Sparse generalized Fourier transforms

Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences. By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via a sparse variant of a generalized Fourier transform (GFT) becomes particularly simple and fast. Characterizations for finite element triangulations of a symmetric domain are given, and formulas for assembling the block-diagonalized matrix directly are presented. It is emphasized that the GFT preserves symmetric (Hermitian) properties of an equivariant matrix. By simulating the heat equation at the surface of a sphere discretized by an icosahedral grid, it is demonstrated that the block-diagonalization is beneficial. The gain is significant for a direct method, and modest for an iterative method. A comparison with a block-diagonalization approach based upon the continuous formulation is made. It is found that the sparse GFT method is an appropriate way to discretize the resulting continuous subsystems, since the spectrum and the symmetry are preserved. AMS subject classification (2000)  43A30, 65T99, 20B25     

Narrow linewidth 2 μm optical parametric oscillation in periodically poled LiNbO<Subscript>3</Subscript> with volume Bragg grating outcoupler

An optical parametric oscillator using a periodically poled LiNbO₃ crystal and a volume Bragg grating output coupler is presented. Signal and idler wavelengths of 2008 and 2264 nm were generated from the 1064 nm Nd:YVO₄ pump laser. The Bragg grating was reflecting in a narrow band around 2008 nm, creating a purely singly resonant cavity. Signal and idler linewidths of approximately 0.44 and 0.72 nm, respectively, were measured. This is a reduction of 80 and 60 times compared to when using a mirror as output coupler. A total output energy of 156 μJ was measured with 47% slope efficiency. PACS 42.65.Yj; 42.72.Ai; 42.40.Eq     

The N1s ESCA Spectrum of Protonated 1,8-Bis-(Dimethylamino) Naphthalene (“proton sponge”)

The ESCA spectrum of protonated 1,8-bis-(dimethylamino) naphthalene (“proton sponge”) (I) has been recorded in the region of N1s binding energies. The results indicate that IH⁺ possesses an unsymmetrical N? H…?N hydrogen bridge.     

Optical tweezers applied to a microfluidic system

We will demonstrate how optical tweezers can be combined with a microfluidic system to create a versatile microlaboratory. Cells are moved between reservoirs filled with different media by means of optical tweezers. We show that the cells, on a timescale of a few seconds, can be moved from one reservoir to another without the media being dragged along with them. The system is demonstrated with an experiment where we expose E. coli bacteria to different fluorescent markers. We will also discuss how the system can be used as an advanced cell sorter. It can favorably be used to sort out a small fraction of cells from a large population, in particular when advanced microscopic techniques are required to distinguish various cells. Patterns of channels and reservoirs were generated in a computer and transferred to a mask using either a sophisticated electron beam technique or a standard laser printer. Lithographic methods were applied to create microchannels in rubber silicon (PDMS). Media were transported in the channels using electroosmotic flow. The optical system consisted of a combined confocal and epi-fluorescence microscope, dual optical tweezers and a laser scalpel.     

Lyotropic Liquid Crystal to Soft Mesocrystal Transformation in Hydrated Salt–Surfactant Mixtures

Hydrated CaCl₂, LiI, and MgCl₂ salts induce self‐assembly in nonionic surfactants (such as C₁₂H₂₅(OCH₂CH₂)₁₀OH) to form lyotropic liquid‐crystalline (LLC) mesophases that undergo a phase transition to a new type of soft mesocrystal (SMC) under ambient conditions. The SMC samples can be obtained by aging the LLC samples, which were prepared as thin films by spin‐coating, dip‐coating, or drop‐casting of a clear homogenized solution of water, salt, and surfactant over a substrate surface. The LLC mesophase exists up to a salt/surfactant mole ratio of 8, 10, and 4 (corresponding to 59, 68, and 40 wt % salt/surfactant) in the CaCl₂, LiI, and MgCl₂ mesophases, respectively. The SMC phase can transform back to a LLC mesophase at a higher relative humidity. The phase transformations have been monitored using powder X‐ray diffraction (PXRD), polarized optical microscopy (POM), and FTIR techniques. The LLC mesophases only diffract at small angles, but the SMCs diffract at both small and wide angles. The broad surfactant features in the FTIR spectra of the LLC mesophases become sharp and well resolved upon SMC formation. The unit cell of the mesophases expands upon SMC transformation, in which the expansion is largest in the MgCl₂ and smallest in the CaCl₂ systems. The POM images of the SMCs display birefringent textures with well‐defined edges, similar to crystals. However, the surface of the crystals is highly patterned, like buckling patterns, which indicates that these crystals are quite soft. This unusual phase behavior could be beneficial in designing new soft materials in the fields of phase‐changing materials and mesostructured materials, and it demonstrates the richness of the phase behavior in the salt–surfactant mesophases.     

