A hidden symmetry-broken phase of MoS 2 revealed as a superior photovoltaic material
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Meiling Xu↗
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Evolution of symmetry index in minerals
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Marko Bermanec↗
Variability and Hemispheric Symmetry of the Pedersen Conductance in the Jovian Aurora
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J.‐C. Gérard↗
Polarimetric Remote Sensing of Geophysical Medium Structures
Polarimetric remote sensing of structures in geophysical media is studied in this paper based on their symmetry properties. Orientations of spheroidal scatterers described by spherical, uniform, planophile, plagiothile, erectophile, and extremophile distributions are considered to derive their polarimetric backscattering characteristics. These distributions can be identified from the observed scattering coefficients by comparison with theoretical symmetry calculations. A new parameter is defined to study scattering structures in geophysical media. Experimental observations from polarimetric data acquired by the Jet Propulsion Laboratory airborne synthetic aperture radar over forests, sea ice, and sea surface are presented to illustrate the use of symmetry properties. For forests, the coniferous forest in Mount Shasta area and mixed forests neir Presque Isle show evidence of the centrical symmetry at C band. In sea ice from the Beaufort Sea, multiyear sea ice has a cross-polarized ratio e close to e(sub 0), calculated from symmetry, due to the randomness in the scattering structure. For first-year sea ice, e is much smaller than e(sub 0) as a result of preferential alignment of the columnar structure of the ice. From polarimetric data of a sea surface in the Bering sea, it is observed that e and e(sub 0) are increasing with incident angle and e is greater than e(sub 0) at L band because of the directional feature of sea surface waves. Use of symmetry properties of geophysical media for polarimetric radar calibration is also suggested.
Nghiem, S. V.↗
Miniature quadrupole mass spectrometer array
The present invention provides a minature quadrupole mass spectrometer array for the separation of ions, comprising a first pair of parallel, planar, nonmagnetic conducting rods each having an axis of symmetry, a second pair of planar, nonmagnetic conducting rods each having an axis of symmetry parallel to said first pair of rods and disposed such that a line perpendicular to each of said first axes of symmetry and a line perpendicular to each of said second axes of symmetry bisect each other and form a generally 90 degree angle. A nonconductive top positioning plate is positioned generally perpendicular to the first and second pairs of rods and has an aperture for ion entrance along an axis equidistant from each axis of symmetry of each of the parallel rods, a nonconductive bottom positioning plate is generally parallel to the top positioning plate and has an aperture for ion exit centered on an axis equidistant from each axis of symmetry of each of the parallel rods, means for maintaining a direct current voltage between the first and second pairs of rods, and means for applying a radio frequency voltage to the first and second pairs of rods.
Chutjian, Ara↗
Miniature quadrupole mass spectrometer array
The present invention provides a minature quadrupole mass spectrometer array for the separation of ions, comprising a first pair of parallel, planar, nonmagnetic conducting rods each having an axis of symmetry, a second pair of planar, nonmagnetic conducting rods each having an axis of symmetry parallel to said first pair of rods and disposed such that a line perpendicular to each of said first axes of symmetry and a line perpendicular to each of said second axes of symmetry bisect each other and form a generally 90 degree angle. A nonconductive top positioning plate is positioned generally perpendicular to the first and second pairs of rods and has an aperture for ion entrance along an axis equidistant from each axis of symmetry of each of the parallel rods, a nonconductive bottom positioning plate is generally parallel to the top positioning plate and has an aperture for ion exit centered on an axis equidistant from each axis of symmetry of each of the parallel rods, means for maintaining a direct current voltage between the first and second pairs of rods, and means for applying a radio frequency voltage to the first and second pairs of rods.
