Subsidiary Maxima Research Articles

Benchmarking predictive methods for small-angle X-ray scattering from atomic coordinates of proteins using maximum likelihood consensus data.

Stimulated by informal conversations at the XVII International Small Angle Scattering (SAS) conference (Traverse City, 2017), an international team of experts undertook a round-robin exercise to produce a large dataset from proteins under standard solution conditions. These data were used to generate consensus SAS profiles for xylose isomerase, urate oxidase, xylanase, lysozyme and ribonuclease A. Here, we apply a new protocol using maximum likelihood with a larger number of the contributed datasets to generate improved consensus profiles. We investigate the fits of these profiles to predicted profiles from atomic coordinates that incorporate different models to account for the contribution to the scattering of water molecules of hydration surrounding proteins in solution. Programs using an implicit, shell-type hydration layer generally optimize fits to experimental data with the aid of two parameters that adjust the volume of the bulk solvent excluded by the protein and the contrast of the hydration layer. For these models, we found the error-weighted residual differences between the model and the experiment generally reflected the subsidiary maxima and minima in the consensus profiles that are determined by the size of the protein plus the hydration layer. By comparison, all-atom solute and solvent molecular dynamics (MD) simulations are without the benefit of adjustable parameters and, nonetheless, they yielded at least equally good fits with residual differences that are less reflective of the structure in the consensus profile. Further, where MD simulations accounted for the precise solvent composition of the experiment, specifically the inclusion of ions, the modelled radius of gyration values were significantly closer to the experiment. The power of adjustable parameters to mask real differences between a model and the structure present in solution is demonstrated by the results for the conformationally dynamic ribonuclease A and calculations with pseudo-experimental data. This study shows that, while methods invoking an implicit hydration layer have the unequivocal advantage of speed, care is needed to understand the influence of the adjustable parameters. All-atom solute and solvent MD simulations are slower but are less susceptible to false positives, and can account for thermal fluctuations in atomic positions, and more accurately represent the water molecules of hydration that contribute to the scattering profile.

Analytical solutions for irradiance of principal and subsidiary maxima in multiple-slit diffraction

This paper presents analytical solutions for the irradiance of principal and subsidiary maxima in multiple-slit diffraction with arbitrary slit numbers. By analytically solving the equation for the principal and subsidiary maxima, the irradiance of the principal and subsidiary maxima can be obtained up to the twelfth order in a/d, where a is the width of each slit and d is the separation between two adjacent slits.

Analytical Solutions for Irradiance of Principal and Subsidiary Maxima in Multiple Slit Diffraction

Analytical Solutions for Irradiance of Principal and Subsidiary Maxima in Multiple Slit Diffraction

Effects of the slit width on the subsidiary maxima in multiple-slit diffraction: Analytical solutions

We present analytical solutions for the subsidiary maxima in multiple-slit diffraction, considering a nonzero slit width. To find the angular position of the subsidiary and principal maxima, the intensity distribution function is differentiated with respect to the phase associated with the angular position. To solve the resulted transcendental equation analytically, the derivative and phase are expanded in the order of a∕d (a: slit width; d: slit separation), and a set of equations is established by setting each term of the derivative as zero. Solving the equations for the coefficients in the phase, we analytically obtain the phase for the subsidiary maxima as a function of the slit number and a∕d up to the twelfth order in a∕d.

Subsidiary Maxima in Multiple Slit Interference: Algebraic Equations

Subsidiary Maxima in Multiple Slit Interference: Algebraic Equations

Analytical solutions for the subsidiary maxima in multiple slit interference

We present analytical solutions for the subsidiary maxima in multiple slit interference up to eleven slits. For the number of slits N, there exist $$N-2$$ subsidiary maxima between the two adjacent principal maxima. By analytically solving the derivative of the diffracted intensity function with respect to the phase difference, the angular positions and amplitudes of the $$N-2$$ subsidiary maxima are expressed in succinct analytical forms for multiple slits with $$N \le 11$$.

Subsidiary and Principal Maxima in Multiple-Slit Interference

We present a theoretical study on the amplitudes and the linewidths of the subsidiary and principal maxima in multiple-slit interference patterns in the Fraunhofer regime. In the limit of a large slit number, we observe that the calculated amplitudes of the subsidiary maxima relative to the principal maximum are slightly different from the values presented in textbooks. We also present the calculation of the widths for the diffracted intensity patterns of the principal and the first several subsidiary maxima.

Ion-acoustic supersolitons and double layers in plasmas with nonthermal electrons

Supersoliton (SS) can be mainly featured in two ways, namely, by focusing on subsidiary maxima on its electric field or by meeting the requirement that the appropriate Sagdeev pseudopotential (SP) has three local extrema between the equilibrium conditions and its amplitude. In this paper, by using the SP method, double layers and ion-acoustic SSs are studied in a plasma with Maxwellian cold electrons, nonthermal hot electrons, and fluid ions. The existence of the SS regime in parameter space is obtained in a methodical fashion. The existence domains for positive solitary waves are also presented. It is found that there is no SSs at the acoustic speed.

