A New Class of Inhomogeneous Cosmological Models with Electromagnetic Field in Normal Gauge for Lyra’s Manifold

A new class of exact solutions of Einstein’s modified field equations in inhomogeneous space-time for perfect fluid distribution with electromagnetic field is obtained in the context of normal gauge for Lyra’s manifold. We have obtained solutions by considering the time dependent displacement field. The source of the magnetic field is due to an electric current produced along the z-axis. Only F ₁₂ is a non-vanishing component of the electromagnetic field tensor. It has been found that the displacement vector β(t) behaves like the cosmological constant Λ in the normal gauge treatment and the solutions are consistent with the recent observations of Type Ia supernovae. Physical and geometric aspects of the models are also discussed in the presence of magnetic field.     

Exotic decay: Transition from cluster mode to fission mode

Exotic decay of some heavy nuclei with Z≥100 formed in heavy ion ‘cold fusion’ reaction were studied taking interacting barrier consisting of Coulomb and proximity potential. Calculated half-life time shows that some modes of decay are well within the present upper limit for measurements (T _1/2<10³⁰ s). Cluster formation probabilities are calculated for different clusters within fission model. It is found that transition from cluster mode to fission mode take place at mass of the cluster, A ₂=20 in exotic decay which is comparable with the value A ₂=16 of Shanmugam et al based on cubic plus Yukawa plus exponential model (CYEM).     

Competition between crystal field splitting and Hund’s rule coupling in two-orbital magnetic metal-insulator transitions

Competition between crystal field splitting and Hund’s rule coupling in magnetic metal-insulator transitions of half-filled two-orbital Hubbard model is investigated by multi-orbital slave-boson mean field theory. We show that with the increase of Coulomb interaction, the system firstly transits from a paramagnetic (PM) metal to a Néel antiferromagnetic (AFM) Mott insulator, or to a nonmagnetic orbital insulator, depending on the competition of crystal field splitting and the Hund’s rule coupling. The AFM Mott insulating, PM metallic and orbital insulating phases are not, partially and fully orbital polarized, respectively. For a small J _H and a finite crystal field, the orbital insulator is robust. These results demonstrate that large crystal field splitting favors the formation of the orbital insulating phase, while large Hund’s rule coupling tends to destroy it, driving the low-spin to high-spin transition.     

Some Exact Bianchi Type-V Perfect Fluid Cosmological Models with Heat Flow and Decaying Vacuum Energy Density Λ: Expressions for Some Observable Quantities

In this paper we have obtained some new exact solutions of Einstein’s field equations in a spatially homogeneous and anisotropic Bianchi type-V space-time with perfect fluid distribution along with heat-conduction and decaying vacuum energy density Λ by applying the variation law for generalized Hubble’s parameter that yields a constant value of deceleration parameter. We find that the constant value of deceleration parameter is reasonable for the present day universe. The variation law for Hubble’s parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential form. Using these two forms, Einstein’s field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The cosmological constant Λ is found to be a decreasing function of time and positive which is corroborated by results from recent supernovae Ia observations. Expressions for look-back time-redshift, neoclassical tests (proper distance d(z)), luminosity distance red-shift and event horizon are derived and their significance are described in detail. The physical and geometric properties of spatially homogeneous and anisotropic cosmological models are discussed.     

Energy Spectrum of Bound-Spinons in the Quantum Ising Spin-Chain Ferromagnet

We study the excitation energy spectrum in the S=1/2 ferromagnetic Ising spin chain with the easy axis z in a magnetic field h={h _x ,0,h _z }. According to Wu and McCoy’s scenario of weak confinement, the fermionic spinon excitations (kinks), being free at h _z =0 in the ordered phase, are coupled into bosonic bound states at arbitrary small h _z >0. We calculate the energy spectrum of such excitations in the leading order in small h _z , using different perturbative methods developed for the similar problem in the Ising Field Theory.     