Chutjian, Ara↗
Nucleation and Growth According to Lysozyme
How does one take a molecule, strongly asymmetric in both shape and charge distribution, and assemble it into a crystal? We propose a model for the nucleation and crystal growth process for tetragonal lysozyme that may be very germane to other monomeric proteins. The first species formed is postulated to be a dimer. Through repeating associations involving the same intermolecular interactions this becomes the 4(sub 3) helix, that in turn serves as the basic unit for nucleation and crystal growth. High salt attenuates surface charges while promoting hydrophobic interactions. Symmetry facilitates helix self-association. Assembly stability is enhanced when a four helix structure is obtained, with each bound to two neighbors. Only two unique interactions are required. The first are those for helix formation, where the dominant interaction is the intermolecular bridging anion. The second is the anti-parallel side-by-side helix-helix interaction, guided by alternating pairs of symmetry related salt bridges along each side. At this stage all eight unique positions of the P4(sub 3)2(sub 1)2(sub 1) unit cell are filled. From the above, the process is one of a) attenuating the most strongly interacting groups, such that b) the molecules begin to self-associate in defined patterns, so that c) symmetry is obtained, which d) propagates as a growing crystal. Simple and conceptually obvious in hindsight, this tells much about what we are empirically doing when we crystallize macromolecules. By adjusting the solution parameters we are empirically balancing the intermolecular interactions, preferentially attenuating the dominant strong (for lysozyme the charged groups) while strengthening the lesser strong (hydrophobic) interactions. Lysozyme is atypical in the breadth of its crystallization conditions; many proteins only crystallize under narrowly defined conditions, pointing to the criticality of the empirical balancing process. Lack of a singularly defined association pathway leads to formation of multiple species, i.e., amorphous precipitation. Weak interactions, such as hydrogen bonds, are promiscuous, serving to strengthen rather than define specific interactions. Participation in an interaction sequesters that surface from subsequent interactions, and we expect the strongest bonds to form first. When two molecules self associate the resulting species will have an axis of symmetry. Subsequent interactions between two associated species having equivalent interactions will also have symmetry. Only a few unique sets of interactions are required to give any of the commonly found space groups for monomeric proteins. This model and what it suggests will be discussed.
Pusey, Marc L.↗
Axisymmetric Implementation for 3D-Based DSMC Codes
The primary objective in developing NASA s DSMC Analysis Code (DAC) was to provide a high fidelity modeling tool for 3D rarefied flows such as vacuum plume impingement and hypersonic re-entry flows [1]. The initial implementation has been expanded over time to offer other capabilities including a novel axisymmetric implementation. Because of the inherently 3D nature of DAC, this axisymmetric implementation uses a 3D Cartesian domain and 3D surfaces. Molecules are moved in all three dimensions but their movements are limited by physical walls to a small wedge centered on the plane of symmetry (Figure 1). Unfortunately, far from the axis of symmetry, the cell size in the direction perpendicular to the plane of symmetry (the Z-direction) may become large compared to the flow mean free path. This frequently results in inaccuracies in these regions of the domain. A new axisymmetric implementation is presented which aims to solve this issue by using Bird s approach for the molecular movement while preserving the 3D nature of the DAC software [2]. First, the computational domain is similar to that previously used such that a wedge must still be used to define the inflow surface and solid walls within the domain. As before molecules are created inside the inflow wedge triangles but they are now rotated back to the symmetry plane. During the move step, molecules are moved in 3D but instead of interacting with the wedge walls, the molecules are rotated back to the plane of symmetry at the end of the move step. This new implementation was tested for multiple flows over axisymmetric shapes, including a sphere, a cone, a double cone and a hollow cylinder. Comparisons to previous DSMC solutions and experiments, when available, are made.
Stewart, Benedicte↗
Predominance of two-armed spirals
A physical process accounts for the origin and widespread occurrence of two-armed spiral patterns with a high degree of symmetry extending from the nucleus to the outermost part of a galaxy. Self-gravitating systems, starting from a wide variety of initial conditions, settle down into twofold symmetries through a sequence of forms that were identified in numerical experiments. Twofold symmetries rarely develop directly. Instead, the systems pass through a sequence of more complicated shapes. The computer experiments and the sequence leading to twofold symmetries are described. At the end of this process, a two-armed spiral density wave with a 'grand design' has been set up in the galaxy, and the stage has been set for some mechanism, such as that of Lin and Shu (1971), to take over to assure a long lifetime for the pattern.
Miller, R. H.↗
On the photometric axis of the zodiacal light
A model of the zodiacal cloud is used to predict the position of the photometric axis (the locus of points of maximum brightness) of the zodiacal light at any elongation angle from the sun for any time of the year for various symmetry planes: the orbital planes of Venus, Mars, and Jupiter, the invariable plane, and the solar equatorial plane. Using a scattering function which combines isotropic scattering and Fresnel reflection, the geocentric distance of the dust that contributes most of the brightness at each elongation angle is determined by computing the brightness contribution along the line of sight. A comparison of the predicted and observed positions shows that at elongation angles of 15 to 60 deg, the axis of symmetry appears to be close to the orbital plane of Venus. At angles of less than 10 deg, it is difficult to distinguish among the proposed planes of symmetry. Observations of the photometric axis at angles of 60 to 180 deg are scarce and do not permit precise determination of the axis of symmetry in that region.
