Arbitrary Fraction Research Articles

Impact of scaling laws on tokamak reactor dimensioning

A simple and comprehensive method is derived and used to quantify the impact of scaling laws on tokamak reactor dimensioning. Assuming prescribed geometrical coefficients, we find the ensemble of possible triplets R, B and normalized beta which allow one to reach target fusion gain Q and fusion power , at an arbitrary Greenwald fraction. The model is generic and derived for any scaling law of the energy confinement time. Using the IPB98(y,2) scaling law (ITER Physics Expert Group on Confinement and Transport and Confinement Modeling and Database and ITER Physics Basis Editors 1999 Nucl. Fusion 39 2175) leads to ITER specifications, as expected. The recently proposed new scaling law for H-mode plasmas (DS03, (Sips et al 2018 Nucl. Fusion 58 126010)) is shown to lead to modest changes to the dimensioning, except for B which could be significantly smaller for the same target performance. The impact on the dimensioning of critical exponents of the scaling law—both regarding engineer and dimensionless variables—is assessed, pushing for their determination with refined accuracy. Finally, the method is applied to a DEMO-like machine. The DS03 scaling law is found to have favorable consequences on the dimensioning as compared to IPB98(y,2), provided one is able to operate at larger , which can reveal challenging in a reactor aiming at zero disruption. Importantly, the opposite scaling of both scaling laws with respect to the aspect ratio are shown to have significant consequences on the optimal choice of this critical parameter.

Applying Two Orthogonal Methods to Assess Accuracy of Plasma Protein Binding Measurements for Highly Bound Compounds

Significant advances have been made over the years to accurately measure plasma protein binding (PPB) of highly bound compounds. However, because of perceived uncertainty based on historical suboptimal methods and limitation of radiochemical purity of radiolabeled materials, current regulatory guidelines recommend using an arbitrary cutoff fraction unbound (fu) of 0.01 as the lower limit for drug-drug interaction (DDI) prediction. This can result in significant overprediction of DDI for highly bound compounds, unnecessary DDI clinical trials and more restrictive drug product labels. To build confidence in the accuracy of PPB measurement for highly bound compounds, 2 orthogonal methods, equilibrium dialysis and ultracentrifugation, are assessed in this study to measure PPB of 10 highly bound drugs (fu < 0.01). The results show that the 2 very different methods yield comparable fu values, generally within 2-fold of each other. The data suggest that PPB of highly bound compounds can be measured accurately using current state-of-art methods, and the experimental fu should be used for DDI prediction to provide a more realistic evaluation of DDI risk in the clinic.

A novel model of laser energy attenuation by powder particles for laser solid forming

Laser energy attenuation greatly influences the amount and distribution of laser energy, which affects the forming precision and quality in laser solid forming. Most of the existing models cannot be used to calculate the laser energy attenuation when the volume fraction of powder particles in the powder stream exceeds a certain threshold. Considering the effects of overlap phenomenon among the powder particles, a model of laser energy attenuation was established by introducing the concept of the effective number of powder particles. The model can realize an accurate calculation of the laser energy attenuation in an arbitrary volume fraction of powder particles. The calculated results show that laser energy attenuation increases nonlinearly along with the powder feeding rate and decreases with the carrier gas flow rate. A simple method for measuring the laser energy attenuation was also proposed and applied. It is found that the calculated energy attenuation agrees well with the measurement. The model was verified valid.

Finite-temperature Extension for Cold Neutron Star Equations of State

Abstract Observations of isolated neutron stars place constraints on the equation of state (EOS) of cold, neutron-rich matter, while nuclear physics experiments probe the EOS of hot, symmetric matter. Many dynamical phenomena, such as core-collapse supernovae, the formation and cooling of proto-neutron stars, and neutron star mergers, lie between these two regimes and depend on the EOS at finite temperatures for matter with varying proton fractions. In this paper, we introduce a new framework to accurately calculate the thermal pressure of neutron–proton–electron matter at arbitrary density, temperature, and proton fraction. This framework can be expressed using a set of five physically motivated parameters that span a narrow range of values for realistic EOS and are able to capture the leading-order effects of degenerate matter on the thermal pressure. We base two of these parameters on a new approximation of the Dirac effective mass, with which we reproduce the thermal pressure to within ≲30% for a variety of realistic EOS at densities of interest. Three additional parameters, which are based on the behavior of the symmetry energy near the nuclear saturation density, allow us to extrapolate any cold EOS in β-equilibrium to arbitrary proton fractions. Our model thus allows a user to extend any cold nucleonic EOS, including piecewise polytropes, to arbitrary temperature and proton fraction for use in calculations and numerical simulations of astrophysical phenomena. We find that our formalism is able to reproduce realistic finite-temperature EOS with errors of ≲20% and offers a 1–3 orders-of-magnitude improvement over existing ideal-fluid models.

