Miracle-dz/UniFAR-FTUs huggingface dataset:
Size of Atoms in RW Universe: a Correction to Dirac Equation for Curved Space-Time

Dirac equation for curved space-time is solved in Cartesian coordinates giving a result which is contrary to the generally accepted notion in cosmology that space expansion does not impact size of atoms. The solution shows that size of atoms reduces in proportion to the square of scale factor in an expanding universe. Work of McVittie, who solved the same equation with a different result is reviewed, highlighting his mistake and why he got an incorrect result. As the result is completely counter-intuitive a correction to the Dirac equation for curved space-time is attempted, which is desired due to many other reasons as well. The corrected equation when solved, shows that size of atoms changes in proportion to square of scale factor. Same result has been reported earlier as well using Schrdinger equation indicating that correction proposed is in right direction. Gravitational redshift formula is derived using the new equation, which matches with general relativistic prediction. The new equation proposed in this paper is thus indeed correct Dirac equation for curved space-time. Validity of standard model of cosmology is questioned due to this discovery.
Shear Excitation of Atmospheric Gravity Waves. Part II: Nonlinear Radiation from a Free Shear Layer

Abstract This paper addresses the efficiency and characteristics of two mechanisms that have been proposed to account for the excitation of radiating gravity waves by Kelvin-Helmholtz (KH) instabilities at a free shear layer in a stratified atmosphere. These mechanisms are the vortex pairing or subharmonic interaction observed to occur at the interface between two homogeneous fluid layers and the KH interaction or “envelope radiation” mechanism found to occur in the presence of propagating unstable modes. Vortex pairing in a stratified environment is found to be highly dependent on the minimum mean Richardson number, being very efficient when the subharmonic is itself a KH mode and relatively unimportant when the subharmonic has propagating character. The envelope radiation mechanism, in contrast, is observed to provide efficient radiating wave excitation in the absence of propagating unstable modes, as anticipated by Fritts. It is suggested that this latter mechanism may lead naturally to the excitation .
Heat transport by turbulent Rayleigh–Bénard convection in 1 m diameter cylindrical cells of widely varying aspect ratio

High-precision measurements of the Nusselt number Nu as a function of the Rayleigh number Ra have been made in water-filled 1m diameter cylindrical cells of aspect ratio $\Gamma {=} $0.67, 1, 2, 5, 10 and 20. The measurements were conducted at the Prandtl number $Pr {\approx} 4$ with Ra varying from $1{\times} 10^7$ to $5{\times} 10^{12}$. When corrections for the finite conductivity of the top and bottom plates are made, the estimates obtained of $Nu_{\infty}$ for perfectly conducting plates may be described by a combination of two power laws $Nu_{\infty} {=} C_{1}(\Gamma)Ra^{\beta_1}+C_{2}(\Gamma)Ra^{\beta_2}$ for all the aspect ratios. The fitted exponents $\beta_1 {=}0.211$ and $\beta_2 {=} 0.332$ are very close to $1/5$ and $1/3$ respectively, which have been predicted by Grossmann & Lohse for the II$_u$ and IV$_u$ regimes in their model. It is also found that $Nu_{\infty}$ is generally smaller for larger $\Gamma$ but the difference is only a few percent and for $\Gamma{\gtrsim} 10$ the asymptotic large-$\Gamma$ behaviour may have been reached.
Mathematical foundation of convexity correction

A broad class of exotic interest rate derivatives can be valued simply by adjusting the forward interest rate. This adjustment is known in the market as convexity correction. Various ad hoc rules are used to calculate the convexity correction for different products, many of them mutually inconsistent. In this research paper we put convexity correction on a firm mathematical basis by showing that it can be interpreted as the side-effect of a change of probability measure. This provides us with a theoretically consistent framework to calculate convexity corrections. Using this framework we review various expressions for LIBOR in arrears and diff swaps that have been derived in the literature. Furthermore, we propose a simple method to calculate analytical approximations for general instances of convexity correction.
Hydrodynamics with a chiral hadronic equation of state including quark degrees of freedom

