Showing papers in "European Physical Journal Plus in 2011"

FIGARO: The new horizontal neutron reflectometer at the ILL

Abstract: Fluid Interfaces Grazing Angles ReflectOmeter (FIGARO) is the new horizontal neutron reflectometer at the Institut Laue-Langevin, Grenoble, France. It is a versatile, high-flux time-of-flight instrument with features suitable for a range of studies in soft condensed matter, chemistry, physics and biology both at free air/liquid interfaces and buried liquid/liquid and solid/liquid interfaces. Most of the experiments exploit isotopic contrast variation to determine the structure and composition of surface layers. Multiple chopper discs allow variable wavelength resolution, with the loose-resolution options increasing the available neutron flux for fast kinetic studies of thin films and improving the data acquisition efficiency from complex samples requiring multiple contrast measurements. It is possible to approach the interface with neutrons from below or above the horizon. The instrument is equipped with a range of sample environments including free liquid adsorption troughs, a Langmuir trough, an overflowing cylinder and a range of solid/liquid sample cells. FIGARO was launched as a user instrument in April 2009 and its success has been steadily increasing since. This article includes an introduction to the scientific case, detailed sections on the instrument components and performance, and descriptions of standard sample environments developed to date as well as some selected early scientific highlights.

N-body simulations of gravitational dynamics

Abstract: We describe the astrophysical and numerical basis of N -body simulations, both of collisional stellar systems (dense star clusters and galactic centres) and collisionless stellar dynamics (galaxies and large-scale structure). We explain and discuss the state-of-the-art algorithms used for these quite different regimes, attempt to give a fair critique, and point out possible directions of future improvement and development. We briefly touch upon the history of N -body simulations and their most important results.

Design and performance of horizontal-type neutron reflectometer SOFIA at J-PARC/MLF

Abstract: Neutron reflectometry is a powerful method for investigating the surface and interfacial structures of materials in the spatial range from nanometers to sub-micrometers. At the Japan Proton Accelerator Research Complex (J-PARC), a high-intensity pulsed neutron beam is produced with a proton accelerator at 220kW, which will be upgraded to 1MW in future. Beamline 16 (BL16) at the Materials and Life Science Experimental Facility (MLF) in J-PARC is dedicated to a horizontal-type reflectometer, and in this beamline, neutrons are transported downward at two different angles, 2.2° and 5.7° , relative to the horizontal. In December 2008, we started to accept the neutron beam at BL16 with the old ARISA reflectometer relocated from the KENS facility, KEK, Japan; and we have now replaced it with the brand-new reflectometer SOFIA (SOFt Interface Analyzer). With a high-flux beam and instrumental upgrade, the observable reflectivity of SOFIA reaches around 10−7 within a few hours for specimens on 3” substrates. In this paper, we will present the design and performance of the SOFIA reflectometer, and discuss some preliminary results on the device development for further upgrade.

Ultraviolet Complete Quantum Gravity

Abstract: An ultraviolet complete quantum gravity theory is formulated in which vertex functions in Feynman graphs are entire functions and the propagating graviton is described by a local, causal propagator. The cosmological constant problem is investigated in the context of the ultraviolet complete quantum gravity. In the entire vertex functions, constantsSM andG determine the energy scales in the standard model (SM) of particle interactions and gravitation, respectively. The SM energy scaleSM and the gravity energy scaleG are determined by the UV complete SM particle interactions as compared to the graviton interactions. The SM particle radiative corrections have an energy scaleSM > 1 TeV or a length scale lSM < 10 −16 cm, whereas the graviton radiative corrections remain local at a lower energy scale. Thus, the fundamental energy scales in the theory are determined by the underlying physical nature of the particles and fields and do not correspond to arbitrary cut-offs, which destroy the gauge invariance, unitarity and local Lorentz invariance of the field theory. The accurate values of the energy scalesSM andG can be determined by experiment. They are to be considered fundamental constants of nature. In our quantum

A physical explanation to the controversial Urbach tailing universality

Abstract: Doping-related behavior divergence of some crystalline materials has raised doubts about Urbach tailing universality. In this paper, we infer the atomic scale interpretation of this divergence on the basis of experimental records and comparative studies. We focus on a widely known wurtzite structured crystal and find that Urbach tailing was inhibited once doping charged loci succeeded to establish local coordinated donors networks or so-called topological filaments. The case of doping-free and saturated ZnO networks unexpected Urbach tailing features has been discussed. All the observed behaviors confirm the Urbach tailing universality despite their controversial aspect.

