Sliding in a piecewise-smooth dynamical system with a hold-on effect

In this paper, we study a piecewise-smooth dynamical system of a Filippov type that has a specific discontinuity in the form of a hold-on term. The system resembles a driven dry-friction oscillator with the difference that the magnitude of the friction depends on the value of a local maximum of the oscillator displacement. Due to the hold-on term, the definition of the sliding region is not trivial. Along with a sliding region that is found analytically and is valid for any orbits, there exists a sliding region that we name ‘virtual’ because it is specific for each particular orbit. The existence of the virtual sliding region is explained by the specific discontinuity — the hold-on term — and the behavior associated with the sliding region and its boundaries can be considered as a new type of sliding-associated behavior.     

Expanded scope of heterocyclic biaryl synthesis via a palladium-catalysed thermal decarboxylative cross-coupling reaction

The palladium-catalysed decarboxylative cross-coupling of heterocyclic aromatic carboxylates and aryl halides is described. The cross-coupling proceeds under relatively mild conditions using catalytic Pd(0) and tetrabutylammonium bromide (TBAB). Utilizing a mixed solvent system consisting of N,N-dimethylformamide (DMF) and N-methyl-2-pyrrolidone (NMP), the cross-coupling system operated at temperatures ranging from 80 to 140 °C.     

The Finite Element Method on the Sierpinski Gasket

For certain classes of fractal differential equations on the Sierpinski gasket, built using the Kigami Laplacian, we describe how to approximate solutions using the finite element method based on piecewise harmonic or piecewise biharmonic splines. We give theoretical error estimates, and compare these with experimental data obtained using a computer implementation of the method (available at the web site http://mathlab.cit.cornell.edu/\sim gibbons). We also explain some interesting structure concerning the spectrum of the Laplacian that became apparent from the experimental data. March 29, 2000. Date revised: March 6, 2001. Date accepted: March 21, 2001.     

Multiplexed enzyme assays in capillary electrophoretic single-use microfluidic devices.

We describe a method of performing multiple enzyme assays in a single reaction vessel. The resolving power of capillary electrophoresis enables several enzyme assays to be analyzed at high speed in microfluidic arrays. Multiplexed measurement can increase throughput significantly without requiring highly dense microfluidic arrays. Enzyme assays in a multiplexed format for selected kinases in this work show essentially identical performance to assays performed individually. This establishes an approach for screening one compound against multiple enzyme targets simultaneously. Another potential application for performing multiplexed enzyme assay is to study protein-protein (especially enzyme-enzyme) interaction by monitoring the enzymatic activity changes.     

Ricci-Flat Metrics,Harmonic Forms and Brane Resolutions

 We discuss the geometry and topology of the complete, non-compact, Ricci-flat Stenzel metric, on the tangent bundle of S ⁿ⁺¹ . We obtain explicit results for all the metrics, and show how they can be obtained from first-order equations derivable from a superpotential. We then provide an explicit construction for the harmonic self-dual (p, q)-forms in the middle dimension p+q=(n+1) for the Stenzel metrics in 2(n+1) dimensions. Only the (p, p)-forms are L ² -normalisable, while for (p, q)-forms the degree of divergence grows with . We also construct a set of Ricci-flat metrics whose level surfaces are U(1) bundles over a product of N Einstein-K?hler manifolds, and we construct examples of harmonic forms there. As an application, we construct new examples of deformed supersymmetric non-singular M2-branes with such 8-dimensional transverse Ricci-flat spaces. We show explicitly that the fractional D3-branes on the 6-dimensional Stenzel metric found by Klebanov and Strassler is supported by a pure (2,1)-form, and thus it is supersymmetric, while the example of Pando Zayas-Tseytlin is supported by a mixture of (1,2) and (2,1) forms. We comment on the implications for the corresponding dual field theories of our resolved brane solutions. Received: 22 February 2001 / Accepted: 16 August 2002 Published online: 7 November 2002     

The Darwin Direct Implicit Particle-in-Cell (DADIPIC) Method for Simulation of Low Frequency Plasma Phenomena

We describe a new algorithm for simulating low frequency, kinetic phenomena in plasmas. Darwin direct implicit particle-in-cell (DADIPIC), as its name implies, is a combination of the Darwin and direct implicit methods. Through the Darwin method the hyperbolic Maxwell's equations are reformulated into a set of elliptic equations. Propagating light waves do not exist in the formulation so the Courant constraint on the time step is eliminated. The direct implicit method is applied only to the electrostatic field with the result that electrostatic plasma oscillations do not have to be resolved for stability. With the elimination of these constraints spatial and temporal discretization can be much larger than that possible with explicit, electrodynamic PIC. We discuss the algorithms for pushing the particles and solving for the fields in 2D cartesian geometry. We also detail boundary conditions for conductors and dielectrics. Finally, we present two test cases, electron cyclotron waves and collisionless heating in inductively coupled plasmas. For these test cases DADIPIC shows agreement with analytic kinetic theory and good energy conservation characteristics.     

Alignment of guest-host liquid crystals with polarized laser light

Surface-mediated alignment of nematic liquid crystals with polarized laser light was reported recently [1]. In this communication we describe the alignment of a guest-host liquid crystal medium with polarized laser light. Liquid crystals in the illuminated region orient perpendicular to the direction of the laser polarization and remain aligned in the absence of laser radiation. The liquid crystals can be reoriented again by subsequent illumination. The kinetic feature of this surface-mediated liquid crystal orientation is characterized by the presence of coexisting liquid crystal regions of directors pointing away from the initial alignment.     

Black holes and critical points in moduli space

We study the stabilization of scalars near a supersymmetric black hole horizon using the equation of motion of a particle moving in a potential and background metric. When the relevant 4-dimensional theory is described by special geometry, the generic properties of the critical points of this potential can be studied. We find that the extremal value of the central charge provides the minimal value of the BPS mass and of the potential under the condition that the moduli space metric is positive at the critical point. This is a property of a regular special geometry. We also study the critical points in all N 2 supersymmetric theories. We relate these ideas to the Weinhold and Ruppeiner metrics introduced in the geometric approach to thermodynamics and used for the study of critical phenomena.     

On the Chaotic Behavior of a Third-Order Log-Domain Filter

Operation of log-domain filters revolves around the large-signal forward-active mode exponential current-voltage relationship of the bipolar junction transistor, which is used to map the input currents to the logarithmic domain, where the analog processing takes place, and to convert the filtered voltage waveforms back to the linear domain. Sometimes, the inherent internal nonlinearity of such circuits is the cause of unwanted externally-nonlinear effects. In this paper a differential third-order log-domain Chebyshev low-pass filter is designed by applying the method of operational simulation of doubly-terminated LC ladders. When the six grounded shunt capacitors of this filter are properly replaced with three half-sized floating capacitors, as is common practice in internally-linear fully-differential capacitively-loaded circuits, under particular conditions the resulting system exhibits limit-cycle oscillations, period-doubling bifurcations and chaotic behavior for zero-input. The presence of chaos is confirmed by extracting the spectrum of Lyapunov exponents of the system from the time series of the output voltage.