Phase transitions of quasistationary states in the Hamiltonian Mean Field model

The out-of equilibrium dynamics of the Hamiltonian Mean Field (HMF) model is studied in presence of an externally imposed magnetic field h. Lynden-Bell’s theory of violent relaxation is revisited and shown to adequately capture the system dynamics, as revealed by direct Vlasov based numerical simulations in the limit of vanishing field. This includes the existence of an out-of-equilibrium phase transition separating magnetized and non magnetized phases. We also monitor the fluctuations in time of the magnetization, which allows us to elaborate on the choice of the correct order parameter when challenging the performance of Lynden-Bell’s theory. The presence of the field h removes the phase transition, as it happens at equilibrium. Moreover, regions with negative susceptibility are numerically found to occur, in agreement with the predictions of the theory.     

Interlaboratory comparison for the measurement of particle size and zeta potential of silica nanoparticles in an aqueous suspension

The Institute for Reference Materials and Measurements has organised an interlaboratory comparison (ILC) to allow the participating laboratories to demonstrate their proficiency in particle size and zeta potential measurements on monomodal aqueous suspensions of silica nanoparticles in the 10–100 nm size range. The main goal of this ILC was to identify competent collaborators for the production of certified nanoparticle reference materials. 38 laboratories from four different continents participated in the ILC with different methods for particle sizing and determination of zeta potential. Most of the laboratories submitted particle size results obtained with centrifugal liquid sedimentation (CLS), dynamic light scattering (DLS) or electron microscopy (EM), or zeta potential values obtained via electrophoretic light scattering (ELS). The results of the laboratories were evaluated using method-specific z scores, calculated on the basis of consensus values from the ILC. For CLS (13 results) and EM (13 results), all reported values were within the ±2 |z| interval. For DLS, 25 of the 27 results reported were within the ±2 |z| interval, the two other results were within the ±3 |z| interval. The standard deviations of the corresponding laboratory mean values varied between 3.7 and 6.5%, which demonstrates satisfactory interlaboratory comparability of CLS, DLS and EM particle size values. From the received test reports, a large discrepancy was observed in terms of the laboratory’s quality assurance systems, which are equally important for the selection of collaborators in reference material certification projects. Only a minority of the participating laboratories is aware of all the items that are mandatory in test reports compliant to ISO/IEC 17025 (ISO General requirements for the competence of testing and calibration laboratories. International Organisation for Standardization, Geneva, 2005b). The absence of measurement uncertainty values in the reports, for example, hindered the calculation of zeta scores.     

Local field distribution revisited in the light of percolation model of spin glass transition

The existence of a ‘hole’ in the local field distributionP(H) in canonical spin glasses is proved in the framework of Mookerjee and Chowdhury’s percolation model of spin glass transition.     

Lunar topographic model CLTM-s01 from Chang’E-1 laser altimeter

More than 3 million range measurements from the Chang’E-1 Laser Altimeter have been used to produce a global topographic model of the Moon with improved accuracy. Our topographic model, a 360th degree and order spherical harmonic expansion of the lunar radii, is designated as Chang’E-1 Lunar Topography Model s01 (CLTM-s01). This topographic field, referenced to a mean radius of 1738 km, has an absolute vertical accuracy of approximately 31 m and a spatial resolution of 0.25o (～7.5 km). This new lunar topogr...     

Field theoretic calculation of energy cascade rates in non-helical magnetohydrodynamic turbulence

Energy cascade rates and Kolmogorov’s constant for non-helical steady magnetohydrodynamic turbulence have been calculated by solving the flux equations to the first order in perturbation. For zero cross helicity and space dimensiond = 3, magnetic energy cascades from large length-scales to small length-scales (forward cascade). In addition, there are energy fluxes from large-scale magnetic field to small-scale velocity field, large-scale velocity field to small-scale magnetic field, and large-scale velocity field to large-scale magnetic field. Kolmogorov’s constant for magnetohydrodynamics is approximately equal to that for fluid turbulence (≈ 1.6) for Alfvén ratio 05 ≤r _A ≤ ∞. For higher space-dimensions, the energy fluxes are qualitatively similar, and Kolmogorov’s constant varies asd ^1/3. For the normalized cross helicity σ_c →1, the cascade rates are proportional to (1 − σ_c)/(1 + σ_c , and the Kolmogorov’s constants vary significantly with σ_cc.     

