Miracle-dz/UniFAR-FTUs huggingface dataset:
A method to determine the water kerma in a phantom for x-rays with energies up to 40 keV

In brachytherapy, as in any form of radiation therapy, accurate dosimetry in terms of absorbed dose to water is required. The output of brachytherapy sources has, up to now, been specified as the reference air kerma rate at 1 m distance. For this reason, the Physikalisch-Technische Bundesanstalt is developing a primary standard to determine the absorbed dose to water at the point of measurement within a water phantom. A candidate for the standard to be newly established is a water-equivalent parallel-plate ionization chamber with continuously adjustable electrode spacing, forming an extrapolation chamber in a phantom of water-equivalent material. In this work, a method is introduced to determine the absorbed dose to water with an extrapolation chamber in a phantom of water-equivalent material. Thereby, a conversion factor C(xi+1, xi) is applied to the difference of the ionization charges measured at two different plate separations xi and xi+1. In contrast to already described methods, the applied method is based on fundamental dosimetric relations without the use of a wall-less chamber approximation. It will be shown that by using the wall-less chamber approximation, a term contributing to the absorbed dose to water is overlooked. This term is given by the net energy fluence of the secondary electrons at the surface of the measuring volume. The introduced method is verified experimentally by a comparison with water kerma values obtained from air kerma measurements free in air and applying a conversion factor to water kerma obtained by Monte Carlo (MC) calculations for the conditions of the experiment. Evidence is produced showing that the new model significantly increases the consistency of experimental and MC results.
On Wright–Fisher diffusion and its relatives

We present a series of elementary stochastic models arising from population genetics. Various mathematical aspects are investigated at the intuitive level. Special emphasis is put on the diffusion method. The focus is on the Wright–Fisher diffusion model and its variations, describing the forward evolution of one colony undergoing random sampling, possibly under the additional forces arising from mutation and selection with or without dominance. Some aspects of their dual coalescents obtained while running the diffusion process backward in time are also investigated.
High critical current density in Y-Ba-Cu-O bulk superconductors with very fine Y211 particles

We have succeeded in enhancing the critical current density (Jc) of melt-textured Y? Ba? Cu? O superconductors by employing ultra-fine Y211 powder as precursor. The Y211 starting powders were reduced down to 110? nm in diameter with ball-milling. Single-grain Y? Ba? Cu? O samples up? to? 33? mm in diameter were fabricated from the precursors containing finely milled Y211 powders. The Y211 inclusions in the melt-textured samples could be refined by decreasing the particle size of the Y211 starting powders. The maximum value of Jc at 77? K was 1.1 ? 105? A? cm? 2 in a self-field. However, the size reduction of Y211 led to an inhomogeneous distribution of Y211 particles, in which the volume fraction of the Y211 phase greatly decreased near a seed crystal. An Ag-added bulk sample 33? mm in diameter exhibited a high trapped magnetic field of 1.6? T at 77? K.
Polynomial Pell’s equations

The polynomial Pell's equation is p2 _ (X2 + d )Q2 = 1, where d is an integer and the solutions P, Q must be polynomials with integer coefficients. It is proved that this equation has nonconstant solutions if and only if d = +1 +2, and in these cases all solutions are determined. Let d be an integer. We consider the polynomial Pell's equation (1) p2 _ (x2 + d)Q2 = l where P and Q are polynomials with integer coefficients. This equation always has the trivial solutions P = +1, Q = 0, and these are the only constant solutions. In this note we prove that (1) has nontrivial solutions if and only if d = ? 1, ? 2, and in these cases we determine all solutions. This answers a question posed by S. Chowla. Lower case letters (# x) denote integers, and upper case letters denote polynomials with integer coefficients. The degree of F is denoted deg F. THEOREM 1. Let d # ? 1, ? 2. Then the polynomial Pell's equation p2 (x2 + d)Q2 = 1 has no nontrivial solution. PROOF. The proof is by Fermat descent on deg P. Let |dl > 3, and suppose that (1) has nontrivial solutions. Choose a solution P, Q of (1) with deg P minimal and deg P > 0. There are two cases. If d # -c2, then x2 + d is irreducible, and (P 1)(P + 1) = p2 _ 1 = (X2 + d)Q2. It follows that x2 + d divides P-I or P + 1, say P-1. Then P 1 = (x2 + D)P1 and P + 1 = (x2 + d)PI + 2, and so (2) P1((x2 + d)P1 + 2) = Q2 Since the greatest common divisor of P1 and (x + d)P, + 2 is 1 or 2, it follows from (2) that one of the following four cases must hold: (i)(x2+d)P ? +2 =-P2 ,P2 =-Q2. (ii) (x2 + d)PI + 2 p2 PJ Q2. (i)(2+ d)PI + 2 = -2P 2, PI = 2Q2 (iv) (X2 + d)PI + 2 = 2P2, P1 = 2Q2 . SettinZ x = V=-d in (i), (ii), (iii), we find that (a + b -d)2 = +2 or (a + b-d) = for some integers a, Received by the editors July 1, 1975. AMS (MOS) subject classifications (1970). Primary lOB05, 12A20.
Normal and Non‐Normal Points of Self‐Similar Sets and Divergence Points of Self‐Similar Measures

