Box Geometry Research Articles

Inherently phase-stable coherent two-dimensional spectroscopy using only conventional optics

We introduce an inherently phase-stable setup for coherent two-dimensional femtosecond spectroscopy in noncollinear box geometry using only conventional beam splitters, mirrors, and delay stages. Avoiding diffractive optics, pulse shapers, and active phase-locking loops, our spectroscopy setup is simple, robust, and works for ultrabroad bandwidths in all spectral regimes (infrared, visible, and ultraviolet).

Implementation of an LED backlight for avionics displays

Abstract— The replacement of conventional light sources used to backlight displays with LEDs is very attractive in avionics. Today's LED technology provides devices suitable to implement display backlight sources but specific requirements need to be satisfied for avionics displays. This paper covers the development of an innovative LED backlight dedicated to avionics displays, realized in a new box geometry in order to generate more than 10,000 cd/m2 on a 6 × 5‐in. active area using less than 28 W of power.

Effects of system geometry and other physical factors on photon sensitivity of high-resolution positron emission tomography

We are studying two new detector technologies that directly measure the three-dimensional coordinates of 511 keV photon interactions for high-resolution positron emission tomography (PET) systems designed for small animal and breast imaging. These detectors are based on (1) lutetium oxyorthosilicate (LSO) scintillation crystal arrays coupled to position-sensitive avalanche photodiodes (PSAPD) and (2) cadmium zinc telluride (CZT). The detectors have excellent measured 511 keV photon energy resolutions (⩽12% FWHM for LSO-PSAPD and ⩽3% for CZT) and good coincidence time resolutions (2 ns FWHM for LSO-PSAPD and 8 ns for CZT). The goal is to incorporate the detectors into systems that will achieve 1 mm3 spatial resolution (∼1 mm3, uniform throughout the field of view (FOV)), with excellent contrast resolution as well. In order to realize 1 mm3 spatial resolution with high signal-to-noise ratio (SNR), it is necessary to significantly boost coincidence photon detection efficiency (referred to as photon sensitivity). To facilitate high photon sensitivity in the proposed PET system designs, the detector arrays are oriented ‘edge-on’ with respect to incoming 511 keV annihilation photons and arranged to form a compact FOV with detectors very close to, or in contact with, the subject tissues. In this paper, we used Monte Carlo simulation to study various factors that limit the photon sensitivity of a high-resolution PET system dedicated to small animal imaging. To optimize the photon sensitivity, we studied several possible system geometries for a fixed 8 cm transaxial and 8 cm axial FOV. We found that using rectangular-shaped detectors arranged into a cylindrical geometry does not yield the best photon sensitivity. This is due to the fact that forming rectangular-shaped detectors into a ring produces significant wedge-shaped inter-module gaps, through which Compton-scattered photons in the detector can escape. This effect limits the center point source photon sensitivity to <6% for a cylindrical system with rectangular-shaped blocks, 8 cm diameter and 8 cm axial FOV, and a 350–650 keV energy window setting. On the other hand, if the proposed rectangular-shaped detectors are arranged into an 8 × 8 × 8 cm3 FOV box configuration (four detector panels), there are only four inter-module gaps and the favorable distribution of these gaps yields >8% photon sensitivity for the LSO-PSAPD box configuration and >15% for CZT box geometry, using a 350–650 keV energy window setting. These simulation results compare well with analytical estimations. The trend is different for a clinical whole-body PET system that uses conventional LSO-PMT block detectors with larger crystal elements. Simulations predict roughly the same sensitivity for both box and cylindrical detector configurations. This results from the fact that a large system diameter (>80 cm) results in relatively small inter-module gaps in clinical whole-body PET. In addition, the relatively large block detectors (typically >5 × 5 cm2 cross-sectional area) and large crystals (>4 × 4 × 20 mm3) enable a higher fraction of detector scatter photons to be absorbed compared to a small animal system. However, if the four detector sides (panels) of a box-shaped system geometry are configured to move with respect to each other, to better fit the transaxial FOV to the actual size of the object to be imaged, a significant increase in photon sensitivity is possible. Simulation results predict a 60–100% relative increase of photon sensitivity for the proposed small animal PET box configurations and >60% increase for a clinical whole-body system geometry. Thus, simulation results indicate that for a PET system built from rectangular-shaped detector modules, arranging them into a box-shaped system geometry may help us to significantly boost photon sensitivity for both small animal and clinical PET systems.