Infinite slabs and other weird plane symmetric space–times with constant positive density

We present the exact solution of Einstein’s equation corresponding to a static and plane symmetric distribution of matter with constant positive density located below z = 0. This solution depends essentially on two constants: the density ρ and a parameter κ. We show that these space–times finish down below at an inner singularity at finite depth. We show that for κ ≥ 0.3513 . . . the dominant energy condition is satisfied all over the space–time. We match this solution to the vacuum one and compute the external gravitational field in terms of slab’s parameters. Depending on the value of κ, these slabs can be attractive, repulsive or neutral. In the first case, the space–time also finishes up above at an empty repelling singular boundary. In the other cases, they turn out to be semi-infinite and asymptotically flat when z → ∞. We also find solutions consisting of joining an attractive slab and a repulsive one, and two neutral ones. We also discuss how to assemble a “gravitational capacitor” by inserting a slice of vacuum between two such slabs.     

Phase transition in liquid 3He in an aerogel at zero temperature

An expansion of the thermodynamic potential in powers of the order parameter of the superfluid phase transition is found for liquid ³He in an aerogel at T=0. The discontinuity in the compressibility (sound velocity), which is the analog of the discontinuity in the specific heat for second-order temperature phase transitions, is calculated. The magnitude of the critical quantum fluctuations (zero-point vibrations) of the order parameter is estimated. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 10, 655–660 (25 November 1997)     

On the phase transition d→(s±id) in high-T c superconductors

A model with an attractive potential in the s and d channels is studied. It is found that in a definite interval of the ratio of the s and d components of the potential the model undergoes a second-order phase transition from the d to the (s±id) state, with breaking of time-reversal symmetry. The transition temperature and the jump in the specific heat are calculated. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 570–574 (25 October 1996)     

An analytical statistical model for the RMS delay spread parameter in millimeter frequencies

A new statistical model for rms delay spread is presented. The model has been developed under the assumption of the existence of two paths (two-path model). It is assumed that the amplitude of each path follows the so-called log-Student distribution with one degree of freedom, while the differential propagation delay of the two paths follows the uniform distribution. The parameters involved with the model are m_z and s_z the mean and standard deviation of the ratio of the two paths’ amplitudes. Theoretical curves for τ_rms as well as for the mean and standard deviation of τ_rms are plotted for different values of m_z and s_z. These curves are extremely useful for the choice of the parameters of the model for different cases. In order to examine the validity of the new model, measurements from the literature have been collected and compared with the theoretical results. In all cases a very good agreement, according to the X-square criterion, between theoretical and experimental curves has been observed. As a result, the new model can be used by system engineers for the development of wireless high bit-rate digital systems that will not suffer from intersymbol interference.     

Impact of Slip Cycles on the Operation Modes and Efficiency of Molecular Motors

Kinesin is a motor molecule that moves processively on microtubule tracks and is involved in active intracellular transport processes. For small loads, it is powered by the hydrolysis of one ATP molecule per step. Here we extent our previously introduced network theory in order to study the possibility of two different mechanical stepping transitions and the general behavior of the motor’s efficiency. Our theory shows explicitly how chemical and mechanical slip cycles emerge that weaken the coupling between ATP hydrolysis and mechanical stepping. Near chemomechanical equilibrium, the motor efficiency η may vary between η=1 for tight coupling and η=0 for loose coupling, depending on the relevance of the slip cycles. Far from chemomechanical equilibrium, on the other hand, the motor efficiency is found to decay as 1/Δμ with increasing Δμ irrespective of the presence of slip cycles, where Δμ represents the reaction free enthalpy or chemical potential difference per ATP hydrolysis.     