Let K and μ be the self‐similar set and the self‐similar measure associated with an IFS (iterated function system) with probabilities (Si, pi)i=1,…,N satisfying the open set condition. Let Σ={1,…,N}N denote the full shift space and let π : Σ → K denote the natural projection. The (symbolic) local dimension of μ at ω ∈ Σ is defined by limn (log μKω|n/log diam Kω|n), where Kω|n=Sω1^…^Sωn(K) for ω = (ω1, ω2,…) ∈ Σ. A point ω for which the limit limn (log μKω|n/log diam Kω|n) does not exist is called a divergence point. In almost all of the literature the limit limn (log μKω|n/log diam Kω|n) is assumed to exist, and almost nothing is known about the set of divergence points. In the paper a detailed analysis is performed of the set of divergence points and it is shown that it has a surprisingly rich structure. For a sequence (χn)n, let A(χn) denote the set of accumulation points of (χn)n. For an arbitrary subset I of R, the Hausdorff and packing dimension of the set { ω∈Σ|A(logμKω|nlog diamKω|n)=I } and related sets is computed. An interesting and surprising corollary to this result is that the set of divergence points is extremely ‘visible’; it can be partitioned into an uncountable family of pairwise disjoint sets each with full dimension.
NONORTHOGONAL TWINNING IN THIN FILM OXIDE PEROVSKITES

We have observed nonorthogonal twinning in thin film oxide perovskites. This twinning geometry is equivalent to a 60° rotation of the twinned crystallites about the [111] direction in an [001] oriented film. This twinning is not detectable by the standard x‐ray tests for film quality (a radial θ–2θ scan and a φ scan at a chi of 45°). In this study we observe this twinning in films of PbZrxTi1−xO3, BaTiO3, and SrRuO3 grown by sputtering and MOCVD on MgO and SrTiO3. These twins are observed in films deposited on a substrate with which there is a large lattice mismatch and in films that are deposited in an oxygen deficient environment. We propose that these twins result from plastic deformation associated with misfit accommodation and discuss the twin geometry and the nature of the twin interface.
The small-scale structure of acceleration correlations and its role in the statistical theory of turbulent dispersion

Some previously accepted results for the form of one- and two-particle Langrangian turbulence statistics within the inertial subrange are corrected and reinterpreted using dimensional methods and kinematic constraints. These results have a fundamental bearing on the statistical theory of turbulent dispersion. One-particle statistics are analysed in an inertial frame [Sscr ] moving with constant velocity (which is different for different realizations) equal to the velocity of the particle at the time of labelling. It is shown that the inertial-subrange form of the Lagrangian acceleration correlation traditionally derived from dimensional arguments constrained by the property of stationarity, ${\cal C}_0^{(a)}\overline{\epsilon}/\tau $, where ${\cal C}_0^{(a)}$ is a universal constant, $\overline{\epsilon}$ is the mean rate of dissipation of turbulence kinetic energy and τ is the time lag, is kinematically inconsistent with the corresponding velocity statistics unless ${\cal C}_0^{(a)} = 0$. On the other hand, velocity and displacement correlations in the inertial subrange are non-trivial and the traditional results are confirmed by the present analysis. Remarkably, the universal constant ${\cal C}_0$ which characterizes these latter statistics in the inertial subrange is shown to be entirely prescribed by the inner (dissipation scale) acceleration covariance; i.e. there is no contribution to velocity and displacement statistics from inertial-subrange acceleration structure, but rather there is an accumulation of small-scale effects. In the two-particle case the (cross) acceleration covariance is deduced from dimensional arguments to be of the form $\overline{\epsilon}t_1^{-1}{\cal R}_2(t_1/t_2)$ in the inertial subrange. In contrast to the one-particle case this is non-trivial since the two-particle acceleration covariance is non-stationary and there is therefore no condition which constraints [Rscr ]2 to a form which is kinematically inconsistent with the corresponding velocity and displacement statistics. Consequently it is possible for two-particle inertial-subrange acceleration structure to make a non-negligible contribution to relative velocity and dispersion statistics. This is manifested through corrections to the universal constant appearing in these statistics, but does not otherwise affect inertial-subrange structure. Nevertheless, these corrections destroy the simple correspondence between relative- and one-particle statistics traditionally derived by assuming that two-particle acceleration correlations are negligible within the inertial subrange. A simple analytic expression which is proposed as an example of the form of [Rscr ]2 provides an excellent representation in the inertial subrange of Lagrangian stochastic simulations of relative velocity and displacement statistics.
On the Rate of Convergence of Discretization in Chebyshev Approximation