BASELINE ECHOCARDIOGRAPHIC PARAMETERS TO PREDICT CARDIOTOXICITY IN BREAST CANCER PATIENTS RECEIVING CHEMOTHERAPY

Breast cancer is often treated with anthracyclines and HER2 inhibitors, which are well-known cardiotoxic agents. Cancer therapeutics related cardiac dysfunction (CTRCD) has been defined by most guidelines using arbitrary left ventricular ejection fraction (LVEF) cut-off points or decreases. Our

Morphometric Approach to Many-Body Correlations in Hard Spheres.

We model the thermodynamics of local structures within the hard sphere liquid at arbitrary volume fractions through the morphometric calculation of n-body correlations. We calculate absolute free energies of local geometric motifs in excellent quantitative agreement with molecular dynamics simulations across the liquid and supercooled liquid regimes. We find a bimodality in the density library of states where fivefold symmetric structures appear lower in free energy than fourfold symmetric structures and from a single reaction path predict a dynamical barrier which scales linearly in the compressibility factor. The method provides a new route to assess changes in the free energy landscape at volume fractions dynamically inaccessible to conventional techniques.

Longitudinal shear flow over a bubble mattress with curved menisci: arbitrary protrusion angle and solid fraction

Longitudinal shear flow over a bubble mattress with curved menisci: arbitrary protrusion angle and solid fraction

Controllable Photoluminescent and Nonlinear Optical Properties of Polymerizable Carbon Dots and Their Arbitrary Copolymerized Gel Glasses

AbstractIn this work, an efficient method is developed to prepare silane‐functionalized red‐emissive carbon dots and carbon dots gel glasses with arbitrary loading fraction (0–100%). The as‐prepared materials possess strong photoluminescence and significant third‐order nonlinear optical performances. The optical properties can be tuned by either changing solvents and pH of the solution or adjusting the loading fractions of carbon dots in gel glasses. In particular, the photoluminescence of the carbon dots and their polymerized glasses can be linearly modulated from yellow to red emission by increasing the loading fraction of carbon dots or the polarity of solvent. It is also found that the chemical copolymerization leads to superior optical properties of gel glasses to that of the carbon dots solution, because the copolymerization endows stable immobilization of carbon dots in a rigid matrix. This study provides a feasible method to prepare optoelectronic hybrid materials and devices.

Interacting dark sector and precision cosmology

We consider a recently proposed model in which dark matter interacts with a thermal background of dark radiation. Dark radiation consists of relativistic degrees of freedom which allow larger values of the expansion rate of the universe today to be consistent with CMB data (H0-problem). Scattering between dark matter and radiation suppresses the matter power spectrum at small scales and can explain the apparent discrepancies between ΛCDM predictions of the matter power spectrum and direct measurements of Large Scale Structure LSS (σ8-problem). We go beyond previous work in two ways: 1. we enlarge the parameter space of our previous model and allow for an arbitrary fraction of the dark matter to be interacting and 2. we update the data sets used in our fits, most importantly we include LSS data with full k-dependence to explore the sensitivity of current data to the shape of the matter power spectrum. We find that LSS data prefer models with overall suppressed matter clustering due to dark matter - dark radiation interactions over ΛCDM at 3–4 σ. However recent weak lensing measurements of the power spectrum are not yet precise enough to clearly distinguish two limits of the model with different predicted shapes for the linear matter power spectrum. In two appendices we give a derivation of the coupled dark matter and dark radiation perturbation equations from the Boltzmann equation in order to clarify a confusion in the recent literature, and we derive analytic approximations to the solutions of the perturbation equations in the two physically interesting limits of all dark matter weakly interacting or a small fraction of dark matter strongly interacting.

Slip length for transverse shear flow over a periodic array of weakly curved menisci

By exploiting the reciprocal theorem of Stokes flow, we find an explicit expression for the first order slip length correction, for small protrusion angles, and for transverse shear over a periodic array of curved menisci. The result is the transverse flow analogue of the longitudinal flow result of Sbragaglia and Prosperetti [“A note on the effective slip properties for microchannel flows with ultrahydrophobic surfaces,” Phys. Fluids 19, 043603 (2007)]. For small protrusion angles, it also generalizes the dilute-limit result of Davis and Lauga [“Geometric transition in friction for flow over a bubble mattress,” Phys. Fluids 21, 011701 (2009)] to arbitrary no-shear fractions. While the leading order slip lengths for transverse and longitudinal flow over flat no-shear slots are well-known to differ by a factor of 2, the first order slip length corrections for weakly protruding menisci in each flow are found to be identical.