Pencil beam characteristics of the next-generation proton scanning gantry of PSI: design issues and initial commissioning results

Abstract: In this paper we report on the main design features, on the realization process and on selected first results of the initial commissioning of the new Gantry 2 of PSI for the delivery of proton therapy with new advanced pencil beam scanning techniques. We present briefly the characteristics of the new gantry system with main emphasis on the beam optics, on the characterization of the pencil beam used for scanning and on the performance of the scanning system. The idea is to give an overview of the major components of the whole system. The main long-term technical goal of the new equipment of Gantry 2 is to expand the use of pencil beam scanning to the whole spectrum of clinical indications including moving targets. We report here on the initial experience and problems encountered in the development of the system with selected preliminary results of the ongoing commissioning of Gantry 2.

Discovering Technicolor

Abstract: We provide a pedagogical introduction to extensions of the Standard Model in which the Higgs is composite These extensions are known as models of dynamical electroweak symmetry breaking or, in brief, Technicolor Material covered includes: motivations for Technicolor, the construction of underlying gauge theories leading to minimal models of Technicolor, the comparison with electroweak precision data, the low energy effective theory, the spectrum of the states common to most of the Technicolor models, the decays of the composite particles and the experimental signals at the Large Hadron Collider The level of the presentation is aimed at readers familiar with the Standard Model but who have little or no prior exposure to Technicolor Several extensions of the Standard Model featuring a composite Higgs can be reduced to the effective Lagrangian introduced in the text We establish the relevant experimental benchmarks for Vanilla, Running, Walking, and Custodial Technicolor, and a natural fourth family of leptons, by laying out the framework to discover these models at the Large Hadron Collider

The status of CNAO

Abstract: The CNAO (Italian acronym that stands for National Centre for Oncological Hadrontherapy) has been realised in Pavia, Italy. It is a clinical facility created and financed by the Italian Ministry of Health and conceived to supply hadrontherapy treatments to patients recruited all over the Country. A qualified network of clinical and research institutes, the CNAO Collaboration, has been created to build and to run the centre. This organizational model turned out to be very efficient and fruitful to reach the goal of introducing the most advanced techniques and procedures of hadrontherapy. Three treatment rooms with four beam ports (three horizontal and one vertical) are operational and one experimental room has been built. Beams of protons with kinetic energies up to 250MeV and beams of carbon ions with maximum kinetic energy of 400MeV/u are transported and delivered by active scanning systems. The machine operation started in 2009 with the commissioning of the high-technology components that form the acceleration chain from the sources to the patient. The dosimetry and radiobiology tests have been completed with proton beams and CNAO obtained the authorisation to start treating patients. Statistics from the Italian Association of Radiotherapists and Oncologists (AIRO) have estimated that more than 3% of the overall Italian radiotherapy annual patients, i.e. more than 3000 new patients per year, would preferably be treated with hadrontherapy, but this number is steadily increasing. Pre-selection criteria are defined on the basis of established clinical protocols and the hospitals and the clinics in the network will address to the CNAO those patients that satisfy the criteria. This paper outlines the project development, the technical aspects of the realisation and commissioning and the clinical issues relevant for the patients treatments at CNAO.

Which group velocity of light in a dispersive medium

Abstract: The interaction between a light pulse, traveling in air, and a generic linear, non-absorbing and dispersive structure is analyzed. It is shown that energy conservation imposes a constraint between the group velocities of the transmitted and reflected light pulses. It follows that the two fields propagate with group velocities depending on the dispersive properties of the environment (air) and on the transmission properties of the optical structure, and are one faster and the other slower than that of the incident field. In other words, the group velocity of a light pulse in a dispersive medium is reminiscent of previous interactions. One example is discussed in detail.

The TOP-IMPLART project

Abstract: A new proton therapy center is planned to be built in Rome, Italy. The project, named TOP-IMPLART, is developed by three institutions, ENEA (Agenzia Nazionale per le Nuove tecnologie, l’Energia e lo Sviluppo Economico Sostenibile - Italian national agency for new technologies, energy and sustainable economic development), ISS (Istituto Superiore di Sanita, Italian National Institute of Health) and IFO-IRE (Istituto Fisioterapico Ospedaliero - Istituto Regina Elena, Regina Elena, National Cancer Institute in Rome). The project is centered on a medium-energy proton accelerator designed as a sequence of linear accelerators. Two phases of construction are foreseen: the first (funded by the Italian Regione Lazio for 11 M€ spread over four years) with a maximum energy of 150 MeV and the second one up to 230 MeV. The segment up to 150 MeV is under construction and will be tested at the ENEA Research Center in Frascati before the transfer to IFO that is the clinical user. The basic concepts of the design are described here.

