Symmetry relation in relaxation dispersions.
Symmetry relation between dispersion function of frequency variable and distribution function of relaxation time variable
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Order-of-scattering of partially polarized radiation in inhomogeneous, anisotropically scattering atmospheres. II - Reciprocity and symmetry relations
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Fymat, A. L.↗
Symmetry in polarimetric remote sensing
Relationships among polarimetric backscattering coefficients are derived from the viewpoint of symmetry groups. For both reciprocal and non-reciprocal media, symmetry encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered. The derived properties are general and valid to all scattering mechanisms, including volume and surface scatterings and their interactions, in a given symmetrical configuration. The scattering coefficients calculated from theoretical models for layer random media and rough surfaces are shown to obey the symmetry relations. Use of symmetry properties in remote sensing of structural and environmental responses of scattering media is also discussed. 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 then defined to study scattering structures in geophysical media. Observations from polarimetric data acquired by the Jet Propulsion Laboratory airborne synthetic aperture radar over forests, sea ice, and sea surface are presented. Experimental evidences of the symmetry relationships are shown and their use in polarimetric remote sensing is illustrated. For forests, the coniferous forest in Mt. Shasta area (California) and mixed forest near Presque Isle (Maine) exhibit characteristics of the centrical symmetry at C-band. For sea ice in the Beaufort Sea, multi-year sea ice has a cross-polarized ratio e close to e(sub 0), calculated from symmetry, due to the randomness in the scattering structure. First-year sea ice has e much smaller than e(sub 0) due to the 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. Symmetry properties of geophysical media can also be used to calibrate polarimetric radars.
Nghiem, S. V.↗
Radiative transfer in a sphere illuminated by a parallel beam - An integral equation approach
The problem of multiple scattering of nonpolarized light in a planetary body of arbitrary shape illuminated by a parallel beam is formulated using the integral equation approach. There exists a simple functional whose stationarity condition is equivalent to solving the equation of radiative transfer and whose value at the stationary point is proportional to the differential cross section. The analysis reveals a direct relation between the microscopic symmetry of the phase function for each scattering event and the macroscopic symmetry of the differential cross section for the entire planetary body, and the interconnection of these symmetry relations and the variational principle. The case of a homogeneous sphere containing isotropic scatterers is investigated in detail. It is shown that the solution can be expanded in a multipole series such that the general spherical problem is reduced to solving a set of decoupled integral equations in one dimension. Computations have been performed for a range of parameters of interest, and illustrative examples of applications to planetary problems as provided.
Shia, R.-L.↗
Three-dimensional structure of Schistosoma japonicum glutathione S-transferase fused with a six-amino acid conserved neutralizing epitope of gp41 from HIV
The 3-dimensional crystal structure of glutathione S-transferase (GST) of Schistosoma japonicum (Sj) fused with a conserved neutralizing epitope on gp41 (glycoprotein, 41 kDa) of human immunodeficiency virus type 1 (HIV-1) was determined at 2.5 A resolution. The structure of the 3-3 isozyme rat GST of the mu gene class was used as a molecular replacement model. The structure consists of a 4-stranded beta-sheet and 3 alpha-helices in domain 1 and 5 alpha-helices in domain 2. The space group of the Sj GST crystal is P4(sub 3)2(sub 1)2 with unit cell dimensions of a = b = 94.7 A, and c = 58.1 A. The crystal has 1 GST monomer per asymmetric unit, and 2 monomers that form an active dimer are related by crystallographic 2-fold symmetry. In the binding site, the ordered structure of reduced glutathione is observed. The gp41 peptide (Glu-Leu-Asp-Lys-Trp-Ala) fused to the C-terminus of Sj GST forms a loop stabilized by symmetry-related GSTs. The Sj GST structure is compared with previously determined GST structures of mammalian gene classes mu, alpha, and pi. Conserved amino acid residues among the 4 GSTs that are important for hydrophobic and hydrophilic interactions for dimer association and glutathione binding are discussed.
Lim, Kap↗
Three-dimensional structure of Schistosoma japonicum glutathione S-transferase fused with a six-amino acid conserved neutralizing epitope of gp41 from HIV
The 3-dimensional crystal structure of glutathione S-transferase (GST) of Schistosoma japonicum (Sj) fused with a conserved neutralizing epitope on gp41 (glycoprotein, 41 kDa) of human immunodeficiency virus type 1 (HIV-1) (Muster T et al., 1993, J Virol 67:6642-6647) was determined at 2.5 A resolution. The structure of the 3-3 isozyme rat GST of the mu gene class (Ji X, Zhang P, Armstrong RN, Gilliland GL, 1992, Biochemistry 31:10169-10184) was used as a molecular replacement model. The structure consists of a 4-stranded beta-sheet and 3 alpha-helices in domain 1 and 5 alpha-helices in domain 2. The space group of the Sj GST crystal is P4(3)2(1)2, with unit cell dimensions of a = b = 94.7 A, and c = 58.1 A. The crystal has 1 GST monomer per asymmetric unit, and 2 monomers that form an active dimer are related by crystallographic 2-fold symmetry. In the binding site, the ordered structure of reduced glutathione is observed. The gp41 peptide (Glu-Leu-Asp-Lys-Trp-Ala) fused to the C-terminus of Sj GST forms a loop stabilized by symmetry-related GSTs. The Sj GST structure is compared with previously determined GST structures of mammalian gene classes mu, alpha, and pi. Conserved amino acid residues among the 4 GSTs that are important for hydrophobic and hydrophilic interactions for dimer association and glutathione binding are discussed.
