Scalar field visualization via extraction of symmetric structures

Identifying symmetry in scalar fields is a recent area of research in scientific visualization and computer graphics communities. Symmetry detection techniques based on abstract representations of the scalar field use only limited geometric information in their analysis. Hence they may not be suited for applications that study the geometric properties of the regions in the domain. On the other hand, methods that accumulate local evidence of symmetry through a voting procedure have been successfully used for detecting geometric symmetry in shapes. We extend such a technique to scalar fields and use it to detect geometrically symmetric regions in synthetic as well as real-world datasets. Identifying symmetry in the scalar field can significantly improve visualization and interactive exploration of the data. We demonstrate different applications of the symmetry detection method to scientific visualization: query-based exploration of scalar fields, linked selection in symmetric regions for interactive visualization, and classification of geometrically symmetric regions and its application to anomaly detection.

Interplay of structural distortions, dielectric effects and magnetic order in multiferroic GdMnO3

Multiferroic materials are characterized by simultaneous magnetic and ferroelectric ordering making them good candidates for magneto-electrical applications. We conducted thermal expansion and magnetostriction measurements in magnetic fields up to 14 T on perovskitic GdMnO3 by highresolution capacitive dilatometry in an effort to determine all longitudinal and transversal components of the magnetostriction tensor. Below the ordering temperature T (N) = 42 K, i.e., within the different complex (incommensurate or complex) antiferromagnetic phases, lattice distortions of up to 100 ppm have been found. Although no change of the lattice symmetry occurs, the measurements reveal strong magneto-structural phenomena, especially in the incommensurate sinusoidal antiferromagnetic phase. A strong anisotropy of the magnetoelastic properties was found, in good agreement with the type and propagation vector of the magnetic structure. We demonstrate that our capacitive dilatometry can detect lattice expansion effects and changes of the dielectric permittivity simultaneously because the sample is housed inside the capacitor. A separation of both effects is possible by shielding the sample. Dielectric transitions could be detected by this method and compared to the critical values of H and T in the magnetic phase diagram. Dielectric changes measured at 1 kHz excitation frequency are detected in GdMnO3 at about 180 K, and between 10 K and 25 K in the canted antiferromagnetic structure which is characterized by a complex magnetic order on both the Gd- and Mn-sites.

Fermions in synthetic non-Abelian gauge potentials: rashbon condensates to novel Hamiltonians

Recent advances in the generation of synthetic gauge fields in cold atomic systems have stimulated interest in the physics of interacting bosons and fermions in them. In this paper, we discuss interacting two-component fermionic systems in uniform non-Abelian gauge fields that produce a spin-orbit interaction and uniform spin potentials. Two classes of gauge fields discussed include those that produce a Rashba spin-orbit interaction and the type of gauge fields (SM gauge fields) obtained in experiments by the Shanxi and MIT groups. For high symmetry Rashba gauge fields, a two-particle bound state exists even for a vanishingly small attractive interaction described by a scattering length. Upon increasing the strength of a Rashba gauge field, a finite density of weakly interacting fermions undergoes a crossover from a BCS like ground state to a BEC state of a new kind of boson called the rashbon whose properties are determined solely by the gauge field and not by the interaction between the fermions. The rashbon Bose-Einstein condensate (RBEC) is a quite intriguing state with the rashbon-rashbon interactions being independent of the fermion-fermion interactions (scattering length). Furthermore, we show that the RBEC has a transition temperature of the order of the Fermi temperature, suggesting routes to enhance the transition temperatures of weakly interacting superfluids by tuning the spin-orbit coupling. For the SM gauge fields, we show that in a regime of parameters, a pair of particles with finite centre-of-mass momentum is the most strongly bound. In other regimes of centre-of-mass momenta, there is no two-body bound state, but a resonance like feature appears in the scattering continuum. In the many-body setting, this results in flow enhanced pairing. Also, strongly interacting normal states utilizing the scattering resonance can be created opening the possibility of studying properties of helical Fermi liquids. This paper contains a general discussion of the physics of Feshbach resonance in a non-Abelian gauge field, where several novel features such as centre-of-mass-momentum-dependent effective interactions are shown. It is also shown that a uniform non-Abelian gauge field in conjunction with a spatial potential can be used to generate novel Hamiltonians; we discuss an explicit example of the generation of a monopole Hamiltonian.