On the black-hole/qubit correspondence

Abstract: The entanglement classification of four qubits is related to the extremal black holes of the 4-dimensional STU model via a time-like reduction to three dimensions. This correspondence is generalised to the entanglement classification of a very special four-way entanglement of eight qubits and the black holes of the maximally supersymmetric N = 8 and exceptional magic N = 2 supergravity theories.

Testing gravitational physics with satellite laser ranging

Abstract: Laser ranging, both Lunar (LLR) and Satellite Laser Ranging (SLR), is one of the most accurate techniques to test gravitational physics and Einstein’s theory of General Relativity. Lunar Laser Ranging has provided very accurate tests of both the strong equivalence principle, at the foundations of General Relativity, and of the weak equivalence principle, at the basis of any metric theory of gravity; it has provided strong limits to the values of the so-called PPN (Parametrized Post-Newtonian) parameters, that are used to test the post-Newtonian limit of General Relativity, strong limits to conceivable deviations to the inverse square law for very weak gravity and accurate measurements of the geodetic precession, an effect predicted by General Relativity. Satellite laser ranging has provided strong limits to deviations to the inverse square gravity law, at a different range with respect to LLR, and in particular has given the first direct test of the gravitomagnetic field by measuring the gravitomagnetic shift of the node of a satellite, a frame-dragging effect also called Lense-Thirring effect. Here, after an introduction to gravitomagnetism and frame-dragging, we describe the latest results in measuring the Lense-Thirring effect using the LAGEOS satellites and the latest gravity field models obtained by the space mission GRACE. Finally, we describe an update of the LARES (LAser RElativity Satellite) mission. LARES is planned for launch in 2011 to further improve the accuracy in the measurement of frame-dragging.

CATANA protontherapy facility: The state of art of clinical and dosimetric experience

Abstract: After nine years of activity, about 220 patients have been treated at the CATANA Eye Protontherapy facility. A 62MeV proton beam produced by a Superconducting Cyclotron is dedicated to radiotherapy of eye lesions, as uveal melanomas. Research and development work has been done to test different dosimetry devices to be used for reference and relative dosimetry, in order to achieve dose delivering accuracy. The follow-up results demonstrated the efficacy of proton beams and encouraged us in our activity in the fight against cancer.

Reflectometry techniques on the Second Target Station at ISIS: Methods and science

Abstract: Three reflectometers have been built on the Second Target Station at the ISIS neutron facility. These instruments: INTER, POLREF and OFFSPEC take advantage of the high flux and broad bandwidth available on the Second Target Station to provide experimental opportunities in the study of soft matter and thin film magnetism.

Cosmic evolution in Brans-Dicke chameleon cosmology

Abstract: We have investigated the Brans-Dicke chameleon theory of gravity and obtained exact solutions of the scale factor a(t) , the scalar field $ \phi$ (t) , an arbitrary function f ( $ \phi$ ) which interact with the matter Lagrangian in the action of the Brans-Dicke chameleon theory and the potential V( $ \phi$ ) for different epochs of the cosmic evolution. We plot the functions a(t) , $ \phi$ (t) , f (t) and V( $ \phi$ ) for different values of the Brans-Dicke parameter. In our models, there is no accelerating solution, only a decelerating one with q > 0 . The physical cosmological distances have been investigated carefully. Further, the statefinder parameters pair and deceleration parameter are discussed.

Transverse spin structure of the nucleon through target single-spin asymmetry in semi-inclusive deep-inelastic (e, e′π ±) reaction at Jefferson lab

