A Maximum Mass-to-Size Ratio in Scalar-Tensor Theories of Gravity

We derive a modified Buchdahl inequality for scalar-tensor theories of gravity. In general relativity, Buchdahl has shown that the maximum value of the mass-to-size ratio, $2M/R$, is 8/9 for static and spherically symmetric stars under some physically reasonable assumptions. We formally apply Buchdahl's method to scalar-tensor theories and obtain theory-independent inequalities. After discussing the mass definition in scalar-tensor theories, these inequalities are related to a theory-dependent maximum mass-to-size ratio. We show that its value can exceed not only Buchdahl's limit, 8/9, but also unity, which we call {\it the black hole limit}, in contrast to general relativity. Next, we numerically examine the validity of the assumptions made in deriving the inequalities and the applicability of our analytic results. We find that the assumptions are mostly satisfied and that the mass-to-size ratio exceeds both Buchdahl's limit and the black hole limit. However, we also find that this ratio never exceeds Buchdahl's limit when we impose the further condition, $\rho-3p\ge0$, on the density, $\rho$, and pressure, $p$, of the matter.Comment: 23 pages, 13 figures and 1 tabl

Anti-arthritic actions of β-cryptoxanthin against the degradation of articular cartilage in vivo and in vitro

An inverse correlation between the morbidity of rheumatoid arthritis and daily intake of β-cryptoxanthin has been epidemiologically shown. In this study, we investigated the effects of β-cryptoxanthin on the metabolism of cartilage extracellular matrix in vivo and in vitro. Oral administration of β-cryptoxanthin (0.1–1 mg/kg) to antigen-induced arthritic rats suppressed the loss of glycosaminoglycans in articular cartilage, which is accompanied by the interference of aggrecanase-mediated degradation of aggrecan. Inhibition of the interleukin 1α (IL-1α)-induced aggrecan degradation by β-cryptoxanthin was also observed with porcine articular cartilage explants in culture. β-Cryptoxanthin (1–10 μM) dose-dependently down-regulated the IL-1α-induced gene expression of aggrecanase 1 (ADAMTS-4) and aggrecanase 2 (ADAMTS-5) in cultured human chondrocytes. Moreover, β-cryptoxanthin was found to augment the gene expression of aggrecan core protein in chondrocytes. These results provide novel evidence that β-cryptoxanthin exerts anti-arthritic actions and suggest that β-cryptoxanthin may be useful in blocking the progression of rheumatoid arthritis and osteoarthritis

Matrix biorthogonal polynomials on the unit circle and non-Abelian Ablowitz-Ladik hierarchy

Adler and van Moerbeke \cite{AVM} described a reduction of 2D-Toda hierarchy called Toeplitz lattice. This hierarchy turns out to be equivalent to the one originally described by Ablowitz and Ladik \cite{AL} using semidiscrete zero-curvature equations. In this paper we obtain the original semidiscrete zero-curvature equations starting directly from the Toeplitz lattice and we generalize these computations to the matrix case. This generalization lead us to the semidiscrete zero-curvature equations for the non-abelian (or multicomponent) version of Ablowitz-Ladik equations \cite{GI}. In this way we extend the link between biorthogonal polynomials on the unit circle and Ablowitz-Ladik hierarchy to the matrix case.Comment: 23 pages, accepted on publication on J. Phys. A., electronic link: http://stacks.iop.org/1751-8121/42/36521

Positive and negative ion emission from microdroplets by MeV energy ions

XXIX International Conference on Photonic, Electronic, and Atomic Collisions (ICPEAC2015): 22–28 July 2015, Toledo, SpainWe have developed a new experimental setup that allowed us to study collision interactions between fast ion beams and liquid droplets under a vacuum condition. Droplets of water and ethanol are irradiated with 0.4-1.5 MeV H+ and 2.0 MeV C2+ ions. The droplet diameter is estimated from energy loss measurements of projectile ions penetrating through droplets. Time-of-flight mass spectra of positive and negative secondary ions exhibit a series of cluster ions generated via protonation and deprotonation