We investigate the influence of a deconfinement phase transition on the dynamics of hot and dense nuclear matter. To this aim a hybrid model with an intermediate hydrodynamic stage for the hot and dense phase of the system is employed for collisions of Pb+Pb/Au+Au at beam energies of E{sub lab}=2-160 A GeV, while initial and final interactions are performed by a microscopic transport approach (UrQMD). In the hydrodynamic stage an equation of state that incorporates a critical end point in line with lattice data is used. It follows from coupling the Polyakov loop (as an order parameter for deconfinement) to a chiral hadronic SU(3){sub f} model. In this configuration the equation of state describes chiral restoration as well as the deconfinement phase transition. We compare the results from this new equation of state to results obtained, by applying a hadron resonance gas equation of state, focusing on bulk observables deemed to be sensitive to the phase transition to a quark-gluon plasma.
Multiscale low-frequency circulation modes in the global atmosphere

Abstract In this paper, fundamental multiscale circulation modes in the global atmosphere are identified with the objective of providing better understanding of atmospheric low-frequency variabilities over a wide range of spatial and temporal scales. With the use of a combination of rotated principal component technique, singular spectrum analysis, and phase space portraits, three categories of basic multiscale modes in the atmosphere are found. The first is the interannual mode (IAM), which is dominated by time scales longer than a year and can be attributed to heating and circulation anomalies associated with the coupled tropical ocean-atmosphere, in particular the E1 Nino–Southern Oscillation. The second is a set of tropical intraseasonal modes consisting of three separate multiscale patterns (ISO-1, -2, -3) related to tropical heating that can be identified with the different phases of the Madden–Julian Oscillation (MJO), including its teleconnection to the extratropics. The ISO spatial and temporal p.
Shallow water flows over flooding areas by a flux-corrected finite element method

In this work we construct a finite element method for shallow water flows with focus on problems with evolutionary coastlines. The method does not utilize ad hoc techniques to track the water-terrain interfaces and fulfills global conservation and positivity. The basis of the procedure is a generalized flux correction technique, and its application can be extended to diverse finite element solutions of the shallow water equations. Experiments are mainly concentrated on frictional flows with fronts propagating over dry regions.
The effect of friction and topography on coastal internal Kelvin waves at low latitudes

The effects of bottom Ekman layer friction and slope topography on freely propagating coastal internal Kelvin waves in a stratified ocean are examined. Frictional effects are assumed weak and specific slope topographies are chosen so that perturbation methods may be used to obtain solutions. Two models for slope topography are utilized: a steep slope model, which corresponds to the low latitude case where the Rossby radius scale δ R is assumed large compared to the slope width L s , and a weak slope model, which corresponds to the case δ R ≪ L s . For both cases, internal Kelvin waves are damped by bottom friction, and offshore and vertical phase lags are induced, as well as an onshore flow. However, there are substantial differences between the results obtained with the two different models. For example, vertical phase shifts due to friction for the steep slope case imply that alongshore velocity v at the surface leads v below, while motions at the bottom lead for the weak slope case. For the weak slope, frictional effects are proportional to bottom velocity, implying that, for mid-latitudes, bottom stress effects on barocline modes are minimal. However, results from the steep slope model imply that baroclinic modes are significantly affected by bottom stress at low latitudes. In both cases, the topography changes the frequency and alongshore phase speed of the wave, the modal structure is altered, and an onshore flow is induced. For the weak slope case, the wave speed is proportional to the mean bottom depth averaged over the Rossby radius scale. For the steep slope, changes in wave speed depend on the details of the slope geometry: a slope that is concave downward increases the speed while a slope that is concave upward decreases the speed. Both models are compared with observations from the Peru coast. DOI: 10.1111/j.1600-0870.1984. tb00256.x
The Effect of a Vertical Magnetic Field on the Propagation of Gravity Waves Along the Plane Surface of a Semi-Infinite Viscous, Electrically Conducting Fluid.