Schistosoma japonicum/enzymology/genetics/immunolo↗
Theorems on symmetrics and flux conservation in radiative transfer using the matrix operator theory
The matrix operator approach to radiative transfer is shown to be a very powerful technique in establishing symmetry relations for multiple scattering in inhomogeneous atmospheres. Symmetries are derived for the reflection and transmission operators using only the symmetry of the phase function. These results will mean large savings in computer time and storage for performing calculations for realistic planetary atmospheres using this method. The results have also been extended to establish a condition on the reflection matrix of a boundary in order to preserve reciprocity. Finally energy conservation is rigorously proven for conservative scattering in inhomogeneous atmospheres.
Kattawar, G. W.↗
Theorems on symmetries and flux conservation in radiative transfer using the matrix operator theory.
The matrix operator approach to radiative transfer is shown to be a very powerful technique in establishing symmetry relations for multiple scattering in inhomogeneous atmospheres. Symmetries are derived for the reflection and transmission operators using only the symmetry of the phase function. These results will mean large savings in computer time and storage for performing calculations for realistic planetary atmospheres using this method. The results have also been extended to establish a condition on the reflection matrix of a boundary in order to preserve reciprocity. Finally energy conservation is rigorously proven for conservative scattering in inhomogeneous atmospheres.
Kattawar, G. W.↗
Oscillation of the geomagnetic field line and associated magnetic perturbations at conjugate points
Symmetry relations in magnetic perturbation at conjugate points due to oscillation of geomagnetic field line
SYMMETRY↗
Tests of unitary symmetry and possible higher symmetries
Unitary and higher symmetries related to selection rules to provide insight into underlying dynamical theory in high energy interactions
THEORETICAL PHYSICS↗
Vortex studies relating to boundary layer turbulence and noise
The present study considers the two-dimensional case of an array of N rectilinear, like-sign vortices above an infinite flat boundary. The method of images can be employed with this configuration to reduce the problem to that of 2N vortices in free space, constrained by 2N symmetry relations. This system is Hamiltonian and therefore certain invariants of the motion are known. Futher, from the Hamiltonian constant, the equations of motion are readily derived and may be integrated numerically to determine the vortex trajectories. This knowledge of the time-dependent vortex motion then allows the resulting noise radiation to be computed by standard aeroacoustic techniques.
Adelman, J. L.↗
Vortex Studies Relating to Boundary Layer Turbulence and Noise
The present study considers the two-dimensional case of an array of N rectilinear, like-sign vortices above an infinite flat boundary. The method of images can be employed with this configuration to reduce the problem to that of 2N vortices in free space, constrained by 2N symmetry relations. This system is Hamiltonian and therefore certain invariants of the motion are known. Further, from the Hamiltonian constant, the equations of motion are readily derived and may be integrated numerically to determine the vortex trajectories. This knowledge of the time-dependent vortex motion then allows the resulting noise radiation to be computed by standard aeroacoustic techniques.
Adelman, J. L.↗
Surface polarimetry of the Milky Way
Two methods of determining the state of polarization of the integrated light from the Milky Way are discussed. In the symmetry method, it is assumed that the polarized foreground zodiacal light possesses north/south symmetry relative to the ecliptic. In the method of two epochs, the above assumption is not needed, but instead time variations of the zodiacal light are assumed to be insignificant; the results obtained by this method, although compatible with the values found by the symmetry method, do however show that time variations may have influenced this result. Although the evidence for a definite polarization of the Milky Way is persuasive it cannot yet be considered conclusive.
Wolstencroft, R. D.↗
A Proposed Model for Protein Crystal Nucleation and Growth
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, based upon fluorescence, light, neutron, and X-ray scattering data, size exclusion chromatography experiments, dialysis kinetics, AFM, and modeling of growth rate data, from this and other laboratories. The first species formed is postulated to be a 'head to side' dimer. Through repeating associations involving the same intermolecular interactions this grows to a 4(sub 3) helix structure, that in turn serves as the basic unit for nucleation and subsequent crystal growth. High salt attenuates surface charges while promoting hydrophobic interactions. Symmetry facilitates subsequent helix-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(sub3)2(sub 1),2(sub 1) unit cell are filled. 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 growth 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. In the general case for proteins the lack of a singularly defined association pathway may lead 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. This model, its basis, how it fits into the currently understood osmotic second virial coefficient approach to crystallization, and what it suggests will be discussed.
Pusey, Marc↗
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.↗
Self-decoration effect in lithium ferrite.
Self-decoration effect in thermally etched polycrystalline lithium ferrite, discussing geometric symmetry relation to crystallographic surface orientation
CRYSTAL SURFACE↗
An explicit form of the Mie phase matrix for multiple scattering calculations in the I, Q, U, and V representation
An explicit expression is obtained for the phase matrix in the I, Q, U, and V Stokes vector representation for a system containing a polydispersion of spherical particles. All of the symmetry relations derived by Hovenier using general arguments are established explicitly. Convenient algorithms are given for the computation of the phase matrix for a spherical polydispersion. Since this theory is so vitally important in radiative transfer, many researchers will need to compute these functions for realistic aerosols distributions. Therefore, results are presented for a haze L distribution so that other researchers will have a way of checking their programs which compute these quantities.
Kattawar, G. W.↗
Atmospheric transfer of radiation above an inhomogeneous non-Lambertian reflective ground. II - Computational considerations and results
The theoretical foundation for solution of the three-dimensional radiative transfer problem described in the preceding paper is reviewed. Practical considerations involved in implementing the Fourier transform/Gauss-Seidel method on a minicomputer are discussed, along with derivations of symmetry relations and approximations which can be used to enhance the computational efficiency. Model results for a surface whose albedo varies as a step function are presented and compared with published solutions obtained by using the Monte Carlo method.
Diner, D. J.↗