Abstract: Jefferson Lab (JLab) 12 GeV energy upgrade provides a golden opportunity to perform precision studies of the transverse spin and transverse-momentum-dependent structure in the valence quark region for both the proton and the neutron. In this paper, we focus our discussion on a recently approved experiment on the neutron as an example of the precision studies planned at JLab. The new experiment will perform precision measurements of target Single-Spin Asymmetries (SSA) from semi-inclusive electro-production of charged pions from a 40 cm long transversely polarized ^3He target in deep-inelastic-scattering kinematics using 11 and 8.8 GeV electron beams. This new coincidence experiment in Hall A will employ a newly proposed solenoid spectrometer (SoLID). The large acceptance spectrometer and the high polarized luminosity will provide precise 4D (x , z , PT and Q^2) data on the Collins, Sivers, and pretzelosity asymmetries for the neutron through the azimuthal angular dependence. The full 2π azimuthal angular coverage in the lab is essential in controlling the systematic uncertainties. The results from this experiment, when combined with the proton Collins asymmetry measurement and the Collins fragmentation function determined from the e^+e^- collision data, will allow for a quark flavor separation in order to achieve a determination of the tensor charge of the d quark to a 10% accuracy. The extracted Sivers and pretzelosity asymmetries will provide important information to understand the correlations between the quark orbital angular momentum and the nucleon spin and between the quark spin and nucleon spin.

Ultraviolet Complete Electroweak Model Without a Higgs Particle

Abstract: An electroweak model with running coupling constants described by an energy dependent entire function is utraviolet complete and avoids unitarity violations for energies above 1 TeV. The action contains no physical scalar fields and no Higgs particle and the physical electroweak model fields are local and satisfy microcausality. The W and Z masses are compatible with a symmetry breaking SU(2)L×U(1)Y $ \rightarrow$ U(1)em , which retains a massless photon. The vertex couplings possess an energy scale $ \Lambda_{W}^{}$ > 1 TeV predicting scattering amplitudes that can be tested at the LHC.

MedAustron—Project overview and status

Abstract: MedAustron is the Austrian ion therapy and research centre, presently under construction in Wiener Neustadt, Austria. The facility is based on a synchrotron which will deliver proton beams with kinetic energies up to 250 MeV and carbon ion beams up to 400 MeV/nucleon for clinical applications. In addition to the clinical applications, the accelerator will provide beams for nonclinical research in the fields of medical radiation physics, radiation biology and experimental physics with a proton energy range extended beyond medical requirements to 800MeV. An overview is given on the historical development of the project. The main design features of the accelerator facilities and medical facilities are presented and the actual status of the project is summarized.

On the Weyl algebra for a particle on a sphere

Abstract: We study the Weyl algebra A pertaining to a particle constrained on a sphere, which is generated by the coordinates n and by the angular momentum J . A is the algebra E3 of the Euclidean group in space. We find its irreducible representations by a novel approach, by showing that they are the irreducible representations (l0, 0) of so(3, 1) , with l0 or -l0 being equal to the Casimir operator J.n . Any integer or half-integer l0 is allowed. The Hilbert space of a particle of spin S hosts 2S + 1 such representations. J can be analyzed into the sum L + S , i.e. pure spin states can be identified, provided 2S + 1 irreducible representations of A are glued together. These results apply to any surface which is diffeomorphic to S2.

A compact biquaternionic formulation of massive field equations in gravi-electromagnetism

Abstract: In this paper, after presenting the biquaternion formalism, a new formulation is proposed for the massive gravi-electromagnetism with monopole terms. By combining the generalized field equations in electromagnetism with the Maxwell-type field equations in gravity, a compact expression for gravi-electromagnetism has been derived. The gravi-electromagnetic wave equation including Proca-type generalization and monopole terms is obtained in compact and elegant manner. Similarly, the most generalized form of Klein-Gordon equation has been developed for the particle carrying simultaneously both electromagnetic charges and gravitational masses.

SPEAR — ToF neutron reflectometer at the Los Alamos Neutron Science Center

Abstract: This article discusses the Surface ProfilE Analysis Reflectometer (SPEAR), a vertical scattering geometry time-of-flight reflectometer, at the Los Alamos National Laboratory Lujan Neutron Scattering Center. SPEAR occupies flight path 9 and receives spallation neutrons from a polychromatic, pulsed (20Hz) source that pass through a liquid-hydrogen moderator at 20K coupled with a Be filter to shift their energy spectrum. The spallation neutrons are generated by bombarding a tungsten target with 800MeV protons obtained from an accelerator. The process produces an integrated neutron flux of ∼ 3.4×106 cm−2 s−1 at a proton current of 100μA. SPEAR employs choppers and frame overlap mirrors to obtain a neutron wavelength range of 4.5–16 A. SPEAR uses a single 200mm long 3He linear position-sensitive detector with ∼ 2 mm FWHM resolution for simultaneous studies of both specular and off-specular scattering. SPEAR’s moderated neutrons are collimated into a beam which impinges from above upon a level sample with an average angle of 0.9° to the horizontal, to facilitate air-liquid interface studies. In the vertical direction, the beam converges at the sample position. The neutrons can be further collimated to the desired divergence by finely slitting the beam using a set of two 10B4C slit packages. The instrument is ideally suited to study organic and inorganic thin films with total thicknesses between 5 and 3000 A in a variety of environments. Specifically designed sample chambers available at the instrument provide the opportunity to study biological systems at the solid-liquid interface. SPEAR’s unique experimental capabilities are demonstrated by specific examples in this article. Finally, an outlook for SPEAR and perspectives on future instrumentation are discussed.