Fast-ion-induced secondary ion emission from submicron droplet surfaces studied using a new coincidence technique with forward-scattered projectiles

A mass spectrometric study of secondary ions emitted from droplet surfaces by MeV-energy heavy ion impact was performed to investigate fast-ion-induced molecular reaction processes on liquid surfaces. Herein, a new coincidence technique was developed between secondary ions and scattered projectile ions at a small forward angle. The advantages of this technique were demonstrated by measurement of the collision between 4-MeV C3+ and ethanol droplets. Secondary ion emission probabilities were obtained directly from the coincidence data. Notably, this technique enabled positive fragment ions that had not been identified in previous measurements to be observed by suppressing the strong background originating from gas-phase molecules more than 104-fold. H+, H3O+, C2H5+, and C2H5O+ were found to be produced as major positive fragment ions, in addition to minor fragments H2+, C2H3+, and CH2OH+. Production of these ions suggests that competition between rapid hydrogen ion emission from multiply ionized states and intermolecular proton transfer accompanied by fragmentation through protonated ethanol occurs after fast heavy-ion collisions. Clarification of the positive fragment ions also revealed the characteristic features of negative ions. Negative ions were realized to exhibit higher degrees of fragmentation and reactivity compared with positive ions. Furthermore, the energy loss by forward-scattered ions during droplet penetration was used to evaluate the target thickness at a submicron level. Variations in secondary ion yield, mass distribution, and kinetic energies depending on the penetration length were observed below 1 µm. These results highlight the unknown mechanism of these “submicron effects” observed in secondary ion emission processes as a new phenomenon

A systematic method for constructing time discretizations of integrable lattice systems: local equations of motion

We propose a new method for discretizing the time variable in integrable lattice systems while maintaining the locality of the equations of motion. The method is based on the zero-curvature (Lax pair) representation and the lowest-order "conservation laws". In contrast to the pioneering work of Ablowitz and Ladik, our method allows the auxiliary dependent variables appearing in the stage of time discretization to be expressed locally in terms of the original dependent variables. The time-discretized lattice systems have the same set of conserved quantities and the same structures of the solutions as the continuous-time lattice systems; only the time evolution of the parameters in the solutions that correspond to the angle variables is discretized. The effectiveness of our method is illustrated using examples such as the Toda lattice, the Volterra lattice, the modified Volterra lattice, the Ablowitz-Ladik lattice (an integrable semi-discrete nonlinear Schroedinger system), and the lattice Heisenberg ferromagnet model. For the Volterra lattice and modified Volterra lattice, we also present their ultradiscrete analogues.Comment: 61 pages; (v2)(v3) many minor correction

Real-space local polynomial basis for solid-state electronic-structure calculations: A finite-element approach

We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the method is completely general and its convergence can be controlled systematically. Because the basis functions are strictly local in real space, the method allows for variable resolution in real space; produces sparse, structured matrices, enabling the effective use of iterative solution methods; and is well suited to parallel implementation. The method thus combines the significant advantages of both real-space-grid and basis-oriented approaches and so promises to be particularly well suited for large, accurate ab initio calculations. We develop the theory of our approach in detail, discuss advantages and disadvantages, and report initial results, including the first fully three-dimensional electronic band structures calculated by the method.Comment: replacement: single spaced, included figures, added journal referenc

Timesaving Double-Grid Method for Real-Space Electronic-Structure Calculations

We present a simple and efficient technique in ab initio electronic-structure calculation utilizing real-space double-grid with a high density of grid points in the vicinity of nuclei. This technique promises to greatly reduce the overhead for performing the integrals that involves non-local parts of pseudopotentials, with keeping a high degree of accuracy. Our procedure gives rise to no Pulay forces, unlike other real-space methods using adaptive coordinates. Moreover, we demonstrate the potential power of the method by calculating several properties of atoms and molecules.Comment: 4 pages, 5 figure