Effects of granular temperature on inter-phase drag in gas-solid flows

Direct numerical simulations with a second-order immersed boundary-lattice Boltzmann method are used to investigate the effect of particle fluctuation on flows in fixed random arrays of spheres at low and moderate particle Reynolds numbers. Random velocities obeying the isotropic Maxwellian distribution are imposed to all particles in the computational domain to mimic the granular temperature due to particle collisions. The simulation results show that the effect of particle fluctuation on the drag force is significant especially when the solid volume fraction and the particle Reynolds number are small. The drag increment due to the particle fluctuation increases with the increase of the granular temperature-based Reynolds number, however, it decreases with the increase of the solid volume fraction and the particle Reynolds number. On the basis of the simulation results, a new drag force relation based on the stationary drag in random arrays of spheres for arbitrary solid volume fractions, granular temperature-based Reynolds numbers, and particle Reynolds numbers is formulated. The fluctuations of the drag force on individual particles with respect to the mean drag are also analyzed. It is found that the drag on individual particles can differ up to 40% from the mean at small granular temperature-based Reynolds numbers and the difference increases rapidly with the increase of the granular temperature-based Reynolds number, indicating the particle fluctuation can affect the individual drag force significantly. The present results also show the drag force on individual particles well follows Gaussian distribution. The mean relative deviation is found to increase with the increase of the granular temperature-based Reynolds number and the solid volume fraction but is not affected much by the particle Reynolds number.

Elastic deformation of twinned microstructures.

Many crystalline materials exhibit twinned microstructures, where well-defined orientation relationships define the special symmetry between different, elastically anisotropic twin variants. When such twins are subjected to external loading, additional internal stresses necessarily occur at the twin boundaries in order to maintain compatibility. These compatibility stresses are constant inside each variant in repeating stacks of twins and considerably affect the local stress state. In this paper, we use anisotropic linear elasticity to derive general analytical solutions for compatibility stresses in a stack of twin variants in arbitrary materials, for arbitrary variant volume fractions and twin types, subjected to arbitrary applied stresses. By considering two examples, growth twins in electrodeposited Cu and B19′ martensite twins in the shape memory alloy NiTi, we further demonstrate that compatibility stresses can considerably alter the preferred slip systems for dislocation plasticity as well as the effective macroscopic behaviour of twinned microstructures.

Computation of Equilibrium Bilayer Monodisperse Foam Structures Using the Surface Evolver

The Surface Evolver is used to minimize the surface energy of two ordered structures for bilayer monodisperse wet foams with arbitrary liquid fraction. Previous researchers have found a reversible structural transition in bilayer monodisperse foams by changing the foam liquid fraction in a physical experiment. We simulated this phenomenon by analyzing the interfacial energy of two bilayer foam systems with varying liquid fractions. The calculations reported here show that the Tóth structure is energy minimizing when the liquid fraction is below a critical value, around 2.26%, above which point the honeycomb structure becomes preferable, although the Tóth structure remains metastable.

Numerical investigation of fiber random distribution on the mechanical properties of yarn in-plain woven carbon fiber-reinforced composite based on a new perturbation algorithm

Interior fibers in yarns of plain woven carbon fiber-reinforced composite are distributed randomly, which further influences the mechanical properties of yarns. To explore the stochastic nature of fibers’ distribution in yarn and its effect on the properties of yarn, this study proposes a new perturbation algorithm named Sequential Random Perturbation algorithm to reconstruct the microstructure of randomly distributed fibers, based on which representative volume element micromechanical models consisting of three phases to accurately predict the mechanical properties of yarn are established. The algorithm is based on successive smart perturbations of fibers to gain microstructures of arbitrary volume fraction, and statistical study shows that the algorithm is in good agreement with experimental results. Finally, representative volume element models are simulated to predict the whole mechanical properties of composite yarns to reflect the failure mechanisms and microstructure–property relations. The randomness of fiber distribution has some degree of influence on mechanical properties of yarn, especially strength responses. The failures under axial tension and compression are dominated by fiber breakage, while under transverse and shear loading conditions, the failures are mostly decided by interface debonding and matrix damage.

Incorporating Light Beam Search in a Vector Normal Boundary Intersection Method for Linear Antenna Array Optimization

An high directivity and low side lobe level antenna array is essential in wireless communication systems. Currently, the array design is often based on the experience of the designer. To combine the preferences of a decision maker into the evolution process of a multi-objective linear antenna array design problem, the light beam search method is proposed to be incorporated into a vector normal boundary intersection method to find an arbitrary fraction of the Pareto front. To adapt different preferences, a new transformed projection mechanism is introduced. To enhance the diversity of the algorithm, a dynamic transitional sub-domain strategy is proposed and used. Typical mathematical test functions and a ten-element linear antenna array optimization problem are used to testify the effectiveness of the proposed method.