Local Lead–Lag Relationships and Nonlinear Granger Causality: An Empirical Analysis

The Granger causality test is essential for detecting lead–lag relationships between time series. Traditionally, one uses a linear version of the test, essentially based on a linear time series regression, itself being based on autocorrelations and cross-correlations of the series. In the present paper, we employ a local Gaussian approach in an empirical investigation of lead–lag and causality relations. The study is carried out for monthly recorded financial indices for ten countries in Europe, North America, Asia and Australia. The local Gaussian approach makes it possible to examine lead–lag relations locally and separately in the tails and in the center of the return distributions of the series. It is shown that this results in a new and much more detailed picture of these relationships. Typically, the dependence is much stronger in the tails than in the center of the return distributions. It is shown that the ensuing nonlinear Granger causality tests may detect causality where traditional linear tests fail.     

Light charged particle emission and fission in238U+238U collisions at 1,740 MeV

Inclusive⁴He and⁴H energy spectra and heavy fragment coincidence correlations have been measured for reactions of 7.31 MeV/u²³⁸U with²³⁸U and^?197Au targets. The H/He production cross sections are in the range 15–26 mb, and their emission spectra are very similar for the two systems. The observed strong kinematic shifts with angle are reproduced in shape and magnitude by Monte Carlo simulations of particle evaporation from projectile-like and target-like fragments, indicating competition between charged particle emission and sequential fission. No evidence is found for high energy charged particle emission associated with ultra-highZ composite systems. Heavy fragment measurements indicate an abundance of quasielastic and deeply inelastic reaction fragments, as well as sequential fission of target and projectile nuclei. For²³⁸U nuclei, the fission occurs predominantly in an asymmetric mode, reminiscent of fission at low excitation energy. For²³⁸+²³⁸U reactions in the vicinity of the grazing angle, the frequency of single sequential fission (with survival of the partner fragment) is twice as large as double sequential fission in which both the target and projectile undergo fission. In²³⁸U+¹⁹⁷Au reactions, the survival probability of the heavy fragments is even greater. The surprisingly high survival probabilities of high-Z fragments imply a preponderance of very soft collisions in these very-heavy-ion reactions, at least at energies not very far over the Coulomb barrier.     

Taylor collocation method for the numerical solution of the nonlinear Schrödinger equation using quintic B-spline basis

In this study, we construct a Taylor collocation method for the numerical solution of the nonlinear Schrödinger (NLS) equation. We use suitable initial and boundary conditions. Taylor series expansion is used for time discretization. The cubic B-spline collocation method is applied to spatial discretization. Test problems concerning the single soliton motion, interaction of two colliding solitons, and the formation and bound states of solitons of the NLS equation are studied to evaluate the method. The L ₂ and L _∞ error norms are calculated to improve the accuracy of the numerical results.     

Universal scaling in transient creep

We present experimental evidence that pressure solution creep does not establish a steady-state interface microstructure as previously thought. Conversely, pressure solution controlled strain and the characteristic length scale of interface microstructures grow as the cubic root of time. Transient creep with the same scaling is known in metallurgy (Andrade creep). The apparent universal scaling of pressure solution transient creep is explained using an analogy with spinodal dewetting.