Lead-free piezoelectric system (Na0.5Bi0.5)TiO3-BaTiO3: Equilibrium structures and irreversible structural transformations driven by electric field and mechanical impact

The structure-property correlation in the lead-free piezoelectric (1 - x)(Na0.5Bi0.5)TiO3-(x)BaTiO3 has been systematically investigated in detail as a function of composition (0 < x <= 0.11), temperature, electric field, and mechanical impact by Raman scattering, ferroelectric, piezoelectric measurement, x-ray, and neutron powder diffraction methods. Although x-ray diffraction study revealed three distinct composition ranges characterizing different structural features in the equilibrium state at room temperature: (i) monoclinic (Cc) + rhombohedral (R3c) for the precritical compositions, 0 <= x <= 0.05, (ii) cubiclike for 0.06 <= x <= 0.0675, and (iii) morphotropic phase boundary (MPB) like for 0.07 <= x < 0.10, Raman and neutron powder diffraction studies revealed identical symmetry for the cubiclike and the MPB compositions. The cubiclike structure undergoes irreversible phase separation by electric poling as well as by pure mechanical impact. This cubiclike phase exhibits relaxor ferroelectricity in its equilibrium state. The short coherence length (similar to 50A degrees) of the out-of-phase octahedral tilts does not allow the normal ferroelectric state to develop below the dipolar freezing temperature, forcing the system to remain in a dipolar glass state at room temperature. Electric poling helps the dipolar glass state to transform to a normal ferroelectric state with a concomitant enhancement in the correlation length of the out-of-phase octahedral tilt.

Quantum entropic ambiguities: Ethylene

In a quantum system, there may be many density matrices associated with a state on an algebra of observables. For each density matrix, one can compute its entropy. These are, in general, different. Therefore, one reaches the remarkable possibility that there may be many entropies for a given state R. Sorkin (private communication)]. This ambiguity in entropy can often be traced to a gauge symmetry emergent from the nontrivial topological character of the configuration space of the underlying system. It can also happen in finite-dimensional matrix models. In the present work, we discuss this entropy ambiguity and its consequences for an ethylene molecule. This is a very simple and well-known system, where these notions can be put to tests. Of particular interest in this discussion is the fact that the change of the density matrix with the corresponding entropy increase drives the system towards the maximally disordered state with maximum entropy, where Boltzman's formula applies. Besides its intrinsic conceptual interest, the simplicity of this model can serve as an introduction to a similar discussion of systems such as colored monopoles and the breaking of color symmetry.

Transport across a junction of topological insulators and a superconductor

We study transport across a line junction lying between two orthogonal topological insulator surfaces and a superconductor which can have either s-wave (spin-singlet) or p-wave (spin-triplet) pairing symmetry. The junction can have three time-reversal invariant barriers on three sides. We compute the charge and the spin conductance across such a junction and study their behaviors as a function of the bias voltage applied across the junction and the three parameters used to characterize the barrier. We find that the presence of topological insulators and a superconductor leads to both Dirac- and Schrodinger-like features in charge and spin conductances. We discuss the effect of bound states on the superconducting side of the barrier on the conductance; in particular, we show that for triplet p-wave superconductors, such a junction may be used to determine the spin state of its Cooper pairs. Our study reveals that there is a nonzero spin conductance for some particular spin states of the triplet Cooper pairs; this is an effect of the topological insulators which break the spin rotation symmetry. Finally, we find an unusual satellite peak (in addition to the usual zero bias peak) in the spin conductance for p-wave symmetry of the superconductor order parameter.

Anomalous optical phonons in Cs-0.9(NH4)(0.1)H2AsO4: a temperature-dependent Raman study

We determine the nature of coupled phonons in mixed crystal of Cs-0.9(NH4)(0.1)H2AsO4 using inelastic light scattering studies in the temperature range of 5 K to 300 K covering a spectral range of 60-1100 cm(-1). The phase transition in this system are marked by the splitting of phonon modes, appearance of new modes and anomalies in the frequency as well as linewidth of the phonon modes near transition temperature. In particular, we observed the splitting of symmetric (v(1)) and antisymmetric (v(3)) stretching vibrations associated with AsO4 tetrahedra below transition temperature (T-c(*) similar to 110 K) attributed to the lowering of site symmetry of AsO4 in orthorhombic phase below transition temperature. In addition, the step-up (hardening) and step-down (softening) of the AsO4 bending vibrations (v(4) (S9, S11) and v(2) (S6)) below transition temperature signals the rapid development of long range ferroelectric order and proton ordering. The lowest frequency phonon (S1) mode observed at similar to 92 cm(-1) shows anomalous blue shift (similar to 12 %) from 300 K to 5 K with no sharp transition near T-c(*) unlike other observed phonon modes signaling its potential coupling with the proton tunneling mode. (C) 2013 Author(s).