Quantum reflection of bright solitary matter waves from a narrow attractive potential

We report the observation of quantum reflection from a narrow attractive potential using bright solitary matter waves formed from a $^{85}\mathrm{Rb}$ Bose-Einstein condensate. We create the attractive potential using a tightly focused, red-detuned laser beam, and observe reflection of up to 25% of the atoms, along with the confinement of atoms at the position of the beam. We show that the observed reflected fraction is much larger than theoretical predictions for a simple Gaussian potential well. A more detailed model of bright soliton propagation, accounting for the generic presence of small subsidiary intensity maxima in the red-detuned beam, suggests that these small intensity maxima are the cause of this enhanced reflection.

Ion-acoustic supersolitons in plasmas with two-temperature electrons: Boltzmann and kappa distributions

Acoustic supersolitons arise when a plasma model is able to support three consecutive local extrema of the Sagdeev pseudopotential between the undisturbed conditions and an accessible root. This leads to a characteristic electric field signature, where a simple bipolar shape is enriched by subsidiary maxima. Large-amplitude nonlinear acoustic modes are investigated, using a pseudopotential approach, for plasmas containing two-temperature electrons having Boltzmann or kappa distributions, in the presence of cold fluid ions. The existence domains for positive supersolitons are derived in a methodological way, both for structure velocities and amplitudes, in terms of plasma compositional parameters. In addition, typical pseudopotentials, soliton, and electric field profiles have been given to illustrate that positive supersolitons can be found in the whole range of electron distributions from Maxwellian to a very hard nonthermal spectrum in kappa. However, it is found that the parameter ranges that support supersolitons vary significantly over the wide range of kappa considered.

Molecular Modelling of the Conformational Flexibility and Elastic Behaviour of Short Poly(ethylene terephthalate) Chains

The Monte-Carlo (MC) rotational-isomeric-state (RIS) method developed previously to model the stress–strain behaviour of poly(ethylene terephthalate) (PET) is now applied to short PET chains of between 42 and 84 skeletal bonds. The effects on the radial and probability density distribution functions of the long, flexible virtual bond used to represent the terephthaloyl unit are investigated. The distribution functions generated, based on finite samples of chains, are found to be discontinuous with subsidiary maxima in their tails. The discontinuities lead to uncertainties in the simulated network elasticity properties and, in order to reduce the uncertainty, it is necessary to truncate the distributions at the values of r where they first become discontinuous. The stress–strain properties calculated from the truncated distributions are shown to be consistent with those presented previously for longer PET chains, for which discontinuities in the sampled functions are not apparent.

First observations of tidal oscillations by an MF radar over Kunming (25.6°N, 103.8°E)

One year's data of an MF (medium frequency) radar installed at Kunming (25.6°N, 103.8°E) station, China, are used to study the tidal structure over Kunming. The tidal parameters including amplitudes and phases are analyzed, which show a strong diurnal tide and weak semidiurnal tide for both zonal and meridional components. The maxima diurnal and semidiurnal amplitudes are approximately 40 and 20m/s, respectively. The diurnal phases and amplitudes show strong seasonal variability. Maximum amplitudes occur in March, and subsidiary maxima are attained in August and October, while the phase indicates an annual cycle. Semidiurnal amplitudes vary not so evidently. The vertical structures of the tidal parameters are compared with the Global Scale Wave Model (GSWM-09) values. The observed amplitudes of diurnal tide are smaller than the model values, but reversed for the semidiurnal tide. The observed phases of the diurnal tide show similar variations to GSWM-09 values. The agreement between the observed semidiurnal phase and model values is not so good.

Quantum critical metamagnetism of Sr3Ru2O7under hydrostatic pressure

Using ac susceptibility, we have determined the pressure dependence of the metamagnetic critical end point temperature T* for field applied in the ab-plane in the itinerant metamagnet Sr3Ru2O7. We find that T* falls monotonically to zero as pressure increases, producing a quantum critical end point (QCEP) at Pc~13.6 kbar. New features are observed near the QCEP -- the slope of T* vs pressure changes at ~12.8 kbar, and weak subsidiary maxima appear on either side of the main susceptibility peak at pressures near Pc -- indicating that some new physics comes into play near the QCEP. Clear signatures of a nematic phase, however, that were seen in field-angle tuning of T*, are not observed. As T* is suppressed by pressure, the metamagnetic peak in the susceptibility remains sharp as a function of applied magnetic field. As a function of temperature, however, the peak becomes broad with only a very weak maximum, suggesting that, near the QCEP, the uniform magnetization density is not the order parameter for the metamagnetic transition.

Design of a pulsed spatial neutron magnetic spin resonator

It is well known that upon passage through a spatially alternating transverse magnetic field, produced by a meander-shaped conducting foil, in its rest frame each neutron creates its individual frequency which depends on its velocity and the period of the meander. A resonant spin flip process takes place, if this frequency equals the Larmor frequency determined by a homogeneous vertical field. Clearly, this effect can be used to monochromatise a polarised neutron beam. Here we propose a novel design of such a magnetic resonator consisting of a sequence of separate compact modules, which provide high homogeneity of the transversal field oscillations and allow rapid beam chopping since they meet the specifications of fast electronic switching. The wavelength resolution of this resonator device can be changed in an instant and likewise an arbitrary amplitude modulation of the transversal field can be established, which is required for an efficient suppression of subsidiary maxima of the wavelength-dependent spin flip probability.