We compare complex or real linear Chebyshev approximation on a compact interval X with approximation on one of its closed subsets Y. We show that under suitable conditions the best approximation on X approaches the best approximation on X like $({\text{density of}}\,Y)^2 $. This indicates that we can obtain very good near best approximations on the interval by solving best approximation problems on subsets of the interval which contain only “small” numbers of points.
Kinetic Flux-Vector Splitting for the Navier-Stokes Equations

Before a hybrid scheme can be developed combining the direct simulation Monte Carlo (DSMC) method and a Navier? Stokes (NS) representation, one must have access to compatible kinetic-split fluxes from the NS portion of the hybrid scheme. The kinetic theory basis is given for the development of the required fluxes from the Chapman? Enskog velocity distribution function for a simple gas; and these are then extended to a polyatomic gas by use of the Eucken approximation. The derived fluxes are then used to implement boundary conditions at solid surfaces that are based on concepts associated with kinetic theory and the DSMC method. This approach is shown to lead to temperature slip and velocity slip as a natural outcome of the new formulation, a requirement for use in the near-continuum regime where DSMC and NS must be joined. Several different flows, for which solid boundaries are not present, are computed using the derived fluxes, together with a second-order finite-volume scheme, and the results are shown to agree well with several established numerical schemes for the NS equations.
Electromagnetohydrodynamic flow through a microparallel channel with corrugated walls

In this paper a perturbation method is introduced to study the electromagnetohydrodynamic (EMHD) flow in a microparallel channel with slightly corrugated walls. The corrugations of the two walls are periodic sinusoidal waves of small amplitude either in phase or half-period out of phase, and the perturbation solutions of velocity and volume flow rate are obtained. Using numerical computation the effects of the corrugations on the flow are graphically analysed. The results show that the influence of corrugation on the flow decreases with Hartmann number. The phase difference of wall corrugations becomes unimportant when the wavenumber is greater than 3 or when the Hartmann number is greater than 4. With the increase in wavenumber, the decreasing effects of corrugations on the flow increase. When the wavenumber is smaller than the threshold wavenumber (it is a function of Hartmann number) and the wall corrugations are half-period out of phase, the corrugations can enhance the mean velocity of EMHD flow. However, the mean velocity is always decreased when the corrugations are in phase.
Stiffness measurement of a biomaterial by optical manipulation of microparticle

Since the discovery of the trapping nature of laser beam, optical tweezers have been extensively employed to measure various parameters at micro/nano level. Optical tweezers show exceptional sensitivity to weak forces making it one of the most sensitive force measurement devices. In this work, we present a technique to measure the stiffness of a biomaterial at different points. For this purpose, a microparticle stuck at the bottom of the dish is illuminated by the trapping laser and respective QPD signal as a function of the distance between the focus of the laser and the center of the microparticle is monitored. After this, microparticle is trapped and manipulated towards the target biomaterial and when it touches the cell membrane, QPD signal shows variation. By comparing two different QPD signals and measuring the trap stiffness, a technique is described to measure the stiffness of the biomaterial at a particular point. We believe that this parameter can be used as a tool to identify and classify different biomaterials.
East Asian Climate Change in the 21st Century as Simulated by the Coupled Climate Model ECHO-G under IPCC SRES Scenarios

