The impact of celestial pole offset modelling on VLBI UT1 Intensive results

Very Long Baseline Interferometry (VLBI) Intensive sessions are scheduled to provide operational Universal Time (UT1) determinations with low latency. UT1 estimates obtained from these observations heavily depend on the model of the celestial pole motion used during data processing. However, even the most accurate precession-nutation model, IAU 2000/2006, is not accurate enough to realize the full potential of VLBI observations. To achieve the highest possible accuracy in UT1 estimates, a celestial pole offset (CPO), which is the difference between the actual and modelled precession-nutation angles, should be applied. Three CPO models are currently available for users. In this paper, these models have been tested and the differences between UT1 estimates obtained with those models are investigated. It has been shown that neglecting CPO modelling during VLBI UT1 Intensive processing causes systematic errors in UT1 series of up to 20 microarcseconds. It has been also found that using different CPO models causes the differences in UT1 estimates reaching 10 microarcseconds. Obtained results are applicable to the satellite data processing as well.Comment: 8 pp., accepted for publication in Journal of Geodes

The influence of Galactic aberration on precession parameters determined from VLBI observations

The influence of proper motions of sources due to Galactic aberration on precession models based on VLBI data is determined. Comparisons of the linear trends in the coordinates of the celestial pole obtained with and without taking into account Galactic aberration indicate that this effect can reach 20 $\mu$as per century, which is important for modern precession models. It is also shown that correcting for Galactic aberration influences the derived parameters of low-frequency nutation terms. It is therefore necessary to correct for Galactic aberration in the reduction of modern astrometric observations

Recognizing Graph Theoretic Properties with Polynomial Ideals

Many hard combinatorial problems can be modeled by a system of polynomial equations. N. Alon coined the term polynomial method to describe the use of nonlinear polynomials when solving combinatorial problems. We continue the exploration of the polynomial method and show how the algorithmic theory of polynomial ideals can be used to detect k-colorability, unique Hamiltonicity, and automorphism rigidity of graphs. Our techniques are diverse and involve Nullstellensatz certificates, linear algebra over finite fields, Groebner bases, toric algebra, convex programming, and real algebraic geometry.Comment: 20 pages, 3 figure

Spin-Orbit Qubits of Rare-Earth-Metal Ions in Axially Symmetric Crystal Fields

Contrary to the well known spin qubits, rare-earth qubits are characterized by a strong influence of crystal field due to large spin-orbit coupling. At low temperature and in the presence of resonance microwaves, it is the magnetic moment of the crystal-field ground-state which nutates (for several $\mu$s) and the Rabi frequency $\Omega_R$ is anisotropic. Here, we present a study of the variations of $\Omega_R(\vec{H}_{0})$ with the magnitude and direction of the static magnetic field $\vec{H_{0}}$ for the odd $^{167}$Er isotope in a single crystal CaWO$_4$:Er$^{3+}$. The hyperfine interactions split the $\Omega_R(\vec{H}_{0})$ curve into eight different curves which are fitted numerically and described analytically. These "spin-orbit qubits" should allow detailed studies of decoherence mechanisms which become relevant at high temperature and open new ways for qubit addressing using properly oriented magnetic fields

Supersymmetry and a Time-Dependent Landau System

A general technique is outlined for investigating supersymmetry properties of a charged spin-\half quantum particle in time-varying electromagnetic fields. The case of a time-varying uniform magnetic induction is examined and shown to provide a physical realization of a supersymmetric quantum-mechanical system. Group-theoretic methods are used to factorize the relevant Schr\"odinger equations and obtain eigensolutions. The supercoherent states for this system are constructed.Comment: 47 pages, submitted to Phys. Rev. A, LaTeX, IUHET 243 and LA-UR-93-20

Ground Based Program for the Physical Analysis of Macromolecular Crystal Growth

During the past year we have focused on application of in situ Atomic Force Microscopy (AFM) for studies of the growth mechanisms and kinetics of crystallization for different macromolecular systems. Mechanisms of macrostep formation and their decay, which are important in understanding of defect formation, were studied on the surfaces of thaumatin, catalase, canavalin and lysozyme crystals. Experiments revealed that step bunching on crystalline surfaces occurred either due to two- or three-dimensional nucleation on the terraces of vicinal slopes or as a result of uneven step generation by complex dislocation sources. No step bunching arising from interaction of individual steps in the course of the experiment was observed. The molecular structure of the growth steps for thaumatin and lipase crystals were deduced. It was further shown that growth step advance occurs by incorporation of single protein molecules. In singular directions growth steps move by one-dimensional nucleation on step edges followed by lateral growth. One-dimensional nuclei have different sizes, less then a single unit cell, varying for different directions of step movement. There is no roughness due to thermal fluctuations, and each protein molecule which incorporated into the step remained. Growth kinetics for catalase crystals was investigated over wide supersaturation ranges. Strong directional kinetic anisotropy in the tangential step growth rates in different directions was seen. The influence of impurities on growth kinetics and cessation of macromolecular crystals was studied. Thus, for catalase, in addition to pronounced impurity effects on the kinetics of crystallization, we were also able to directly observe adsorption of some impurities. At low supersaturation we repeatedly observed filaments which formed from impurity molecules sedimenting on the surfaces. Similar filaments were observed on the surfaces of thaumatin, canavalin and STMV crystals as well, but the frequency was low compared with catalase crystallization. Cessation of growth of xylanase and lysozyme crystals was also observed and appeared to be a consequence of the formation of dense impurity adsorption layers. Attachment: "An in situ AFM investigation of catalase crystallization", "Atomic force microscopy studies of living cells: visualization of motility, division, aggregation, transformation, and apoptosis", AFM studies on mechanisms of nucleation and growth of macromolecular crystals", and "In situ atomic force microscopy studies of surface morphology, growth kinetics, defect structure and dissolution in macromolecular crystallization"