Energy Absorption Behaviour of Austenitic and Duplex Stainless Steels in a Crash Box Geometry

The improvement of the passive safety plays an important role in the development of new steels for automotive parts. At the same time aspects of weight reduction as well as the industrial feasibility have to be considered. Powered by these objectives, the development and application of new steel concepts for various purposes is promoted. For the present investigation especially weight reduction combined with an improvement of the passive safety are emphasised. As example one representative part of the body structure, the crash box, is considered. At the moment different steel grades (dual phase‐, TRIP‐and HSLA‐steels) as well as fibre reinforced materials are applied. New materials for this special purpose have to exhibit outstanding formability, a high capacity to absorb energy during a possible crash and should be cost effective compared to already existing material concepts. During this project different grades of austenitic stainless steels with varying stability were compared to duplex stainless steels and a TRIP grade with regard to their possible application as crash‐box material. The austenitic grades show excellent gradual formability according to their strength level. All of them exhibit an extraordinary strain hardening behaviour. The duplex grades show a lower formability but on a much higher yield level.Besides the determination of classical material data such as uni‐ and multi‐axial flow curves, dynamic tensile tests and forming tests for the determination of forming limit curves were performed. The material data were used in the simulation of a drop tower test which is commonly used to evaluate the performance of different materials in car components. The results were then evaluated with regard to the absorbed energy, the folding behaviour and the resulting forces.

Quasi-periodic Oscillations from Magnetorotational Turbulence

Quasi-periodic oscillations (QPOs) in the X-ray lightcurves of accreting neutron star and black hole binaries have been widely interpreted as being due to standing wave modes in accretion disks. These disks are thought to be highly turbulent due to the magnetorotational instability (MRI). We study wave excitation by MRI turbulence in the shearing box geometry. We demonstrate that axisymmetric sound waves and radial epicyclic motions driven by MRI turbulence give rise to narrow, distinct peaks in the temporal power spectrum. Inertial waves, on the other hand, do not give rise to distinct peaks which rise significantly above the continuum noise spectrum set by MRI turbulence, even when the fluid motions are projected onto the eigenfunctions of the modes. This is a serious problem for QPO models based on inertial waves.

Methods to Accelerate Ray Tracing in the Monte Carlo Method for Surface-to-Surface Radiation Transport

Two different algorithms to accelerate ray tracing in surface-to-surface radiation Monte Carlo calculations are investigated. The first algorithm is the well-known binary spatial partitioning (BSP) algorithm, which recursively bisects the computational domain into a set of hierarchically linked boxes that are then made use of to narrow down the number of ray-surface intersection calculations. The second algorithm is the volume-by-volume advancement (VVA) algorithm. This algorithm is new and employs the volumetric mesh to advance the ray through the computational domain until a legitimate intersection point is found. The algorithms are tested for two classical problems, namely an open box, and a box in a box, in both two-dimensional (2D) and three-dimensional (3D) geometries with various mesh sizes. Both algorithms are found to result in orders of magnitude gains in computational efficiency over direct calculations that do not employ any acceleration strategy. For three-dimensional geometries, the VVA algorithm is found to be clearly superior to BSP, particularly for cases with obstructions within the computational domain. For two-dimensional geometries, the VVA algorithm is found to be superior to the BSP algorithm only when obstructions are present and are densely packed.

Magnetic Pressure Support and Accretion Disk Spectra

Stellar atmosphere models of ionized accretion disks have generally neglected the contribution of magnetic fields to the vertical hydrostatic support, although magnetic fields are widely believed to play a critical role in the transport of angular momentum. Simulations of magnetorotational turbulence in a vertically stratified shearing box geometry show that magnetic pressure support can be dominant in the upper layers of the disk. We present calculations of accretion disk spectra that incorporate vertical magnetic pressure and dissipation profiles derived from the radiation magnetohydrodynamical simulation of Hirose, Krolik, & Stone. Magnetic pressure support generically produces a more vertically extended disk atmosphere with a larger density scale height. This acts to harden the spectrum compared to models that neglect magnetic pressure support. We estimate the significance of this effect on disk-integrated spectra by calculating an illustrative disk model for a stellar mass black hole, assuming that similar magnetic pressure support exists at all radii.