Future climate changes over East Asia are studied from ensemble simulations of the coupled climate model ECHO-G, based on the Intergovernmental Panel on Climate Change (IPCC), Special Report on Emissions Scenarios (SRES) A2 and B2 scenarios. Three ensemble experiments are performed: the A2 scenario experiment with greenhouse-gas (GHG) plus sulfate aerosol forcing (referred to as A2), and the A2 and B2 scenario experiments, with GHG forcing only (A2G and B2G respectively). All experiments show that East Asian near surface temperature (T2m) and precipitation (PCP) will increase in the 21st century with larger amplitudes than global means. Seasonally varying changes are found as a larger warming in winter and fall and a stronger PCP in summer. Relative roles of large-scale and convective precipitations (LSP and CP) are analyzed extensively. A mass flux scheme with an adjustment closure is used for cumulus parameterization. In the global mean, LSP dominates total PCP increase whereas CP controls PCP reductions near the equator in December. January-February (DJF) and 30-40° S in June-July-August (JJA). The latter originates from a weakening of the northern winter Hadley circulation and an increased static stability in the Southern Hemisphere, supporting previous results. For the East Asian mean, the CP change explains most of the increase of total PCP in JJA while the LSP change plays a more critical role in DJF. The LSP increase over the North Pacific in DJF is well associated with strengthened [weakened] baroclinicity north [south] of 40°N, i.e., a poleward shift of storm track. Aerosol effects on East Asian climate change (A2 minus A2G patterns) are characterized by cooling and drying with patterns similar to those of the mean changes. This is inconsistent with localized features found in previous works, indicating large uncertainty in regional responses to aerosol forcing. A possible impact of GHG mitigation over the late 21st century (A2G minus B2G patterns) is more pronounced in T2m than in PCP changes, with similar patterns as in aerosol effects. Simulated CP and LSP contributions to PCP changes are insensitive to the aerosol effect as well as that of GHG mitigations.
Temperature and Pressure Sensitivities of Burning Wave Parameters of Nitramine-Containing Propellants and HMX

Burning rate and burning surface temperatures have been obtained experimentally for modern double-base propellants containing nitramine additives and for HMX. Temperature sensitivities of burning wave parameters were estimated from the experimental data measured at pressures of 20 and 100 atm and at sample temperatures of i 80, +20, +100 C. Evaluation of standard deviations of the estimations shows that smoothing procedures for dependencies of burning wave parameters on pressure and temperature are necessary to obtain correct values of thesensitivities. Calculations ofthecriteria forstable combustion show that Novozhilov’ s [Novozhilov, B. V. , “ Nonstationary Combustion of Solid Rocket Fuels,” Nauka, Moscow, 1973 (Translation AFSC FTD-MD-24-317-74) (in Russian) and Novozhilov, B. V. , “ Theory of Nonsteady Burning and Combustion Stability of Solid Propellants by Zel’ dovich‐ Novozhilov Method,” Nonsteady Burning and Combustion Stability of Solid Propellants , edited by L. DeLuca, E.W. Price,and M. Summere eld, Vol. 143,Progressin Astronauticsand Aeronautics,AIAA,Washington, DC, 1992, Chap. 15, pp. 601‐ 641] criterion correctly predicts regimes of stable combustion of the propellants and HMX. An analysis of burned surface irregularities of the propellants cone rms one-dimensional character of the combustion under the investigated conditions.
Baroclinicity Influences on Storm Divergence and Stratiform Rain: Subtropical Upper-Level Disturbances

Abstract Divergence structures associated with the spectrum of precipitating systems in the subtropics and midlatitudes are not well documented. A mesoscale model is used to quantify the relative importance different baroclinic environments have on divergence profiles for storms primarily caused by upper-level disturbances in southeastern Texas, a subtropical region. The divergence profiles simulated for a subset of the modeled storms are consistent with those calculated from an S-band Doppler radar. Realistic convective and stratiform divergence signals are also generated when applying a two-dimensional convective–stratiform separation algorithm to reflectivities derived from the mesoscale model, although the model appears to underestimate stratiform rain area. Divergence profiles from the modeled precipitating systems vary in magnitude and structure across the wide range of baroclinicities common in southeastern Texas. Barotropic storms more characteristic of the tropics generate the most elevated diver.
Tunneling of a quantum breather in a one-dimensional chain

