Creating Ioffe-Pritchard micro-traps from permanent magnetic film with in-plane magnetization

We present designs for Ioffe-Pritchard type magnetic traps using planar patterns of hard magnetic material. Two samples with different pattern designs were produced by spark erosion of 40 μm thick FePt foil. The pattern on the first sample yields calculated axial and radial trap frequencies of 51 Hz and 6.8 kHz, respectively. For the second sample the calculated frequencies are 34 Hz and 11 kHz. The structures were used successfully as a magneto-optical trap for ⁸⁷Rb and loaded as a magnetic trap. A third design, based on lithographically patterned 250 nm thick FePt film on a Si substrate, yields an array of 19 traps with calculated axial and radial trap frequencies of 1.5 kHz and 110 kHz, respectively.     

Quantum simulation of the Klein paradox with trapped ions

We report on quantum simulations of relativistic scattering dynamics using trapped ions. The simulated state of a scattering particle is encoded in both the electronic and vibrational state of an ion, representing the discrete and continuous components of relativistic wave functions. Multiple laser fields and an auxiliary ion simulate the dynamics generated by the Dirac equation in the presence of a scattering potential. Measurement and reconstruction of the particle wave packet enables a frame-by-frame visualization of the scattering processes. By precisely engineering a range of external potentials we are able to simulate text book relativistic scattering experiments and study Klein tunneling in an analogue quantum simulator. We describe extensions to solve problems that are beyond current classical computing capabilities.     

Quantum simulation of quantum field theories in trapped ions

We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.     

Direct Minimization of the least-squares spectral element functional – Part I: Direct solver

This paper describes an equivalent but improved least-squares formulation for the numerical approximation of the solution of partial differential equations. Instead of using variational analysis to impose the conditions for minimizing the residual, the residuals are minimized directly, thus leading to a method we will denote by Direct Minimization (DM). DM circumvents setting up the normal equations which consists of matrix–matrix multiplications. Matrix–matrix multiplications are expensive, may lead to loss of accuracy and destroy the sparsity pattern present in the original system. The condition number of the DM formulation is the square root of the condition number which would be obtained if variational analysis was employed. An element-by-element procedure will be presented which allows for parallelization of DM. A computational comparison between DM and the conventional least-squares formulation based on variational analysis will be presented.     

The use of Chebyshev Polynomials in the space-time least-squares spectral element method

Chebyshev polynomials of the first kind are employed in a space-time least-squares spectral element formulation applied to linear and nonlinear hyperbolic scalar equations. No stabilization techniques are required to render a stable, high order accurate scheme. In parts of the domain where the underlying exact solution is smooth, the scheme exhibits exponential convergence with polynomial enrichment, whereas in parts of the domain where the underlying exact solution contains discontinuities the solution displays a Gibbs-like behavior. An edge detection method is employed to determine the position of the discontinuity. Piecewise reconstruction of the numerical solution retrieves a monotone solution. Numerical results will be given in which the capabilities of the space-time formulation to capture discontinuities will be demonstrated.     

PHOTODECOMPOSITION OF CATECHOLAMINES. PHOTOPRODUCTS, QUANTUM YIELDS AND ACTION SPECTRUM OF ADRENALINE

The photochemical decomposition of several catecholamines in aqueous solution was investigated. The respective aminochromes were found to be products of adrenaline and isoprenaline. Irradiation of adrenochrome and N-isopropylnoradrenochrome produced their respective 5, 6-dihydroxyindoles in addition to the ultimate formation of melanine. No trihydroxyindoles could be detected amongst the photoproducts of catecholamines. The action spectrum of adrenaline suggested that the catecholamine itself, in excited state, initiated the first step in the transformation process. The quantum yields for the decomposition were determined for several catecholamines: N-alkyl compounds. decompose more rapidly under influence of light (λ 254 nm) than those with an unsubstituted amino group. In determining the quantum yields the use of corrections for the inner filter effect could be avoided.     

Least-squares spectral element method for non-linear hyperbolic differential equations

The least-squares spectral element method has been applied to the one-dimensional inviscid Burgers equation which allows for discontinuous solutions. In order to achieve high order accuracy both in space and in time a space–time formulation has been applied. The Burgers equation has been discretized in three different ways: a non-conservative formulation, a conservative system with two variables and two equations: one first order linear PDE and one linearized algebraic equation, and finally a variant on this conservative formulation applied to a direct minimization with a QR-decomposition at elemental level. For all three formulations an h/p-convergence study has been performed and the results are discussed in this paper.     

Magnetic-field-induced motion of disclinations in a twisted nematic layer

In a twisted nematic layer oppositely twisted regions can exist, separated by a disclination line, as demonstrated by the orientation of Williams domains. The disclination line can move under the influence of a magnetic field. Measurements of the velocity as a function of magnetic field strength and sample thickness lead to an estimate of the size of the disclination core.     

Instabilities in electric fields of nematic liquid crytals with positive dielectric anisotropy: domains,loop domains and reorientation

Instabilities in electric fields are reported for p,p′-di-n-butyl azoxybenzene (DIBAB), a new room temperature nematic with a positive dielectric anisotropy. The threshold voltage is found to be almost independent of the frequency up to 100 kHz. However, unlike in nematics with negative dielectric anisotropy usually no normal domains are observed. The instabilities take the form of a reorientation, while loop domains are observed as a transiet effect. These loop domains indicate that the instability is not purely dielectric in origin.