Piezoelectric coefficients by molecular dynamics simulations in the constant stress ensemble: A case study of quartz

Piezoelectric (strain) coefficients d i j of quartz are calculated in terms of molecular dynamics as a function of pressure and temperature. We review the necessary formulas for the computation of electromechanical materials coefficients obtained at constant stress and temperature, and discuss how to overcome complications of the definition of polarization variations due to fluctuating box geometries. A method is employed suppressing significantly stochastic fluctuations of the estimators for piezoelectric coefficients. A recently suggested force field for the simulation of SiO 2 reproduces available experimental data quite accurately. Predictions are made for the pressure dependence of d i j of quartz.

Oscillatory surface tension due to finite-size effects

The simulation results of surface tension at the liquid-vapor interface are presented for fluids interacting with Lennard Jones and square-well potentials. From the simulation of liquids we have reported [M. González-Melchor et al., J. Chem. Phys. 122, 4503 (2005)] that the components of pressure tensor in parallelepiped boxes are not the same when periodic boundary conditions and small transversal areas are used. This fact creates an artificial oscillatory stress anisotropy in the system with even negative values. By doing direct simulations of interfaces we show in this work that surface tension has also an oscillatory decay at small surface areas; this behavior is opposite to the monotonic decay reported previously for the Lennard Jones fluid. It is shown that for small surface areas, the surface tension of the square-well potential artificially takes negative values and even increases with temperature. The calculated surface tension using a direct simulation of interfaces might have two contributions: one from finite-size effects of interfacial areas due to box geometry and another from the interface. Thus, it is difficult to evaluate the true surface tension of an interface when small surface areas are used. Care has to be taken to use the direct simulation method of interfaces to evaluate the predicted surface tension as a function of interfacial area from capillary-wave theory. The oscillations of surface tension decay faster at temperatures close to the critical point. It is also discussed that a surface area does not show any important effect on coexisting densities, making this method reliable to calculate bulk coexisting properties using small systems.

Fabrication and Characterization of Superconducting Circuit QED Devices for Quantum Computation

We present fabrication and characterization procedures of devices for circuit quantum electrodynamics (cQED). We have made 3 GHz cavities with quality factors in the range 10^4--10^6, which allow access to the strong coupling regime of cQED. The cavities are transmission line resonators made by photolithography. They are coupled to the input and output ports via gap capacitors. An Al-based Cooper pair box is made by ebeam lithography and Dolan bridge double-angle evaporation in superconducting resonators with high quality factor. An important issue is to characterize the quality factor of the resonators. We present an RF-characterization of superconducting resonators as a function of temperature and magnetic field. We have realized different versions of the system with different box-cavity couplings by using different dielectrics and by changing the box geometry. Moreover, the cQED approach can be used as a diagnostic tool of qubit internal losses.

Stress anisotropy induced by periodic boundary conditions

Finite size effects due to periodic boundary conditions are investigated using computer simulations in the canonical ensemble. We study liquids with densities corresponding to typical liquid coexistence densities, and temperatures between the triple and critical points. The components of the pressure tensor are computed in order to analyze the finite size effects arising from the size and geometry of the simulation box. Two different box geometries are considered: cubic and parallelepiped. As expected the pressure tensor is isotropic in cubic boxes, but it becomes anisotropic for small noncubic boxes. We argue this is the origin of the anomalous behavior observed recently in the computation of the surface tension of liquid-vapor interfaces. Otherwise, we find that the bulk pressure is sensitive to the box geometry when small simulation boxes are considered. These observations are general and independent of the model liquid considered. We report results for liquids interacting through short range forces, square well and Lennard-Jones, and also long range Coulombic interactions. The effect that small surface areas have on the surface tension is discussed, and some preliminary results at the liquid vapor-interface for the square well potential are given.

Multiphase modelling of core shooting process

A multiphase model was applied to simulate a core shooting process numerically. At the beginning of the research programme, simulations of the core shooting process with simple core box geometry (e.g. cylindrical core box) were carried out to examine the general applicability of the model used. In the next stage, simulations of core box geometry with complex flow behaviour of the sand–air motion were carried out to test the possibility of application of the model to industrial core box geometries. All the simulations were done in two and three dimensions. Experiments were carried out to validate the simulation results. Good agreement between simulation and experimental results indicates that the implemented multiphase model is suitable for modelling the core shooting process. Finally, the results of the simulation of core shooting of industrial core (wheel hub) are presented.