Crystal growth and nonlinear optical properties of sodium D-isoascorbate monohydrate

Optical quality single crystals of sodium D-isoascorbate monohydrate were grown by a slow cooling technique. The crystal possesses a bulky prismatic morphology. Thermal analyses indicate that the crystals are stable up to 125 degrees C. The optical transmission window ranges from 307 nm to 1450 nm. The principal refractive indices have been measured employing Brewster's angle method. The crystallographic and the principal dielectric axes coincide with each other such that a lies along Z, b along X and c along Y. The optic axis is oriented 58 degrees (at 532 nm) to the crystallographic a axis in the XZ plane and the crystal is negative biaxial. Type 1 and type 2 phase matching curves are generated and experimentally verified. No polarization dependence of the light absorption was observed confirming the validity of Kleinman's symmetry conjecture, leading to a single nonvanishing nonlinear tensor component. According to Hobden's classification the crystal belongs to class 3. The crystal also exhibits second order noncollinear conic sections. The single shot and multiple shot surface laser damage thresholds are determined to be 32.7 GW cm(-2) and 6.5 GW cm(-2) respectively for 1064 nm radiation.

A multi-sheeted three-dimensional potential-energy surface for the H-atom photodissociation of phenol

Extending the previous work of Lan et al. J. Chem. Phys., 122, 224315 (2005)], a multi-state potential model for the H atom photodissociation is presented. All three ``disappearing coordinates'' of the departing H atom have been considered. Ab initio CASSCF computations have been carried out for the linear COH geometry of C-2v symmetry, and for several COH angles with the OH group in the ring plane and also perpendicular to the ring plane. By keeping the C6H5O fragment frozen in a C-2v-constrained geometry throughout, we have been able to apply symmetry-based simplifications in the constructions of a diabatic model. This model is able to capture the overall trends of twelve adiabats at both torsional limits for a wide range of COH bend angles.

Solid-liquid transition in polydisperse Lennard-Jones systems

We study melting of a face-centered crystalline solid consisting of polydisperse Lennard-Jones spheres with Gaussian polydispersity in size. The phase diagram reproduces the existence of a nearly temperature invariant terminal polydispersity (delta(t) similar or equal to 0.11), with no signature of reentrant melting. The absence of reentrant melting can be attributed to the influence of the attractive part of the potential upon melting. We find that at terminal polydispersity the fractional density change approaches zero, which seems to arise from vanishingly small compressibility of the disordered phase. At constant temperature and volume fraction the system undergoes a sharp transition from crystalline solid to the disordered amorphous or fluid state with increasing polydispersity. This has been quantified by second- and third-order rotational invariant bond orientational order, as well as by the average inherent structure energy. The translational order parameter also indicates a similar sharp structural change at delta similar or equal to 0.09 in case of T* = 1.0, phi = 0.58. The free energy calculation further supports the sharp nature of the transition. The third-order rotationally invariant bond order shows that with increasing polydispersity, the local cluster favors a more icosahedral arrangement and the system loses its local crystalline symmetry. Interestingly, the value of structure factor S(k) of the amorphous phase at delta similar or equal to 0.10 (just beyond the solid-liquid transition density at T* = 1) becomes 2.75, which is below the value of 2.85 required for freezing given by the empirical Hansen-Verlet rule of crystallization, well known in the theory of freezing.

Black holes in higher spin supergravity

We study black hole solutions in Chern-Simons higher spin supergravity based on the superalgebra sl(3 vertical bar 2). These black hole solutions have a U(1) gauge field and a spin 2 hair in addition to the spin 3 hair. These additional fields correspond to the R-symmetry charges of the supergroup sl(3 vertical bar 2). Using the relation between the bulk field equations and the Ward identities of a CFT with N = 2 super-W-3 symmetry, we identify the bulk charges and chemical potentials with those of the boundary CFT. From these identifications we see that a suitable set of variables to study this black hole is in terms of the charges present in three decoupled bosonic sub-algebras of the N = 2 super-W-3 algebra. The entropy and the partition function of these R-charged black holes are then evaluated in terms of the charges of the bulk theory as well as in terms of its chemical potentials. We then compute the partition function in the dual CFT and find exact agreement with the bulk partition function.