Basic equations and boundary conditions governing effects of vertical magnetic and gravitational fields on smallamplitude perturbations of the free equilibrium surfuce of a viscous, electrically conducting fluid are presented. Normal modes are examined. A dispersion relationship is derived which relates the complex "frequency" n of the normal mode to the Alfven velocity, V; the viscosity, v,; the magnetic diffusivity, lambda ; and the horizontal wave number, k. This dispersioh relationship is solved in nine extreme cases. In six of these, the magnetic field is too wesk to modify substantially the familiar gravity-wave solution holding in the absence of a magnetic field. The influence of the field is so strong in the remaining three cases that they have no parallel in the zero-field case. 0ne of these holds for any k if the magnetic field is sufficiently strong. In this case n = -gV/sup -1/( lambda /v)1/2i.e. , the effect of the magnetic field is so great that the disturbance is attenuated aperiodically as the Alfven waves radiate energy away from the free surfuce. Another interesting feature demonstrated is the existence (if V is sufficiently large) of a band of wave numbers k for which no normal-mode solution exists. It is neverthelessmore » demonstrated that the associated initialvalue problem can be solved for such values of k. In addition to the nine extreme cases mentioned above, three special cases are solved for all k for particular values of V, namely, v = lambda , v = 0, and lambda = 0. (auth)« less
Multiple reflections and Fresnel absorption in an actual 3D keyhole during deep penetration laser welding

In laser welding experiments of glass, keyhole shapes are observed by two high-speed cameras from two perpendicular directions. From the obtained keyhole pictures, it can be seen that in medium- and low-speed laser penetration welding, the main distortion of the keyhole is not the section metamorphosis from rotational symmetry, but the bending of its centre line. Based on such a keyhole photograph, the keyhole profiles and its centre line are determined by the method of polynomial fitting. Then, under the assumption of a circular cross section at each depth of the keyhole, the behaviour of the laser beam in the keyhole is analysed by tracing a ray of light using geometrical optics theory; the Fresnel absorption and multiple reflections in the keyhole are systematically studied, and the laser intensities absorbed on the keyhole walls are calculated. The absorbed laser intensity is not distributed uniformly on the keyhole wall. The keyhole wall absorbs laser intensity mainly on the half-part of the keyhole wall near the front wall. Because of the high absorptivity of the glass, Fresnel absorption from the first incidence of a laser beam plays a dominant role in the final laser intensity distribution on the keyhole wall, multiple reflections have some minor effects on the intensity distribution on the bottom part of the keyhole.
A Simple Proof of Functional Itô's Lemma for Semimartingales with an Application

The Ito formula was extended recently by Dupire (2009) to functionals of paths of continuous semimartingales, and by Cont and Fournie (2010a) to functionals of paths of RCLL semimartingales. In contrast to the traditional formula that applies to functions of the current value of a process, these extensions apply to functionals of the history of a process. By modifying Dupire’s setup we develop new proofs for both the continuous case and the more general RCLL case that are much simpler. We also examine an application to optimal control.
Optical Dispersion and the Structure of Solids

A new energy parameter ${\mathcal{E}}_{d}$ is introduced to describe dispersion of the electronic dielectric constant. This dispersion energy is found to obey an extraordinarily simple empirical relation in the more than 50 ionic and covalent crystals for which reliable refractive-index dispersion data are available. Based on this result we derive a structure-dependent electronic dielectric response function consisting of constant optical-frequency conductivity with high-and low-frequency cutoffs.
Isothermal blast wave model of supernova remnants