We investigate a chain of particles ~bonds! with harmonic interbond and anharmonic intrabond interactions. In the classical limit we consider a breather solution that is strongly localized ~essentially a single-site excitation! For the quantum case we study tunneling of this excitation to a neighboring site. In that case we neglect the anharmonicity except for the two sites between which the tunneling occurs. Within this model the breather tunneling reduces to the tunneling in a dimer coupled to two adjacent harmonic chains. Application of Feynman’s path instanton technique yields the tunneling splitting DE. For the isolated dimer we reproduce the exponential factor for the splitting DE (0) , obtained earlier by a perturbative approach. Assuming the frequency v of the breather to be much larger than the inverse instanton width we use an adiabatic approximation to derive DE for the dimer coupled to the harmonic chains. We findthat DE can be obtained from DE (0) just by scaling the Planck constant. We argue that independent of the density of states of the harmonic chains tunneling can never be suppressed, if v is large enough. @S1063-651X~98! 11407-1#
Non-linear diffusion equation and relaxation processes in solids

A non-logarithmic time dependence of the magnetization relaxation in superconductors is modeled by certain solutions of the nonlinear equation for flux diffusion, which can be derived either on the assumption of a logarithmic dependence of the pinning potential on the current density or, equivalently, a power-law current-voltage characteristic. Limiting cases of the spatiotemporal evolution of the flux density profile are identified: at one end of the parameters governing non-linearity the classical, linear processes relevant to the reversible part of the H-T diagram of high-T/sub c/ materials are found, whereas at the other end, a true critical-state behaviour emerges. Scaling relations between the sample size, magnetic field and characteristic relaxation times are established, which should characterize the magnetization relaxation process as well as the response to an AC field in susceptibility measurements. >
On embeddings between classical Lorentz spaces

Let p ∈ (0,∞) , let v be a weight on (0,∞) and let Λp(v) be the classical Lorentz space, determined by the norm ‖f ‖Λp(v) := ( ∫∞ 0 (f ∗(t))pv(t) dt)1/p . When p ∈ (1,∞) , this space is known to be a Banach space if and only if v is non-increasing, while it is only equivalent to a Banach space if and only if Λp(v) = Γp(v) , where ‖f ‖Γp(v) := ( ∫∞ 0 (f ∗∗(t))pv(t) dt)1/p . We may thus conclude that, for p ∈ (1,∞) , the space Λp(v) is equivalent to a Banach space if and only if the norm of a function f in it can be expressed in terms of f ∗∗ . We study the question whether an analogous assertion holds when p = 1 . Motivated by this problem, we consider general embeddings between four types of classical and weak Lorentz spaces, namely, Λp(v) , Λp,∞(v) , Γp(v) , Γp,∞(v) , where Λp,∞(v) and Γp,∞(v) are certain weak analogues of the spaces Λp(v) and Γp(v) , respectively. We present a unified approach to these embeddings, based on rearrangement techniques. We survey all the known results and prove new ones. Our main results concern the embedding Γp,∞(v) ↪→ Λq(w) which had not been characterized so far. We apply our results to the characterization of associate spaces of classical and weak Lorentz spaces and we give a characterization of fundamental functions for which the endpoint Lorentz space and the endpoint Marcinkiewicz space coincide. Mathematics subject classification (2000): 46E30, 26D15.
Underlying Mechanism for the Giant Isochoric Compressibility of Solid 4He: Superclimb of Dislocations

In the experiment on superfluid transport in solid $^{4}\mathrm{He}$ [Phys. Rev. Lett. 100, 235301 (2008)], Ray and Hallock observed an anomalously large isochoric compressibility: the supersolid samples demonstrated a significant and apparently spatially uniform response of density and pressure to chemical potential, applied locally through Vycor ``electrodes. '' We propose that the effect is due to superclimb: edge dislocations can climb because of mass transport along superfluid cores. We corroborate the scenario by ab initio simulations of an edge dislocation in solid $^{4}\mathrm{He}$ at $T=0.5\text{ }\text{ }\mathrm{K}$. We argue that at low temperature the effect must be suppressed due to a crossover to the smooth dislocation.