Crystal field in valence-fluctuating CeNi-based compounds

The effects of the crystal field (CF) on the paramagnetic Pr ion in a number of compounds of the type R_1−x Pr_xNi (R = Ce, La, Y), in which a transition of the cerium ions from an intermediate-valence into a Kondo state occurs as La is substituted for Ce, are investigated. The level schemes of the Pr ion in the CF are reconstructed from inelastic neutron scattering spectra and the temperature dependence of the heat capacity in different magnetic fields (B=0–8 T). The parameters of the low-symmetry CF in the compounds RNi are determined from the experimental data. It is established that in the Kondo regime the hybridization of the f electrons with conduction electrons only gives a proportional increase in all the parameters of the CF potential. At the same time, partial delocalization of the f electrons in the intermediate-valence state results in charge redistribution, which is manifested in different scales for the changes in the different CF parameters. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 12, 947–952 (25 June 1996)     

Anisotropy of rotation of nitroxide probes in nematogenic liquid crystals

An electron paramagnetic resonance (EPR) line shape simulation for nitroxide spin probes in the motional narrowing region was carried out assuming axially symmetricg andA tensors and with different anisotropies of rotationN (=R _∥/R _⊥) whereR _∥ andR _⊥ are, respectively, elements of the diffusion tensor along and perpendicular to its principal axisz′. In addition, it was assumed that the principal axes of the diffusion tensor coincide with the molecular axes. Each of three casesz′=x,z′=y andz′=z, which result from cyclic permutations of the molecular axesx, y andz with thez′,y′ andx′ axes of the diffusion tensor, yields its typical EPR spectrum characterized by the relative intensities of the low-, center- and high-field lines. The parameter δ defined by and calculable from the intensities of the three lines was found to vary linearly withN for thez′=x andz′=y cases and, as anticipated, to be practically constant at a value of 1 for thez′=z case. This suggested a method for estimatingN for a probe from its EPR spectrum. Experimental spectra over a narrow temperature range (1°C) in the vicinity of the nematic-to-isotropic transition (about 34.6°C) ofN-(4-n-butylbenzilidene)-4-amino-2,2,6,6-tetramethylpiperidine-1-oxide at a mole fraction of 1·10⁻³ in 4-n-pentyl-4′-cyanobiphenyl showed a pattern of peak heights characteristic of thez′=x case with δ values that gave, neglecting effects of the mean field, higher and lowerN values in the nematic and isotropic regions, respectively. Analysis of other similar systems in the literature gave similar results.     

Planck’s Constant in the Light of Quantum Logic

The goal of quantum logic is the “bottom-top” reconstruction of quantum mechanics. Starting from a weak quantum ontology, a long sequence of arguments leads to quantum logic, to an orthomodular lattice, and to the classical Hilbert spaces. However, this abstract theory does not yet contain Planck’s constant ℏ. We argue, that ℏ can be obtained, if the empty theory is applied to real entities and extended by concepts that are usually considered as classical notions. Introducing the concepts of localizability and homogeneity we define objects by symmetry groups and systems of imprimitivity. For elementary systems, the irreducible representations of the Galileo group are projective and determined only up to a parameter z, which is given by z=m/ℏ, where m is the mass of the particle and ℏ Planck’s constant. We show that ℏ has a meaning within quantum mechanics, irrespective of use the of classical concepts in our derivation.     

Magnetically trapped atoms for compact atomic clocks

We investigate the hyperfine transition of magnetically trapped non-condensed atoms. The two principal frequency shifts, the second order Zeeman effect and the mean field interaction are considered. Analytic models of the mean frequency and its trap induced spread are developed. Comparisons with existing experiments evaluate the role of the atoms’ oscillatory motion. The analytic model proves to be equivalent to existing Monte Carlo simulations. The formulae provide a simple tool for optimising the design of a new experiment. Applied to the two-photon transition |F=1,m _F =−1〉→|F=2,m _F =1〉 in ⁸⁷Rb and the conditions of a typical atom chip experiment, a line spread as small as 11 mHz is predicted giving a quality factor of 10¹². The system is promising for application in precision instruments such as compact atomic clocks.