Validation and Verification of MCNP6 Against Intermediate and High-Energy Experimental Data and Results by Other Codes

Abstract: MCNP6, the latest and most advanced LANL transport code representing a recent merger of MCNP5 and MCNPX, has been Validated and Verified (VV we continue our work to solve all the known problems before MCNP6 is distributed to the public.

Anchoring functional molecules on TiO2 surfaces: A comparison between the carboxylic and the phosphonic acid group

Abstract: The adsorption of formic acid on clean TiO2 anatase (101) and rutile (110) surfaces is studied by density-functional-based methods and compared with the results for coupling related phosphonic acids to titania surfaces. The preferred adsorption mode of the formic acid on both surfaces is a dissociative bridging bidentate complex, which is similar to the adsorption geometry of phosphonic acid. Higher adsorption energies and shorter Ti-O bond lengths indicate that phosphonic acid binds more strongly to TiO2 than formic acid. The preference for the bidentate adsorption mode is supported by a detailed analysis of the charge distribution in the adsorption complexes. The strong interfacial electronic coupling between the adsorbate orbitals and the electronic states of the anatase (101) surface slab leads to additional states in the band gap of the clean surface. For rutile (110) no or only weak coupling of the adsorbate orbitals and the surface states occurs at the band edges, which leads to an increase of the band gap.

Observation of the February 2011 Forbush decrease by the EEE telescopes

Abstract: The Forbush decrease following the large X2 solar flare on mid-February 2011 has been observed by the muon telescopes of the EEE Project, which are located in several Italian sites and at CERN. Data from two different telescopes of the EEE network have been analyzed and compared to those measured by neutron monitor stations. The variation of the muon counting rate during the Forbush decrease was also extracted for different intervals of the azimuthal angle of the incoming muons.

Exact solution of the EM radiation-reaction problem for classical finite-size and Lorentzian charged particles

Abstract: An exact solution is given to the classical electromagnetic (EM) radiation-reaction (RR) problem, originally posed by Lorentz. This refers to the dynamics of classical non-rotating and quasi-rigid finite-size particles subject to an external prescribed EM field. A variational formulation of the problem is presented. It is shown that a covariant representation for the EM potential of the self-field generated by the extended charge can be uniquely determined, consistent with the principles of classical electrodynamics and relativity. By construction, the retarded self-4-potential does not possess any divergence, contrary to the case of point charges. As a fundamental consequence, based on the Hamilton variational principle, an exact representation is obtained for the relativistic equation describing the dynamics of a finite-size charged particle (RR equation), which is shown to be realized by a second-order delay-type ODE. Such equation is proved to apply also to the treatment of Lorentzian particles, i.e., point-masses with finite-size charge distributions, and to recover the usual LAD equation in a suitable asymptotic approximation. Remarkably, the RR equation admits both standard Lagrangian and conservative forms, expressed, respectively, in terms of a non-local effective Lagrangian and a stress-energy tensor. Finally, consistent with the Newton principle of determinacy, it is proved that the corresponding initial-value problem admits a local existence and uniqueness theorem, namely it defines a classical dynamical system.

Methodological challenges in combining quantum-mechanical and continuum approaches for materials science applications

Abstract: Multi-methodological approaches combining quantum-mechanical and/or atomistic simulations with continuum methods have become increasingly important when addressing multi-scale phenomena in computational materials science. A crucial aspect when applying these strategies is to carefully check, and if possible to control, a variety of intrinsic errors and their propagation through a particular multi-methodological scheme. The first part of our paper critically reviews a few selected sources of errors frequently occurring in quantum-mechanical approaches to materials science and their multi-scale propagation when describing properties of multi-component and multi-phase polycrystalline metallic alloys. Our analysis is illustrated in particular on the determination of i) thermodynamic materials properties at finite temperatures and ii) integral elastic responses. The second part addresses methodological challenges emerging at interfaces between electronic structure and/or atomistic modeling on the one side and selected continuum methods, such as crystal elasticity and crystal plasticity finite element method (CEFEM and CPFEM), new fast Fourier transforms (FFT) approach, and phase-field modeling, on the other side.