Misconi, N. Y.↗
Using NASTRAN to solve symmetric structures with nonsymmetric loads
A method for computation of reflective dihedral symmetry in symmetrical structures under nonsymmetric loads is described. The method makes it possible to confine the analysis to a half, a quarter, or an octagonal segment. The symmetry of elastic deformation is discussed, and antisymmetrical deformation is distinguished from nonsymmetrical deformation. Modes of deformation considered are axial, bending, membrane, and torsional deformation. Examples of one and two dimensional elements are presented and extended to three dimensional elements. The method of setting up a problem within NASTRAN is discussed. The technique is applied to a thick structure having quarter symmetry which was modeled with polyhedra and subjected to five distinct loads having varying degrees of symmetry.
Butler, T. G.↗
Asymptotic structure and similarity solutions for three-dimensional turbulent boundary layers
The asymptotic structure of the three-dimensional turbulent boundary layer is investigated in the limit of large Reynolds numbers. A self-consistent, but relatively complex, two-layer structure exists and the simplest situation, corresponding to a plane of symmetry, is considered in this paper as a first step. The adjustment of the streamwise velocity to relative rest, through an outer defect layer and then an inner wall layer, is similar to that in two-dimensional flow. The adjustment of the cross-streamwise velocity is more complicated and it is shown that two terms in the expansion are required to obtain useful results, and in particular to obtain the velocity skew angle at the wall near the symmetry plane. The conditions under which self-similarity is achieved near a plane of symmetry are investigated. A set of ordinary differential equations is developed which describe the streamwise and cross-streamwise velocities near a plane of symmetry in a self-similar flow through two orders of magnitude. Calculated numerical solutions of these equations yield trends which are consistent with experimental observations.
Degani, A. T.↗
On linear structure and phase rotation invariant properties of block 2(sup l)-PSK modulation codes
Two important structural properties of block 2(l)-ary PSK (phase shift keying) modulation codes, linear structure and phase symmetry, are investigated. For an additive white Gaussian noise (AWGN) channel, the error performance of a modulation code depends on its squared Euclidean distance distribution. Linear structure of a code makes the error performance analysis much easier. Phase symmetry of a code is important in resolving carrier phase ambiguity and ensuring rapid carrier phase resynchronization after temporary loss of synchronization. It is desirable for a code to have as many phase symmetries as possible. A 2(l)-ary modulation code is represented here as a code with symbols from the integer group. S sub 2(l) PSK = (0,1,2,...,2(l)-1), under the modulo-2(l) addition. The linear structure of block 2(l)-ary PSK modulation codes over S sub 2(l)-ary PSK with respect to the modulo-2(l) vector addition is defined, and conditions under which a block 2(l)-ary PSK modulation code is linear are derived. Once the linear structure is developed, phase symmetry of a block 2(l)-ary PSK modulation code is studied. It is a necessary and sufficient condition for a block 2(l)-PSK modulation code, which is linear as a binary code, to be invariant under 180 deg/2(l-h) phase rotation, for 1 is less than or equal to h is less than or equal to l. A list of short 8-PSK and 16-PSK modulation codes is given, together with their linear structure and the smallest phase rotation for which a code is invariant.
Lin, Shu↗
Axial focusing of impact energy in the Earth's interior: Proof-of-principle tests of a new hypothesis
A causal link between major impact events and global processes would probably require a significant change in the thermal state of the Earth's interior, presumably brought about by coupling of impact energy. One possible mechanism for such energy coupling from the surface to the deep interior would be through focusing due to axial symmetry. Antipodal focusing of surface and body waves from earthquakes is a well-known phenomenon which has previously been exploited by seismologists in studies of the Earth's deep interior. Antipodal focusing from impacts on the Moon, Mercury, and icy satellites has also been invoked by planetary scientists to explain unusual surface features opposite some of the large impact structures on these bodies. For example, 'disrupted' terrains have been observed antipodal to the Caloris impact basis on Mercury and Imbrium Basin on the Moon. Very recently there have been speculations that antipodal focusing of impact energy within the mantle may lead to flood basalt and hotspot activity, but there has not yet been an attempt at a rigorous model. A new hypothesis was proposed and preliminary proof-of-principle tests for the coupling of energy from major impacts to the mantle by axial focusing of seismic waves was performed. Because of the axial symmetry of the explosive source, the phases and amplitudes are dependent only on ray parameter (or takeoff angle) and are independent of azimuthal angle. For a symmetric and homogeneous Earth, all the seismic energy radiated by the impact at a given takeoff angle will be refocused (minus attenuation) on the axis of symmetry, regardless of the number of reflections and refractions it has experienced. Mantle material near the axis of symmetry will experience more strain cycles with much greater amplitude than elsewhere and will therefore experience more irreversible heating. The situation is very different than for a giant earthquake, which in addition to having less energy, has an asymmetric focal mechanism and a larger area. Two independent proof-of-principle approaches were used. The first makes use of seismic simulations, which are being performed with a realistic Earth model to determine the degree of focusing along the axis and to estimate the volume of material, if any, that experiences significant irreversible heating. The second involves two-dimensional hydrodynamic code simulations to determine the stress history, internal energy, and temperature rise as a function of radius along the axis.
