Formal Deformations,Contractions and Moduli Spaces of Lie Algebras

Jump deformations and contractions of Lie algebras are inverse concepts, but the approaches to their computations are quite different. In this paper, we contrast the two approaches, showing how to compute the jump deformations from the miniversal deformation of a Lie algebra, and thus arrive at the contractions. We also compute contractions directly. We use the moduli spaces of real 3-dimensional and complex 3 and 4-dimensional Lie algebras as models for explaining a deformation theory approach to computation of contractions. The research of the authors was partially supported by grants from the Mathematisches Forschungsinstitut Oberwolfach, OTKA T043641, T043034 and the University of Wisconsin-Eau Claire.     

Decay of correlations for certain quadratic maps

We prove exponential decay of correlations for (f, ), wheref belongs in a positive measure set of quadratic maps of the interval and is its absolutely continuous invariant measure. These results generalize to other interval maps.The results in this paper are announced in the Tagungsbericht of Oberwolfach, June 1990The author is partially supported by NSF     

Fast three-component magnetometer-variometer based on a cesium sensor

A new fast three-component variometer-magnetometer based on a cesium sensor is developed and tested. The device is intended for measuring the longitudinal component of the geomagnetic field in the range from 20 to 65 μT and two transverse components in the range ±1 μT. The reproducibility of measurements is ±0.15 nT, and the noise-limited sensitivity is 0.01 nT (in terms of the rms deviation) or 0.04˝ for a measurement time of 0.1 s.     

The Dependence of the Deformation of Exotic Nuclei on the Half-Life

A correlation between the parameter β2 and a half-life T1/2 for oblate nuclei with sign β2 < 0 and an anticorrelation for elongated nuclei sign β2 > 0 are found. These analytical expressions for the function β2(T1/2) make it possible to calculate the shape parameters of β2 nuclei if we know the half-lives T1/2 for exotic nuclei for which this value is most accurately measured.     

Thymic Selection of T Cells as Diffusion with Intermittent Traps

T cells orchestrate adaptive immune responses by recognizing short peptides derived from pathogens, and by distinguishing them from self-peptides. To ensure the latter, immature T cells (thymocytes) diffuse within the thymus gland, where they encounter an ensemble of self-peptides presented on (immobile) antigen presenting cells. Potentially autoimmune T cells are eliminated if the thymocyte binds sufficiently strongly with any such antigen presenting cell. We model thymic selection of T cells as a random walker diffusing in a field of immobile traps that intermittently turn “on” and “off”. The escape probability of potentially autoimmune T cells is equivalent to the survival probability of such a random walker. In this paper we describe the survival probability of a random walker on a d-dimensional cubic lattice with randomly placed immobile intermittent traps, and relate it to the result of a well-studied problem where traps are always “on”. Additionally, when switching between the trap states is slow, we find a peculiar caging effect for the survival probability.     

Physical property characterization of bulk MgB<Subscript>2</Subscript> superconductor

We report synthesis, structure/micro-structure, resistivity under magnetic field [ρ(T)H], Raman spectra, thermoelectric power S(T), thermal conductivity κ(T), and magnetization of ambient pressure argon annealed polycrystalline bulk samples of MgB₂, processed under identical conditions. The compound crystallizes in hexagonal structure with space group P6/mmm. Transmission electron microscopy (TEM) reveals electron micrographs showing various types of defect features along with the presence of 3–4 nm thick amorphous layers forming the grain boundaries of otherwise crystalline MgB₂. Raman spectra of the compound at room temperature exhibited characteristic phonon peak at 600 cm^-1. Superconductivity is observed at 37.2 K by magnetic susceptibility χ(T), resistivity ρ(T), thermoelectric power S(T), and thermal conductivity κ(T) measurements. The power law fitting of ρ(T) give rise to Debye temperature (Θ_D) at 1400 K which is found consistent with the theoretical fitting of S(T), exhibiting Θ _D of 1410 K and carrier density of 3.81 × 10²⁸/m³. Thermal conductivity κ(T) shows a jump at 38 K, i.e., at T_c, which was missing in some earlier reports. Critical current density (J_c) of up to 10⁵ A/cm² in 1–2 T (Tesla) fields at temperatures (T) of up to 10 K is seen from magnetization measurements. The irreversibility field, defined as the field related to merging of M(H) loops is found to be 78, 68 and 42 kOe at 4, 10 and 20 K respectively. The superconducting performance parameters viz. irreversibility field (H_irr) and critical current density J_c(H) of the studied MgB₂ are improved profoundly with addition of nano-SiC and nano-diamond. The physical property parameters measured for polycrystalline MgB₂ are compared with earlier reports and a consolidated insight of various physical properties is presented.     

Expression of Galpha14 in sweet-transducing taste cells of the posterior tongue

Background  

"Type II"/Receptor cells express G protein-coupled receptors (GPCRs) for sweet, umami (T1Rs and mGluRs) or bitter (T2Rs), as well as the proteins for downstream signalling cascades. Transduction downstream of T1Rs and T2Rs relies on G-protein and PLCβ2-mediated release of stored Ca²⁺. Whereas Gαgus (gustducin) couples to the T2R (bitter) receptors, which Gα-subunit couples to the sweet (T1R2 + T1R3) receptor is presently not known. We utilized RT-PCR, immunocytochemistry and single-cell gene expression profiling to examine the expression of the Gαq family (q, 11, 14) in mouse taste buds.     

Generating power of a thermoelectric generator under periodically alternating temperature gradients

The thermo-emf ΔV and thermoelectric current ΔI generated by imposing a temperature gradient alternating at a period of T on a thermoelectric (TE) generator were measured as a function of t, where t is the lapsed time and 1/T was varied from 0 to 1/30 s^-1. A TE generator was sandwiched between two Peltier modules connected in series. The alternating temperature gradients were produced by imposing an alternating voltage V on two Peltier modules, where V was varied from 1.0 to 3.7 V. Both ΔV and ΔI generated by the TE generator oscillate at a period of T but their amplitudes tend to increase monotonically with an increase of V. The effective thermo-emf ΔV_eff and current ΔI_eff calculated from ΔV and ΔI increase abruptly with an increase of 1/T and have a local maximum at 1/T=1/120 or 1/240 s^-1. The generating power ΔW_eff(=ΔV_effΔI_eff) tends to increase proportionally with an increase of input power W_input, owing to the increase in the temperature difference. The rate of ΔW_eff to W_input at 1/T=1/240 s^-1 reached approximately 3.2 times as large as that obtained for the steady temperature gradient corresponding to 1/T=0 s^-1. It was thus found that the generating power of the TE generator operating under the temperature gradient alternating at an optimum period is remarkably increased compared to that of a TE generator working under a conventional steady temperature gradient. PACS 72.15.Jf; 84.60.Rb; 85.30De     

Structural phase transition in substituted La2CuO4 and Pr2CuO4−y

The structural phase transition from orthorhombic (T) phase to tetragonal (T′) phase in substituted La_2−x R _x CuO₄ (R = Pr, Nd, Sm, Eu and Gd) and T′ to T-phase in Pr_2−x M _x CuO_4−y (M = Sr, Ca) has been studied by X-ray diffraction technique. The T-phase of La₂CuO₄ is transferred to T′ phase abruptly atx=0.8, 0.4, 0.4, 0.3 and 0.4 respectively for substitution of Pr, Nd, Sm, Eu and Gd for La in La₂CuO₄ without evidence of the T* phase. The T′ structure of Pr₂CuO₄ (x = 0.0) gets transformed to the T* structure at 30% Ca doping (x=0.6) and then to the T structure at 50% Ca doping (x=1.0), while for Sr-contentx=0.0, 0.4 and 1.0 it shows T′, T* and T structure respectively.     

Anisotropy of the upper critical field and specific heat in V3Si — a superconductor with cubic symmetry

The specific heat of a V₃Si single crystal (T _c=17 K, H _c2=20 T) in magnetic fields up to 8 T isinvestigated experimentally for three orientations of the field relative to the crystallographic directions — H∥〈001〉, H∥〈110〉, and H∥〈111〉. Both the upper critical magnetic field and the specific heat of the mixed state are observed to depend on the orientation of the magnetic field relative to the crystallographic directions (anisotropy): The critical field reaches its maximum value and the specific heat its minimum value in a field along the 〈001〉 direction. The anisotropy scale in both phenomena increases as the magnetic field and reaches 3% in a 6 T field. The interrelationship of the upper critical field anisotropy and the specific-heat anisotropy in type-II superconductors is studied. It is shown that the anisotropy of the specific heat in the mixed state in weak fields can serve as a criterion for nontrivial pairing. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 1, 26–29 (10 January 1999)     

Anomalous behavior of the interlayer resistance of a BSCCO-2212 crystal in a parallel magnetic field

The electrical resistance across the Cu-O layers of a BSCCO-2212 single crystal is investigated in the range of angles 0°⩽φ⩽90° between the magnetic field H⩽15 T and the ab plane. It is found that the temperature dependence R(T) at the transition into the mixed state is much sharper for φ≃0° than for 1°≲φ≲90°, where R is determined by the perpendicular component of the magnetic field and is described by the Arrhenius law R∼exp(−U/T). For H∥ ab hysteretic jumps in R(T, H), which vanish as the current increases, are observed at fields in the range 5.5⩽H⩽11 T. This effect can be attributed to a commensurate phase transition in a lattice of Josephson vortices. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 2, 123–128 (25 January 1996)     

Magnetic Field Effects on the Photoinduced Electron-Transfer Reactions in a Ruthenium Porphyrin–C60 Ligand Complex

Magnetic field effects (MFEs) on a photoinduced electron-transfer reaction in a semi-rigid linked system (RuP–C₆₀) were examined in toluene and o-dichlorobenzene. The transient absorption spectra indicated that the photogenerated biradical produced by an intramolecular electron-transfer reaction was observed only in o-dichlorobenzene. The decay rate constants (k _d) for the biradical decreased steeply at lower magnetic fields (≤0.06 T) and rapidly recovered at 0.08 T. The k _d value was observed to decrease gradually above 0.2 T. The MFEs strongly indicated the formation of the singlet-born biradical for RuP–C₆₀. The dip in the MFE at 0.06 T was ascribed to the S–T level crossing mechanism. The MFEs above 0.2 T can be explained by a spin–spin relaxation mechanism due to the anisotropic Zeeman interaction being related to the exchange interaction.     

Muonium states and dynamics in phosphorus and sulphur

Magnetic properties of single crystal Ba₂Cu₃O₄Cl₂ with Cu₃O₄ planes were investigated by temperature‐ and magnetic‐field‐dependent anisotropic magnetization M(T,H) and zero‐field‐μSR. Muon spin precession was observed below as well as above T=32 K where an anomaly in M(T) appears. At this temperature the frequency of the precession changes and the damping of it diverges. This is an evidence for a magnetic transition. We also found the temperature dependence of the H‐linear component of M(H) shows a maximum around T=80 K, which is similar to the behavior of low‐dimensional magnets with an antiferromagnetic interaction. This revised version was published online in July 2006 with corrections to the Cover Date.     

Observation of a cubic defect in nickel by means of β-NMR on oriented114In nuclei

The hyperfine field of substitutional and defect-associated In atoms in Ni has been determined by observing the radiative destruction of β-asymmetry in the decay of¹¹⁴In. It is argued that the associated defect is a cubic vacancy cluster. The hyperfine fields were determined as −3.30(1) T for substitutional In atoms, and +5.12(2) T for the defect associated atoms.     

Efficiency of the muon catalyzed fusion in triple H/D/T mixtures

In this paper, we solve numerically kinetic equations for the chain reactions of μCF in triple H/D/T mixture. Regarding the computational results, we show that μCF efficiency decreases by adding hydrogen H to D/T mixture. This is in contradiction to the usual belief which expects the increase of μCF efficiency in H/D/T mixture. Our results are confirmed by the first and recent experiment on μdt cycling rate in the triple mixture. This revised version was published online in July 2006 with corrections to the Cover Date.     

Pseudo spin gap in high‐Tc oxides observed by NMR

From the temperature dependence of the ⁶³Cu nuclear spin‐lattice relaxation rate, 1/T₁T, in the planar Cu(2) sites, it is now well established that a highly enhanced and strongly temperature dependent relaxation process due to antiferromagnetic Cu spin fluctuations exists in all of the high‐T_c’s. The data also exhibit the opening of a gap in the low‐lying magnetic excitations with an energy comparable to the superconducting gap, particularly for the so‐called low doping regime. It is also found that, irrespective of the system, the temperature at which the spin‐gap opens, T_sg, determined as the peak of 1/T₁T vs. T, has a linear decrease with increasing of the doping concentration. A spin‐gap phase diagram is proposed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Motivations for antigravity in General Relativity

We present arguments showing that it is natural to interpret the negative mass part of the Kerr solution as representing the geometry experienced by antimatter. The C, P and T discrete transformations are considered for this geometry. The C and T properties of the proposed identification are found to be in agreement with the usual representation of antimatter. In addition, we conjecture a property of perfect stigmatism through Kerr wormholes which allows General Relativity to mimic antigravity. Kerr wormholes would then act as “supermirrors” reversing the C, P and T images of an object seen through it. This interpretation is subject to several experimental tests and able to provide an explanation, without any free parameter, of the “CP” violation observed in the neutral kaon system. This revised version was published online in August 2006 with corrections to the Cover Date.     

The impact of renormalization group theory on magnetism

The basic issues of renormalization group (RG) theory, i.e. universality, crossover phenomena, relevant interactions etc. are verified experimentally on magnetic materials. Universality is demonstrated on account of the saturation of the magnetic order parameter for T ↦ 0. Universal means that the deviations with respect to saturation at T = 0 can perfectly be described by a power function of absolute temperature with an exponent ε that is independent of spin structure and lattice symmetry. Normally the T^ε function holds up to ~0.85T_c where crossover to the critical power function occurs. Universality for T ↦ 0 cannot be explained on the basis of the material specific magnon dispersions that are due to atomistic symmetry. Instead, continuous dynamic symmetry has to be assumed. The quasi particles of the continuous symmetry can be described by plane waves and have linear dispersion in all solids. This then explains universality. However, those quasi particles cannot be observed using inelastic neutron scattering. The principle of relevance is demonstrated using the competition between crystal field interaction and exchange interaction as an example. If the ratio of crystal field interaction to exchange interaction is below some threshold value the local crystal field is not relevant under the continuous symmetry of the ordered state and the saturation moment of the free ion is observed for T ↦ 0. Crossover phenomena either between different exponents or between discrete changes of the pre-factor of the T^ε function are demonstrated for the spontaneous magnetization and for the heat capacity.     

First measurements of dtμ cycle characteristics in liquid H/D/T mixture

Muon catalyzed fusion in a dense triple mixture of hydrogen isotopes was investigated for the first time. The experimental method is based on the registration of neutrons from dtμ fusion by a full absorption detector in 4π geometry. The measurements were performed in H/D/T mixture at T=21 K and φ≃ 1.1 LHD using four sets of isotope concentrations. The basic parameters of the dtμ cycle (neutron yield, cycling rate and total sticking) in H/D/T mixtures obtained from neutron time distributions are presented and discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

“Magic numbers” in the melting of a cluster of point charges on a sphere

The thermodynamic properties of a cluster of point Coulomb charges on a sphere have been analyzed using the Monte Carlo method for the number of charges 20 ≤ N ≤ 90. The ground state of the system of charges is described in the model of a closed quasi-two-dimensional triangular lattice with topological defects. We have determined the dependence of the Lindeman parameter δ_L of this system on N and on the dimensionless parameter $ \tilde T $ \tilde T , which is proportional to the temperature T and to the radius R of the cluster: $ \tilde T = {{k_B T\varepsilon R} \mathord{\left/ {\vphantom {{k_B T\varepsilon R} {e^2 }}} \right. \kern-\nulldelimiterspace} {e^2 }} $ \tilde T = {{k_B T\varepsilon R} \mathord{\left/ {\vphantom {{k_B T\varepsilon R} {e^2 }}} \right. \kern-\nulldelimiterspace} {e^2 }} , where ∈ is the dielectric constant of the medium and e is the charge of a particle. The “magic numbers,” i.e., the N values, for which the melting point of the closed triangular lattice of charges is much higher than those for neighboring N values, have been found. The evolution of the lattice-melting mechanisms with an increase in the number of charges N in a mesoscopic cluster has been analyzed. For N ≤ 32, the melting of the lattice does not involve dislocations (nontopological melting); this behavior of the mesoscopic system of charges on the sphere differs from the behavior of the extended planar two-dimensional system. At N ≳ 50, melting is accompanied by the formation of dislocations. The mechanism of dislocation-free non-topological melting of a closed lattice, which occurs at small N values and is associated with the cooperative rotational motion of “rings” of particles, has been analyzed. The model has various implementations in the mesoscopic region; in particular, it describes the system of electrons over the liquid-helium cluster, the liquid-helium cluster with incorporated charged particles, a multielectron bubble in liquid helium, a charged quantum dot, etc.