The validity of the ''adiabatic'' assumption in supernova remnant calculations is examined, and the alternative extreme of an isothermal blast wave is explored. It is concluded that, because of thermal conductivity, the large temperature gradients predicted by the adiabatic model probably are not maintained in nature. Self-similar solutions to the hydrodynamic equations for an isothermal blast wave have been found and studied. These solutions are then used to determine the relationship between X-ray observations and inferred parameters of supernova remnants. A comparison of the present results with those for the adiabatic model indicates differences which are less than present observational uncertainties. It is concluded that most parameters of supernova remnants inferred from X-ray measurements are relatively insensitive to the specifics of the blast wave model. (AIP)
Representation of multipliers on spaces of real analytic functions

Abstract We consider multipliers on the spaces of real analytic functions of one variable, i.e., maps for which monomials are eigenvectors. We prove representation theorems in terms of analytic functionals and in terms of holomorphic functions. We characterize Euler differential operators among multipliers. Then we characterize when such operators are surjective or have a continuous linear right inverse on the space of real analytic functions over an interval not containing zero. In particular we solve the problem when Euler differential equation of infinite order has a solution in the space of real analytic functions on an interval not containing zero.
Variability in Estimating Total Cloud Cover from Satellite Pictures

Abstract Ten qualified weather observers were used to make estimates of the total cloud cover from satellite pictures. Tests were conducted to determine the standard deviation of estimates, the significance of the difference in estimates, and the error of estimates. Results indicate that the variability of the estimates was significant and suggestions are made that experience and training are necessary to cope with problems in this general area.
Global geometry of polygons. I: The theorem of Fabricius-Bjerre

Deformation methods provide a direct proof of a polygonal analogue of a theorem proved by Fabricius-Bjerre and by Halpern relating the numbers of crossings, pairs of inflections, and lines of double tangency for smooth closed plane curves. Let X: \m, b] —> F describe a closed curve with a finite number C of crossings, a finite number F of inflection points (or inflection intervals), and a finite number of double support lines (i.e. lines containing two points of the curve each with a neighborhood lying to one side of the line, I being the number for which the neighborhoods lie on opposite sides of the line and II being the number with both neighborhoods to the same side). For a convex curve all these numbers are zero. Examination of a few examples leads to the conjecture that C + ViF + I II = 0, and in [2] Halpern announced a proof of this result for smooth curves satisfying certain regularity conditions. The proof described there uses techniques of critical points for vector fields and winding numbers and requires that the curve be of differentiability class C . The result was discovered by Fabricius-Bjerre [3], but again the proof made use of regularity slightly stronger than C . In this note we present an elementary proof of this result for polygonal curves in the plane. As in [2], this result generalizes to the case of mappings of an arbitrary 1-manifold into the plane (Theorem 1 ). The techniques developed in this paper will be used in subsequent investigations of polygonal analogues of a number of other global theorems on plane and space curves. There is also a sense in which these techniques fit in with the polyhedral analogue of catastrophe theory as developed in [l]. Definition. By a polygon we mean a mapping X: [a, b] —> E of a closed interval into the Euclidean plane such that for some finite subdivision, a = ? 0 < Zj < • • • < t = b, the mapping X restricted to the interval t. < i < £. + . Presented to the Society, April 27, 1973 under the title Polygonal methods in global curve theory; received by the editors January 17, 1973 and, in revised form, August 29, 1973. AMS (MOS) subject classifications (1970). Primary 53A05, 57C35; Secondary 55A25.
Proton-induced Thermonuclear Reaction Rates for A = 20–40 Nuclei

