.e., they do not take into account how computing entities might be linked to one another, or geographically distributed. To address this lack, as a first contribution, this paper introduces the notion of proximity graph between computing nodes. If two nodes are connected in this graph, their operations must satisfy a strong consistency condition, while the operations invoked by other nodes are allowed to satisfy a weaker condition. The second contribution is the use of such a graph to provide a generic approach to the hybridization of data consistency conditions into the same system. We illustrate this approach on sequential consistency and causal consistency, and present a model in which all data operations are causally consistent, while operations by neighboring processes in the proximity graph are sequentially consistent. The third contribution of the paper is the design and the proof of a distributed algorithm based on this proximity graph, which combines sequential consistency and causal consistency (the resulting condition is called fisheye consistency). In doing so the paper not only extends the domain of consistency conditions, but provides a generic provably correct solution of direct relevance to modern georeplicated systems