Hamiltonian formulation for the classical EM radiation-reaction problem: Application to the kinetic theory for relativistic collisionless plasmas

Abstract: A notorious difficulty in the covariant dynamics of classical charged particles subject to non-local electromagnetic (EM) interactions arising in the EM radiation-reaction (RR) phenomena is due to the definition of the related non-local Lagrangian and Hamiltonian systems. As a basic consequence, the lack of a standard Lagrangian/Hamiltonian formulation in the customary asymptotic approximation for the RR equation may inhibit the construction of consistent kinetic and fluid theories. In this paper the issue is investigated in the framework of Special Relativity. It is shown that, for finite-size spherically-symmetric classical charged particles, non-perturbative Lagrangian and Hamiltonian formulations in standard form can be obtained, which describe particle dynamics in the presence of the exact EM RR self-force. As a remarkable consequence, based on axiomatic formulation of classical statistical mechanics, the covariant kinetic theory for systems of charged particles subject to the EM RR self-force is formulated in Hamiltonian form. A fundamental feature is that the non-local effects enter the kinetic equation only through the retarded particle 4-position. This permits, in turn, the construction of the related fluid equations, in which the non-local contributions carried by the RR effects are explicitly displayed. In particular, it is shown that the moment equations obtained in this way do not contain higher-order moments, allowing as a consequence the adoption of standard closure conditions. A remarkable aspect of the theory is related to the short delay-time asymptotic expansions. Here it is shown that two possible expansions are permitted. Both can be implemented for the single-particle dynamics as well as for the corresponding kinetic and fluid treatments. In the last case, they are performed a posteriori, namely on the relevant moment equations obtained after integration of the kinetic equation over the velocity space. Comparisons with the literature are pointed out.

Does accelerating universe indicate Brans-Dicke theory?

Abstract: The evolution of the universe in Brans-Dicke (BD) theory is discussed in this paper. Considering a parameterized scenario for BD scalar field φ = φ 0 a α which plays the role of gravitational constant G, we apply the Markov Chain Monte Carlo method to investigate a global constraints on BD theory with a self-interacting potential according to the current observational data: the Union2 dataset of type-Ia supernovae (SNIa), the high-redshift Gamma-Ray Bursts (GRBs) data, the observational Hubble data (OHD), the cluster X-ray gas mass fraction, the baryon acoustic oscillation (BAO), and the cosmic microwave background (CMB) data. It is shown that an expanded universe from deceleration to acceleration is given in this theory, and the constraint results of dimensionless matter density Ω 0m and parameter α are, Ω 0m = 0.286 −0.039−0.047 +0.037+0.050 and α = 0.0046 −0.0171−0.0206 +0.0149+0.0171 which is consistent with the result of current experiment exploration, |α| ≤ 0.132124. In addition, we use the geometrical diagnostic method, jerk parameter j, to distinguish the BD theory and the cosmological constant model in Einstein’s theory of general relativity.

On phase-field modeling with a highly anisotropic interfacial energy

Abstract: We report on phase-field approaches that allow for anisotropies sufficiently high so that the interface develops sharp corners due to missing crystallographic orientations. This implies the necessity of a regularization that enforces local equilibrium at the corners, and we use the method of Eggelston et al. (Physica D 150, 91 (2001)), generalized to arbitrary crystal symmetries and rotations of the crystalline axes. Two different anisotropic phase-field formulations are presented and discussed: The classical model that allows the interface to vary with orientation, and another more recent formulation that has a constant interface width. We develop an explicit finite-difference scheme that combines a two-step differentiation with a stagnation grid formulation. The presented numerical implementation is stable and accurate enough to account for odd crystal symmetries and high angle rotations of the initial crystalline orientation. Even in the case of highly anisotropic interfacial energies, both formulations show excellent agreement with the well-known Wulff construction of the equilibrium shape of a particle embedded in a matrix.

FRW universe models in conformally flat-spacetime coordinates I: General formalism

Abstract: The 3 -space of a universe model is defined at a certain simultaneity. Hence space depends on which time is used. We find a general formula generating all known and also some new transformations to conformally flat-spacetime coordinates. A general formula for the recession velocity is deduced.