Quantitative Texture Analysis with the HIPPO TOF Diffractometer

One of the design goals of the neutron time-of-flight (TOF) diffractometer HIPPO (HIgh Pressure - Preferred Orientation) at LANSCE (Los Alamos Neutron Science Center) was efficient quantitative texture analysis. In this paper, the effects of the HIPPO detector geometry and layout on texture analysis, particularly the shape and dimensions of the detector panels, are investigated. An aluminum sample with a strong and asymmetric texture was used to determine the methodological limitations of various methods of quantitative texture analysis. Several algorithms for extracting the orientation distribution function (ODF) from the TOF-spectra are compared: discrete orientations at arbitrary positions, harmonic method in Rietveld codes (MAUD and GSAS) and discrete methods in MAUD. All methods provide a similar representation of the main texture component, but discrete methods have a fundamental advantage over harmonic methods in characterizing regions of the ODF with low orientation densities. For HIPPO data of the present sample, harmonic expansions beyond lmax= 12 introduce subsidiary maxima and minima, which are consistently identified as artifacts. The results of our analysis establishes HIPPO as an efficient instrument to quantitatively determine preferred orientations in relatively short measuring times, if the texture features are not exceedingly sharp (full-width at half-maximum (FWHM) in the ODF > 20-30°).

Use of a birefringent filter for tuning a synchronously pumped optical parametric oscillator

Design considerations are presented for birefringent filters suitable for use as tuning elements in synchronously pumped optical parametric oscillators. A particular design aspect that is important, since typical gains are rather high, is the adequate suppression of subsidiary transmission maxima, in order to maximize the tuning range. Results are presented on the performance of a picosecond synchronously pumped optical parametric oscillator based on periodically poled lithium niobate with an appropriately designed four-plate birefringent filter.

Selected experimental methods for determining droplet parameters from the intensity distribution of scattered light: A review

The present paper summarizes some experimental methods, which have been developed using the results of calculations based on the theory of Gustav Mie. As examples two regions of the scattered light are considered in more detail. The intensity distribution in the forward hemisphere for scattering angles 30 ≤ θ ≤ 60 shows maxima, which can be identified as regular fringes on a screen. The spacing between the fringes is a measure for the droplet size. In the intensity distribution of the backward hemisphere the region of the first rainbow can be found. In the rainbow region a main maximum, subsidiary maxima and a ripple structure can be identified. The angular position of the main maximum is a measure for the refractive index of the droplet. The angular distance between the subsidiary maxima and the angular distance between the ripples both are a function of droplet size. A comparison with other size measurement methods gives information about the sphericity of the droplet. An evaporating droplet shows for instance oscillations of the rainbow position due to morphology dependent resonances. The oscillation frequency is proportional to the evaporation rate.

Selected experimental methods for determining droplet parameters from the intensity distribution of scattered light: A review

AbstractThe present paper summarizes some experimental methods, which have been developed using the results of calculations based on the theory of Gustav Mie. As examples two regions of the scattered light are considered in more detail. The intensity distribution in the forward hemisphere for scattering angles 30 ≤ θ ≤ 60 shows maxima, which can be identified as regular fringes on a screen. The spacing between the fringes is a measure for the droplet size.In the intensity distribution of the backward hemisphere the region of the first rainbow can be found. In the rainbow region a main maximum, subsidiary maxima and a ripple structure can be identified. The angular position of the main maximum is a measure for the refractive index of the droplet. The angular distance between the subsidiary maxima and the angular distance between the ripples both are a function of droplet size. A comparison with other size measurement methods gives information about the sphericity of the droplet.An evaporating droplet shows for instance oscillations of the rainbow position due to morphology dependent resonances. The oscillation frequency is proportional to the evaporation rate.

ON THE CHARACTERIZATION OF METALLIC SUPERLATTICE STRUCTURES BY X-RAY DIFFRACTION

To solve the problem on the microstructural characterization of metallic superlattices, taking the NiFe/Cu superlattices as example, we show that the structures of metallic superlattices can be characterized exactly by combining low-angle X-ray diffraction with high-angle X-ray diffraction. First, we determine exactly the total film thickness by a straightforward and precise method based on a modified Bragg law from the subsidiary maxima around the low-angle X-ray diffraction peak. Then, by combining with the simulation of high-angle X-ray diffraction, we obtain the structural parameters such as the superlattice period, the sublayer and buffer thickness. This characterization procedure is also applicable to other types of metallic superlattices.

Tailoring long period optical fibre gratings for flattening EDFA gain spectra

Loss characteristics of long-period fibre gratings with constant pitch can be made to compensate for a variety of EDFA gain characteristics. Simply by incorporating blank regions within a fixed overall length of grating during its fabrication, the heights of subsidiary maxima and minima can be set at required values.