On finite-size effects in the simulation of high pressure, quartz-like structures

The stability of two recently suggested crystalline structures arising from compressing quartz is investigated. One phase, called quartz II, is obtained by compressing a model of quartz to pressure P slightly above 22 GPa. The second phase is obtained by shock compressing the quartz II sample to P = 50 GPa. The new structure is a modulated structure of quartz II and the corresponding phase is called quartz IIm. We observe strong size effects or compatibility effects above 26 GPa. If the initial system consists of 360 or 720 SiO2 units, an ‘ideal’ quartz II structure remains stable up to 30 GPa, whereas a larger system of 864 SiO2 units shows modulations of the quartz II structure when compressed above 28 GPa. On decompression from the 50 GPa sample, the larger system appears to be more stable than the smaller system, for which the incompatibility of the intrinsic modulation with the box geometry apparently leads to large fluctuations of the cell geometry.

Phase-stabilized two-dimensional electronic spectroscopy.

Two-dimensional (2D) spectroscopy is a powerful technique to study nuclear and electronic correlations between different transitions or initial and final states. Here we describe in detail our development of inherently phase-stabilized 2D Fourier-transform spectroscopy for electronic transitions. A diffractive-optic setup is used to realize heterodyne-detected femtosecond four-wave mixing in a phase-matched box geometry. Wavelength tunability in the visible range is accomplished by means of a 3 kHz repetition-rate laser system and optical parametric amplification. Nonlinear signals are fully characterized by spectral interferometry. Starting from fundamental principles, we discuss the origin of phase stability and the precise calibration of excitation-pulse time delays using movable glass wedges. Automated subtraction of undesired scattering terms removes experimental artifacts. On the theoretical side, the response-function formalism is extended to describe molecules with three electronic levels, and the shape of 2D spectral features is discussed. As an example for this technique, experimental 2D spectra are shown for the dye molecule Nile Blue in acetonitrile at 595 nm, recorded for a series of population times. Simulations explore the influence of different model parameters and qualitatively reproduce the experimental results. We show that correlations between different electronically excited states can be determined from the spectra. The technique described here can be used to measure the third-order response function of complex systems covering several electronic transitions.

Tunable two-dimensional femtosecond spectroscopy.

We have developed a two-dimensional (2D) Fourier-transform femtosecond spectroscopy technique for the visible spectral region. Three-pulse photon echo signals are generated in a phase-matched noncollinear four-wave mixing box geometry that employs a 3-kHz repetition-rate laser system and optical parametric amplification. Nonlinear signals are fully characterized in amplitude and phase by spectral interferometry. Unlike for previous setups, we achieve long-term phase stability by employing diffractive optics and interferometric accuracy of excitation-pulse time delays by using movable glass wedges. As an example of this technique, 2D correlation and relaxation spectra at 600 nm are shown for a solution of Nile Blue dye in acetonitrile.

Andreev bound states for a superconducting-ferromagnetic box

Within the microscopic Bogoliubov--de Gennes (BdG) formalism an exact quantization condition for Andreev bound states of the ferromagnetic-superconducting hybrid systems of box geometry is derived and a semi-classical formula for the density of states is obtained. The semi-classical formula is shown to agree with the exact result, even when the exchange field $h$, is much larger than the superconductor order parameter, provided $h$ is small compared with the Fermi energy.

Boundary condition effects in the simulation study of equilibrium properties of magnetic dipolar fluids

In this paper we investigate the equilibrium properties of magnetic dipolar (ferro-) fluids and discuss finite-size effects originating from the use of different boundary conditions in computer simulations. Both periodic boundary conditions and a finite spherical box are studied. We demonstrate that periodic boundary conditions and subsequent use of Ewald sum to account for the long-range dipolar interactions lead to a much faster convergence (in terms of the number of investigated dipolar particles) of the magnetization curve and the initial susceptibility to their thermodynamic limits. Another unwanted effect of the simulations in a finite spherical box geometry is a considerable sensitivity to the container size. We further investigate the influence of the surface term in the Ewald sum—that is, due to the surrounding continuum with magnetic permeability μBC—on the convergence properties of our observables and on the final results. The two different ways of evaluating the initial susceptibility, i.e., (1) by the magnetization response of the system to an applied field and (2) by the zero-field fluctuation of the mean-square dipole moment of the system, are compared in terms of speed and accuracy.