Boslough, M. B.↗
Covariant harmonic oscillators and coupled harmonic oscillators
It is shown that the system of two coupled harmonic oscillators shares the basic symmetry properties with the covariant harmonic oscillator formalism which provides a concise description of the basic features of relativistic hadronic features observed in high-energy laboratories. It is shown also that the coupled oscillator system has the SL(4,r) symmetry in classical mechanics, while the present formulation of quantum mechanics can accommodate only the Sp(4,r) portion of the SL(4,r) symmetry. The possible role of the SL(4,r) symmetry in quantum mechanics is discussed.
Han, Daesoo↗
What is a Question?
A given question can be defined in terms of the set of statements or assertions that answer it. Application of the logic of inference to this set of assertions allows one to derive the logic of inquiry among questions. There are interesting symmetries between the logics of inference and inquiry; where probability describes the degree to which a premise implies an assertion, there exists an analogous quantity that describes the bearing or relevance that a question has on an outstanding issue. These have been extended to suggest that the logic of inquiry results in functional relationships analogous to, although more general than, those found in information theory. Employing lattice theory, I examine in greater detail the structure of the space of assertions and questions demonstrating that the symmetries between the logical relations in each of the spaces derive directly from the lattice structure. Furthermore, I show that while symmetries between the spaces exist, the two lattices are not isomorphic. The lattice of assertions is described by a Boolean lattice 2(sup N) whereas the lattice of real questions is shown to be a sublattice of the free distributive lattice FD(N) = 2(sup 2(sup N)). Thus there does not exist a one-to-one mapping of assertions to questions, there is no reflection symmetry between the two spaces, and questions in general do not possess unique complements. Last, with these lattice structures in mind, I discuss the relationship between probability, relevance and entropy.
Knuth, Kevin H.↗
Solution-Phase Processes of Macromolecular Crystallization
We have proposed, for the tetragonal form of chicken egg lysozyme, that solution phase assembly processes are needed to form the growth units for crystal nucleation and growth. The starting point for the self-association process is the monomeric protein, and the final crystallographic symmetry is defined by the initial dimerization interactions of the monomers and subsequent n-mers formed, which in turn are a function of the crystallization conditions. It has been suggested that multimeric proteins generally incorporate the underlying multimers symmetry into the final crystallographic symmetry. We posed the question of what happens to a protein that is known to grow as an n-mer when it is placed in solution conditions where it is monomeric. The trypsin-treated, or cut, form of the protein canavalin (CCAN) has been shown to nucleate and grow crystals as a trimer from neutral to slightly acidic solutions. Under these conditions the solution is composed almost wholly of trimers. The insoluble protein can be readily dissolved by weakly basic solution, which results in a solution that is monomeric. There are three possible outcomes to an attempt at crystallization of the protein under monomeric (high pH) conditions: 1) we will obtain the same crystals as under trimer conditions, but at different protein concentrations governed by the self association equilibria; 2) we will obtain crystals having a different symmetry, based upon a monomeric growth unit; 3) we will not obtain crystals. Obtaining the first result would be indicative that the solution-phase self-association process is critical to the crystal nucleation and growth process. The second result would be less clear, as it may also reflect a pH-dependent shift in the trimer-trimer molecular interactions. The third result, particularly for experiments in the transition pH's between trimeric and monomeric CCAN, would indicate that the monomer does not crystallize, and that solution phase self association is not part of the crystal nucleation and growth path. Results are presented for crystallization experiments of CCAN over the pH 6.8 to 9.6 range.
Pusey, Marc L.↗
Polarimetric Analysis of Scatterometer Data for Ocean Surface Wind Measurement
An experiment using a polarimetric scatterometer (POLSCAT) has been conducted by JPL for ocean surface wind measurement. It shows that (sigma) (subscript)0 values for HH, W, HV, and VH have the property of even symmetry with respect to the upwind direction, and correlation coefficients between co- and cross-polarizations have the odd symmetry property. In this paper, the symmetry properties will be further examined using polarimetric analysis to investigate the depolarization effect, the scattering mechanism, and the polarization orientation angle. Theoretical results based on a two scale model are used to verify the derived experiment results. The newly derived symmetry property has the potential to solve the 180(deg) ambiguity in wind direction, and to enhance the accuracy of wind vector measurements.
scatterometers↗