Microwave, infrared-microwave double resonance, and theoretical studies of C2H4 center dot center dot center dot H2S complex

In this manuscript, rotational spectra of four new isotopologues of the S-H center dot center dot center dot pi bonded C2H4 center dot center dot center dot H2S complex, i.e., C2D4 center dot center dot center dot H2S, C2D4 center dot center dot center dot D2S, C2D4 center dot center dot center dot HDS, and (CCH4)-C-13 center dot center dot center dot H2S have been reported and analyzed. All isotopologues except C2D4 center dot center dot center dot HDS show a four line pattern whereas a doubling of the transition frequencies was observed for C2D4 center dot center dot center dot HDS. These results together with our previous report on the title complex M. Goswami, P. K. Mandal, D. J. Ramdass, and E. Arunan, Chem. Phys. Lett. 393(1-3), 22-27 (2004)] confirm that both subunits (C2H4 and H2S) are involved in large amplitude motions leading to a splitting of each rotational transition to a quartet. Further, the results also confirm that the motions which are responsible for the observed splittings involve both monomers. Molecular symmetry group analysis, considering the interchange of equivalent H atoms in H2S and C2H4 could explain the observed four line pattern and their intensities in the microwave spectrum. In addition, hydride stretching fundamentals of the complex were measured using coherence-converted population transfer Fourier Transform Microwave-infrared (IR-MW double resonance) experiments in the S-H and C-H stretch regions. Changes in the tunneling splittings upon vibrational excitation are consistent with the isotopic dependence of pure rotational transitions. A complexation shift of 2.7-6.5 cm(-1) has been observed in the two fundamental S-H stretching modes of the H2S monomer in the complex. Vibrational pre-dissociation in the bound S-H stretch has been detected whereas the instrument-limited line-shapes in other S-H and C-H stretches indicate slower pre-dissociation rate. Some local perturbations in the vibrational spectra have been observed. Two combination bands have been observed corresponding to both the S-H stretching fundamentals and what appears to be the intermolecular stretching mode at 55 cm(-1). The tunneling splitting involved in the rotation of C2H4 unit has been deduced to be 1.5 GHz from the IR-MW results. In addition, ab initio barrier heights derived for different motions of the monomers support the experimental results and provide further insight into the motions causing the splitting. (C) 2013 AIP Publishing LLC.

Generation of Ligand Specificity and Modes of Oligomerization in beta-Prism I Fold Lectins

beta-Prism I fold lectins constitute one of the five widely occurring structural classes of plant lectins. Each single domain subunit is made up of three Greek key motifs arranged in a threefold symmetric fashion. The threefold symmetry is not reflected in the sequence except in the case of the lectin from banana, a monocot, which carries two sugar-binding sites instead of the one in other lectins of known three-dimensional structure, all from dicots. This is believed to be a consequence of the different evolutionary paths followed by the lectin in monocots and dicots. The galactose-specific lectins among them have two chains produced by posttranslational proteolysis and contain three aromatic residues at the binding site. The extended binding sites of galactose- and mannose-specific lectins have been thoroughly characterized. Ligand binding at the sites involves both conformational selection and induced fit. Molecular plasticity of some of the lectins in the family has been characterized. The plasticity appears to be such as to promote variability in quaternary association which could be dimeric, tetrameric, or octameric. Structural and evolutionary reasons for the variability have been explored, and the relation of oligomerization to ligand binding and conformational selection investigated.

Information content of molecular graph and prediction of gas phase thermal entropy of organic compounds

Entropy is a fundamental thermodynamic property that has attracted a wide attention across domains, including chemistry. Inference of entropy of chemical compounds using various approaches has been a widely studied topic. However, many aspects of entropy in chemical compounds remain unexplained. In the present work, we propose two new information-theoretical molecular descriptors for the prediction of gas phase thermal entropy of organic compounds. The descriptors reflect the bulk and size of the compounds as well as the gross topological symmetry in their structures, all of which are believed to determine entropy. A high correlation () between the entropy values and our information-theoretical indices have been found and the predicted entropy values, obtained from the corresponding statistically significant regression model, have been found to be within acceptable approximation. We provide additional mathematical result in the form of a theorem and proof that might further help in assessing changes in gas phase thermal entropy values with the changes in molecular structures. The proposed information-theoretical molecular descriptors, regression model and the mathematical result are expected to augment predictions of gas phase thermal entropy for a large number of chemical compounds.

Entropy of quantum states: Ambiguities

The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. As pointed out to us by Sorkin, this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This non-unique entropy can occur at zero temperature. We will argue elsewhere in detail that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. Finally, we establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix.