Rotating frames in special relativity

A uniformly rotating frame is defined as the rest frame of a particle revolving with constant velocityω in a circle about theZ-axis of an inertial frame Σ⁰. Under the conditionz=Z,r=R, theoretical constraints are established for the solution of the transformation problem Σ⁰→Σ^ω r,Σ^ω r being the cylindrical subframe of Σ^ω. The unique solution of the problem in cylindrical coordinates is isomorphic to the special Lorentz transformationL _x, withβ=v/c replaced byβ _r=ωr/c. Hence the intrinsic geometry on the surface of a rotating cylinder is Euclidean. Though there exists no complete intrinsic geometry on the surface of a rotating disk, the geodesics on it are straight lines while the circumference of a concentric circle isK _r2πr as predicted by Einstein.     

Synthesis, magnetic and dielectric properties of Er-Ni doped Sr-hexaferrite nanomaterials for applications in High density recording media and microwave devices

A sol-gel combustion method has been successfully employed for the synthesis of Sr-hexaferrite nanomaterials doped with Er³⁺ and Ni²⁺ at strontium and iron sites, respectively. The X-ray diffraction analysis confirmed the single magnetoplumbite phase and the crystallite size was found to be in the range of 14-16 nm, suitable for obtaining signal-to-noise ratio in the high density recording media. The magnetic properties such as saturation magnetization (M_s), remanence (M_r) and coercivity (H_c) were calculated from hysteresis loops. M_s, M_r and H_c are observed to increase with the Er-Ni content. The dielectric constant (ε´) and dielectric loss (tan δ) is found to decrease with the increase in frequency and is explained on the basis of Maxwell-Wagner and Koops theory. The decrease in dielectric constant and dielectric loss but increase in saturation magnetization and remanence with Er-Ni content suggests that the materials are suitable for applications in microwave devices and high density recording media .     

Studies on the optical and dielectric properties of a zinc thiourea chloride NLO single crystal

Single crystals of a nonlinear optical material, zinc thiourea chloride were grown by the slow evaporation technique. The crystal structure and lattice parameters of the grown crystal were determined by the single crystal X-ray diffraction studies. The single crystal XRD revealed that the material crystallized in a orthorhombic crystal system. Optical studies were carried out and it was found that the tendency of transmission observed from the specimen, with respect to the wavelength of light, is practically more suitable for opto-electronic applications. The optical band gap is found to be 4.30 eV. Optical constants such as the band gap, refractive index, reflectance, extinction coefficient and real (?_r) and imaginary (?_i) components of the dielectric constant and electric susceptibility were determined from the UV–vis–NIR spectrum. The dielectric constant and dielectric loss of zinc thiourea chloride were measured in the different frequency range from 50 Hz to 5 MHz at different temperatures. Further, electronic properties, such as valence electron plasma energy, Penn gap, Fermi energy and electronic polarizability of the grown crystal have been estimated.     

High multipolarity nuclear excitations in the continuum

The strength distributions of particle-hole isoscalar transitions with high multipolarities are considered in the framework of the independent particle model using the Woods-Saxon potential. It is shown that for the multipole operatorsj _L (qr)Y _LM withL?A ^1/3 andq?p _F the distributions are peaked at the relatively low energy for allL, and their widths decrease asL ^?1/2. In contrast to that, for the surface external fields (?U/?r)Y _LM the centroid excitation energy is proportional toL ² and the distribution widths increase asL ^4/3. The conclusion is drawn that the p-h excitations might be responsible for the structures in the excitation function observed in heavy ion collisions in the energy region up to ≈2ε _F .     

From independent particle towards collective motion for two polarized electrons on a square lattice

The two dimensional crossover from independent particle towards collective motion is studied using 2 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion in a L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. Three regimes characterize the ground state when U/t increases. Firstly, when the fluctuation Δr of the spacing r between the two particles is larger than the lattice spacing a, there is a scaling length L ₀ = π²(t/U) such that the relative fluctuation Δr/〈r〉 is a universal function of the dimensionless ratio L/L ₀, up to finite size corrections of order L^-2. L < L ₀ and L > L ₀ are respectively the limits of the free particle Fermi motion and of the correlated motion of a Wigner molecule. Secondly, when U/t exceeds a threshold U ^*(L)/t, Δr becomes smaller than a, giving rise to a correlated lattice regime where the previous scaling breaks down and analytical expansions in powers of t/U become valid. A weak random potential reduces the scaling length and favors the correlated motion. Received 28 March 2002 Published online 19 November 2002     

Dependence of excess bismuth content in precursor sols on ferroelectric and dielectric properties of Bi3.25La0.75Ti3O12 thin films fabricated by chemical solution deposition

Bi_3.25La_0.75Ti₃O₁₂ (BLT) thin films were fabricated on Pt/Ti/SiO₂/Si(1 0 0) substrates by chemical solution deposition (CSD), and the dependence of ferroelectric and dielectric properties of the as-deposited BLT thin films on excess Bi content in precursor sols was studied. It is found that the prepared BLT thin film shows the best polarization-electric field, capacitance-voltage and dielectric constant (?_r)-frequency characteristics, when the value of excess Bi content in precursor sols is 10%. In detail, its remnant polarization (2P_r) value is 40 μC/cm², the capacitance tunability is 21% measured at room temperature under conditions of an applied voltage of 8 V and measurement frequency of 10 kHz, and the ?_r is 696 at 100 kHz frequency.     

Radiation transfer in an anisotropically scattering plane-parallel medium with space-dependent albedo ω(x)

A method of analysis is presented for solving radiation-transfer problems involving space-dependent albedo ω(x) for an absorbing, emitting and anisotropically scattering plane-parallel medium with reflecting boundaries. The albedo is represented in terms of Legendre polynomials in the form ω(x) = Σ^R_r=0D_rP_r(x/L), where x is the optical variable, L is the half optical-thickness of the slab, P_r(x/L) are the Legendre polynomials and D_r are known expansion coefficients. The effects of spatial variation of albedo on the reflectivity and transmissivity of a medium having a slab geometry are examined for the cases of both forward and backward anisotropic scattering over a wide range of system variables. The effects of ω(x) on the angular distribution of radiation are also shown for some representative cases.     

Searching for a near neighbor particle in DSMC cells using pseudo-subcells

LeBeau et al. (2003) [4] introduced the ‘virtual-subcell’ (VSC) method of finding a collision partner for a given DSMC particle in a cell; all potential collision partners in the cell are examined to find the nearest neighbor, which becomes the collision partner. Here I propose a modification of the VSC method, the ‘pseudo-subcell’ (PSC) method, whereby the search for a collision partner stops whenever a ‘near-enough’ particle is found, i.e. whenever another particle is found within the ‘pseudo-subcell’ of radius δ centered on the first particle. The radius of the pseudo-subcell is given by δ = Fd_n, where d_n is the expected distance to the nearest neighbor and F is a constant which can be adjusted to give a desired trade-off between CPU time and accuracy as measured by a small mean collision separation (MCS). For 3D orthogonal cells, of various aspect ratios, d_n/L ≈ 0.746/N^0.383 where N is the number of particles in the cell and L is the cube root of the cell volume. There is a good chance that a particle will be found in the pseudo-subcell and there is a good chance that such a particle is in fact the nearest neighbor. If no particle is found within the pseudo-subcell the closest particle becomes the collision partner.     

Dual electromagnetism and magnetic monopoles

Dual electromagnetism (proposed some time ago) allows the fractional electric charges and the magnetic monopoles to exist simultaneously. In fact, the Dirac quantization condition can be numerically reduced (with some plausible assumptions) to the third component of the particle total weak isospin, which by definition is always quantized. The field angular momentum,L, of a static particle-magnetic monopole configuration is evaluated exactly; it is found that because the dual photon has a mass,M _c ,L generally depends onr, the separation between a particle and a monopole. However, sinceM _c - 130 GeV, atr > M _c ^–1 ,L is basically dominated by ordinary electromagnetism and as such very weakly dependent onr.     

Relationship between oxide-ion conductivity and dielectric relaxation in the Ln2Zr2O7 system having pyrochore-type compositions (Ln=Yb, Y, Gd, Eu, Sm, Nd, La)

Ln₂Zr₂O₇ (Ln=Yb, Y, Gd, Eu, Sm, Nd, La) system changed from fluorite (F)-type to pyrochlore (P)-type phases when the ionic radius ratios, r(Ln³⁺)/r(Zr⁴⁺), were larger than 1.26. The oxide-ion conductivity showed sharp maximum at the vicinity of the phase boundary between the F- and P-type phases. The frequency dependence of dielectric constant () and dielectric loss factor () were successfully explained by the superimposition of Debye-type polarization due to dopant-vacancy associate and electrode-electrolyte interfacial polarization by the numerical calculation. The peak of dielectric loss tangent (tan δ) was ascribed to the dopant-vacancy associate. The ε_r(0) and dielectric constant of the associate (ε_r0) showed also the maximum values at the vicinity of the phase boundary between the F- and P-type phases.     

Percolation phenomenon in barium samarium titanate-silver composite

Ba₄Sm_9.33Ti₁₈O₅₄-Ag (BST-Ag) composites were prepared by a solid-state ceramic route and its dielectric properties were investigated in the vicinity of percolation threshold. The structure and microstructure of the composites were analyzed by X-ray diffraction along with optical and scanning electron microscopy observations. The effects of silver content and frequency on the dielectric properties of BST-Ag composites were studied using a LCR meter. The relative permittivity (ε_r) of the composite increases with silver content below the percolation limit and is in agreement with power law. A 0.14 volume fraction of silver loading increases the relative permittivity of the composite from 50 to 450 at 10 kHz. Addition of 0.15 volume fraction of silver increases the relative permittivity of the composite in the order of 10⁵. It is found that the giant relative permittivity is almost constant for frequencies from 1 kHz to 1 MHz. This high ε_r composite offers the perspectives for application in electromechanical devices.     

Coadsorbate effects on adsorbate vibrational properties

A quantitative analysis of infrared absorption spectra to determine coadsorbate induced relative changes of the vibrational polarizability α_v of an adsorbate mode and of the dielectric screening ? due to this extra species is presented. Four (ternary) coadsorption systems consisting of the Ru(0 0 0 1)-(2 × 2)-(X + CO + O) layer with additional coadsorbates X = H, NO, CO, or O (all of them occupying the remaining empty fcc site) have been studied with FT-IRAS, TDS, LEED and work function change measurements. On-top CO is thereby used as a probe molecule to monitor coadsorbate effects on the dielectric properties of the layer. The vibrational polarizability α_v associated with the internal C-O stretch mode (ν_C-O) of on-top CO is lowered by all coadsorbates. The dielectric screening ? within the adsorbate layer is reduced in the presence of the atomic coadsorbates O and H whereas an increase of ? is found for the molecular coadsorbates, threefold coordinated CO and NO. The derived changes of α_v and dielectric screening ?, as well as the involved line shifts of ν_C-O and ν_Ru-CO can be understood in terms of the standard Blyholder backbonding model, i.e. CO 5σ charge donation to the metal combined with a backdonation to electronic states with 2π∗ character.     

The interaction between an atom and a surface at large separation

A simple expression is generated for the coefficient C₃ of the asymptotic dispersion interaction ~z^?3 between an atom and a surface. The basis of the derivation is the assumption of simple forms for the frequency dependence of the polarizability of the atom and the dielectric function of the solid. The expression yields the known value of C₃ within a few percent for all cases for which it has been calculated previously. We use it to generate C₃ values for a large number of systems not previously treated.     

Room temperature fabrication Oxide TFT with Y2O3 as a gate oxide and Mo contact

In this investigation, an operating voltage as low as 5 V has been achieved for Oxide TFT with Y₂O₃ as a gate oxide and a-IGZO as an active layer. The OTFT has been fabricated at room temperature using RF sputter. The mobility and threshold voltages are 11.3 cm²/V s and 3.4 V for the device with W/L = 0.8, respectively. The annealing at 400 °C in N₂ containing 5% H₂ ambient has been utilized to improve the electrical performance of TFT. The on-off current which is determined by gate dielectric has been observed to be 10⁴. It has also been observed that the dielectric properties of gate oxide deteriorate on annealing. The dielectric constant of Y₂O₃ is observed in the range between 5.1 and 5.4 measured on various devices.     

On condensation of the vortex solitons in a 2 + 1 dimensional abelian Higgs model

We study the roles of the vortex solitons in a 2 + 1 dimensional abelian Higgs model. From the effective lagrangian L_eff for the soliton field χ, it is found that the appearance of the solitons reduces the dielectric constant to a value smaller than one. If the Higgs field 〈H〉_vac does not vanish, the vacuum is in the Higgs phase and the solitons are not important. If it does vanish, the solitons become massless and L_eff has an infinite number of classically degenerate vacua. In the quantum theory of L_eff with large coupling constant e, no evidence of 〈χ〉_vac ≠ 0 has been discovered. For this conclusion to hold it is crucial that the free energy of scalar QED monotonically increases with e².     

Particle–particle Tamm–Dancoff approximation and particle–particle random phase approximation calculations for 18O and 18F nuclei

The nuclear structures of ¹⁸O and ¹⁸F nuclei are studied using particle–particle Tamm–Dancoff approximation (pp TDA) and particle–particle random phase approximation (pp RPA). All possible single-particle states of the allowed angular momenta are considered in the 0p and 1s–0d shells. The Hamiltonian is diagonalized in the presence of Warburton and Brown interactions. The results containing energy-level schemes and transition strength B(E2) are compared with the available experimental data.     

Resonance fluctuation-electromagnetic energy losses during the glancing reflection of a neutral atomic beam from the smooth amorphous surface of a solid

The energy losses of a Cs⁺ion beam are theoretically studied during its glancing reflection from a smooth amorphous surface of a dielectric or a semiconductor and films made of these materials on a metallic substrate. The conditions of resonance fluctuation-electromagnetic interaction between neutralized Cs atoms and surface polaritons are considered for surfaces where the effects of interest seem to be the most significant. Calculations indicate that, at the optimized initial glancing angle and the Cs⁺ ion beam energy (ψ_in = 0.1–1.0 mrad, E ₀ ～ 50–100 keV), the fluctuation-electromagnetic forces substantially contribute to the total energy losses and this contribution has characteristic dependences on the temperature, particle velocity, and material parameters.     

Surface Microparticles in Liquid Helium. Quantum Archimedes’ Principle

Deviations from Archimedes’ principle for spherical molecular hydrogen particles with the radius R₀ at the surface of ⁴He liquid helium have been investigated. The classical Archimedes’ principle holds if R₀ is larger than the helium capillary length L_cap ? 500 μm. In this case, the elevation of a particle above the liquid is h₊ ~ R₀. At 30 μm < R₀ < 500 μm, the buoyancy is suppressed by the surface tension and h₊ ~ R³₀/L²_cap. At R₀ < 30 μm, the particle is situated beneath the surface of the liquid. In this case, the buoyancy competes with the Casimir force, which repels the particle from the surface deep into the liquid. The distance of the particle to the surface is h_- ~ R^5/3_c/R^2/3₀ if R₀ > R_c. Here, \({R_c} \cong {\left( {\frac{{\hbar c}}{{\rho g}}} \right)^{1/5}} \approx 1\), where ? is Planck’s constant, c is the speed of light, g is the acceleration due to gravity, and ρ is the mass density of helium. For very small particles (R₀ < R_c), the distance h_ to the surface of the liquid is independent of their size, h_ = R_c.     

Phonon–particle coupling effects in the single-particle energies of semi-magic nuclei

A method is presented to evaluate the particle–phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei. In such nuclei, always there is a collective low-lying 2⁺ phonon, and a strong mixture of single-particle and particle–phonon states often occurs. As in magic nuclei the so-called g _L ² approximation, where g _L is the vertex of the L-phonon creation, can be used for finding the PC correction δΣ^PC(ε) to the initial mass operator Σ₀. In addition to the usual pole diagram, the phonon “tadpole” diagram is also taken into account. In semi-magic nuclei, the perturbation theory in δΣ^PC(ε) with respect to Σ₀ is often invalid for finding the PC-corrected single-particle energies. Instead, the Dyson equation with the mass operator Σ(ε) = Σ₀ + δΣ^PC(ε) is solved directly, without any use of the perturbation theory. Results for a chain of semi-magic Pb isotopes are presented.     

High-k Mg-doped ZST for microwave applications

The (Zr_0.8Sn_0.2)TiO₄ material (ZST), has been prepared by solid state reaction and characterized. The samples were sintered in the temperature range of 1260-1320 °C for 2 h. The effects of sintering parameters like sintering temperature (T_s) and MgO addition (0.2 wt.%) on structural and dielectric properties were investigated. Bulk density increases from 4900 to 5050 kg/m³ with the increase of sintering temperature. The effect of MgO addition is to lower the sintering temperature in order to obtain well sintered samples with high value of bulk density. The material exhibits a dielectric constant ?_r ∼ 37 and high values of the Q × f product, greater than 45,000, at microwave frequencies. The dielectric properties make the ZST material very attractive for microwave applications such as dielectric resonators, filters, dielectric antennas, substrates for hybrid microwave integrated circuits, etc.