Proton-induced reaction rates on 26 stable and 29 unstable target nuclei in the mass A = 20–40 region have been evaluated and compiled. Recommended reaction rates, assuming that all interacting nuclei are in the ground state, are presented in tabular form on a temperature grid in the range T = 0.01–10.0 GK. Most reaction rates involving stable targets were normalized to a set of measured standard resonance strengths in the sd shell. For the majority of reaction rates, experimental information from transfer reaction studies has been used consistently. Our results are compared with recent statistical model (Hauser-Feshbach) calculations. Reaction rate uncertainties are presented and amount to several orders of magnitude for many of the reactions. Several of these reaction rates and/or their corresponding uncertainties deviate from results of previous compilations. In most cases, the deviations are explained by the fact that new experimental information became available recently. Examples are given for calculating reaction rates and reverse reaction rates for thermally excited nuclei from the present results. The survey of literature for this review was concluded in 2000 August.
Aerodynamic Noise and Flow Visualization around Two-dimensional Airfoil

The aerodynamic noise from a two-dimensional symmetrical airfoil was studied experimen-tally using a low-noise acoustic wind tunnel. The measurement of the sound spectrum at Reynolds number 1.6 × 10 5 indicates the generation of discrete frequency noise from the airofoil at small incidence angles. The surface flow visualizations over the airofoil were carried out using the oil-film method and the shear-sensitive liquid crystal technique. These visualization results indicate that the reattachment and reseparation of the flow occur near the trailing edge of the pressure side of the airfoil, when the discrete frequency noise is generated. The smoke-wire visualization of the flow around the airfoil showed that the strong trailing edge vortices were shed from the airofoil and they form a stable pattern of Karman vortices in the downstream.
The Comparability of the Standardized Mean Difference Effect Size Across Different Measures of the Same Construct

One of the most important effect sizes used in meta-analysis is the standardized mean difference (SMD). In this article, the conditions under which SMD effect sizes based on different measures of the same construct are directly comparable are investigated. The results show that SMD effect sizes from different measures of the same construct are directly comparable if and only if (Condition 1) there is a linear relationship between the true scores, and (Condition 2) there is a special linear relationship between the magnitude of the error variances of the involved measures. If only Condition 1 is met, then the reliability-corrected SMD effect sizes from the different measures are directly comparable. However, if Condition 1 is not met, then there will be nonlinear relationships between the true score metrics of two or more of the measures and systematic variability between SMD effect sizes that reflects these nonlinear relationships.
Dimensional analysis for robust control of planar vehicle dynamics

Most engineered systems with similar functions, which are designed under strict external constraints, share similar dynamics. Using a dimensionless model as system representation, a dimensionless robust controller can be designed and implemented for a class of dynamically similar systems that are different in physical dimension. Dimensionless transformations of timescale, inputs and outputs determine a nominal plant model and plant‐to‐plant uncertainties in a dimensionless form. Using parameter‐dependent normalization, a normalized dimensionless model can be derived that has lower levels of plant‐to‐plant uncertainty than previous formulations (IEEE Trans. Contr. Syst. Technol. 2005; 13(4):624–630). The benefit of this dimensional analysis is demonstrated by the dynamic analysis of different types of planar vehicle systems. Numerical results show that, by using dimensional analysis, it is possible to obtain a controller that is robust to plant‐to‐plant parametric uncertainties among specific classes of systems designed with widely varying physical dimensions. Copyright © 2007 John Wiley & Sons, Ltd.
Metatarsal Horizontal Angle Variety Information of Female with Different Hallux Valgus

Hallux valgus is a common foot deformity with a multifactorial etiology. Factors associated with the development of hallux valgus (HV) are multifactorial and the etiology of hallux valgus remains unclear. The purpose of this study was to measure the biomechanical relationship between Hallux Valgus Angle (HVA), intermetatarsal Angle (IMA), Interphalangeal Angle (IPA), and metatarsal horizontal angle, in order to reveal the tendency of metatarsal horizontal angle along with hallux valgus angle increasing. Foot models of nine subjects are built through CT scan and editing software and calculated metatarsal horizontal angles using motion analysis system. It showed that with the increased of HVA, the metatarsal horizontal angle of the first to fifth was decreased. This method and results maybe have a new sight to reveal the characters of HV patients. Keywords: Hallux valgus; Metatarsal horizontal angle; Foot Models