Scaling and nonscaling finite-size effects in the Gaussian and the mean spherical model with free boundary conditions.

We calculate finite-size effects of the Gaussian model in a Lx(d-1) box geometry with free boundary conditions in one direction and periodic boundary conditions in d-1 directions for 2<d<4. We also consider film geometry (L--> infinity ). Finite-size scaling is found to be valid for d<3 and d>3 but logarithmic deviations from finite-size scaling are found for the free energy and energy density at the Gaussian upper borderline dimension d*=3. The logarithms are related to the vanishing critical exponent 1-alpha-nu=(d-3)/2 of the Gaussian surface energy density. The latter has a cusplike singularity in d>3 dimensions. We show that these properties are the origin of nonscaling finite-size effects in the mean spherical model with free boundary conditions in d > or =3 dimensions. At bulk T(c), in d=3 dimensions we find an unexpected nonlogarithmic violation of finite-size scaling for the susceptibility chi approximately L3 of the mean spherical model in film geometry, whereas only a logarithmic deviation chi approximately L2 ln L exists for box geometry. The result for film geometry is explained by the existence of the lower borderline dimension d(l)=3, as implied by the Mermin-Wagner theorem, that coincides with the Gaussian upper borderline dimension d*=3. For 3<d<4 we find a power-law violation of scaling chi approximately L(d-1) at bulk T(c) for box geometry and a nonscaling temperature dependence chi(surface) approximately xi(d) of the surface susceptibility above T(c). For 2<d<3 dimensions we show the validity of universal finite-size scaling for the susceptibility of the mean spherical model with free boundary conditions for both box and film geometry and calculate the corresponding universal scaling functions for T > or =T(c).

Discrete Bose‐Einstein systems in a box with low adiabatic invariant

AbstractThe Bose‐Einstein energy spectrum of an ideal quantum gas confined in a box is discrete and strongly dependent on the box geometry and temperature, for low product of the atomic mass number, Aat and the adiabatic invariant, TV2/3, i.e. on γ = Aat TV2/3. Even within the approximation of non‐interacting particles in the gas, the calculation of the thermodynamic properties of Bose‐Einstein systems turns out to be a difficult mathematical problem. The present study compares the total number of particles, the total energy and the specific heat obtained by sums over the discrete states to the results of the approximate integrals (for defined values of γ) and shows the noticeable errors of the last ones at low adiabatic invariant (around condensation). Then, more rigorous and precise analytical approximations of sums are found in the case of finite number of atoms (correlated with the existence of a zero energy level) and the finite volume of the gas. The corrected thermodynamic functions depend on γ (for fixed fugacity). The condensation temperature is corrected also in order to describe more accurately the discrete Bose‐Einstein systems. Under these circumstances, the analysis of the specific heat leads to the conclusion that it shows no discontinuity, for the entire range of γ values.

Excitation spectra for Andreev billiards of box and disk geometries

We study Andreev billiards of box and disk geometries by matching the wave functions at the interface of the normal and the superconducting region using the exact solutions of the Bogoliubov-de Gennes equation. The mismatch in the Fermi wavenumbers and the effective masses of the normal system and the superconductor, as well as the tunnel barrier at the interface are taken into account. A Weyl formula (for the smooth part of the counting function of the energy levels) is derived. The exact quantum mechanical calculations show equally spaced singularities in the density of states. Based on the Bohr-Sommerfeld quantization rule a semiclassical theory is proposed to understand these singularities. For disk geometries two kinds of states can be distinguished: states either contribute through whispering gallery modes or are Andreev states strongly coupled to the superconductor. Controlled by two relevant material parameters, three kinds of energy spectra exist in disk geometry. The first is dominated by Andreev reflections, the second, by normal reflections in an annular disk geometry. In the third case the coherence length is much larger than the radius of the superconducting region, and the spectrum is identical to that of a full disk geometry.