Light splitting with imperfect wave plates.

We discuss the use of wave plates with arbitrary retardances, in conjunction with a linear polarizer, to split linearly polarized light into two linearly polarized beams with an arbitrary splitting fraction. We show that for non-ideal wave plates, a much broader range of splitting ratios is typically possible when a pair of wave plates, rather than a single wave plate, is used. We discuss the maximum range of splitting fractions possible with one or two wave plates as a function of the wave plate retardances, and how to align the wave plates to achieve the maximum splitting range possible when simply rotating one of the wave plates while keeping the other one fixed. We also briefly discuss an alignment-free polarization rotator constructed from a pair of half-wave plates.

Singular effective slip length for longitudinal flow over a dense bubble mattress

We consider the effective hydrophobicity of a periodically grooved surface immersed in liquid, with trapped shear-free bubbles protruding between the no-slip ridges at a $\pi/2$ contact angle. Specifically, we carry out a singular-perturbation analysis in the limit $\epsilon\ll1$ where the bubbles are closely spaced, finding the effective slip length (normalised by the bubble radius) for longitudinal flow along the the ridges as ${\pi}/{\sqrt{2\epsilon}}-(12/\pi)\ln 2 + (13\pi/24)\sqrt{2\epsilon}+ o(\sqrt{\epsilon})$, the small parameter $\epsilon$ being the planform solid fraction. The square-root divergence highlights the strong hydrophobic character of this configuration; this leading singular term (along with the third term) follows from a local lubrication-like analysis of the gap regions between the bubbles, together with general matching considerations and a global conservation relation. The $O(1)$ constant term is found by matching with a leading-order solution in the "outer'" region, where the bubbles appear to be touching. We find excellent agreement between our slip-length formula and a numerical scheme recently derived using a "unified-transform" method (D. Crowdy, IMA J. Appl. Math., 80 1902, 2015). The comparison demonstrates that our asymptotic formula, together with the diametric "dilute-limit" approximation (D. Crowdy, J. Fluid Mech., 791 R7, 2016), provides an elementary analytical description for essentially arbitrary no-slip fractions.

Tracer diffusion coefficients in a sheared inelastic Maxwell gas

We study the transport properties of an impurity in a sheared granular gas, in the framework of the Boltzmann equation for inelastic Maxwell models. We investigate here the impact of a nonequilibrium phase transition found in such systems, where the tracer species carries a finite fraction of the total kinetic energy (ordered phase). To this end, the diffusion coefficients are first obtained for a granular binary mixture in spatially inhomogeneous states close to the simple shear flow. In this situation, the set of coupled Boltzmann equations are solved by means of a Chapman–Enskog-like expansion around the (local) shear flow distributions for each species, thereby retaining all the hydrodynamic orders in the shear rate a. Due to the anisotropy induced by the shear flow, three tensorial quantities Dij, Dp,ij, and DT,ij are required to describe the mass transport process instead of the conventional scalar coefficients. These tensors are given in terms of the solutions of a set of coupled algebraic equations, which can be exactly solved as functions of the shear rate a, the coefficients of restitution and the parameters of the mixture (masses and composition). Once the forms of Dij, Dp,ij, and DT,ij are obtained for arbitrary mole fraction (where nr is the number density of species r), the tracer limit () is carefully considered for the above three diffusion tensors. Explicit forms for these coefficients are derived showing that their shear rate dependence is significantly affected by the order-disorder transition.

Pair mobility functions for rigid spheres in concentrated colloidal dispersions: Force, torque, translation, and rotation.

The formulation of detailed models for the dynamics of condensed soft matter including colloidal suspensions and other complex fluids requires accurate description of the physical forces between microstructural constituents. In dilute suspensions, pair-level interactions are sufficient to capture hydrodynamic, interparticle, and thermodynamic forces. In dense suspensions, many-body interactions must be considered. Prior analytical approaches to capturing such interactions such as mean-field approaches replace detailed interactions with averaged approximations. However, long-range coupling and effects of concentration on local structure, which may play an important role in, e.g., phase transitions, are smeared out in such approaches. An alternative to such approximations is the detailed modeling of hydrodynamic interactions utilizing precise couplings between moments of the hydrodynamic traction on a suspended particle and the motion of that or other suspended particles. For two isolated spheres, a set of these functions was calculated by Jeffrey and Onishi [J. Fluid Mech. 139, 261-290 (1984)] and Jeffrey [J. Phys. Fluids 4, 16-29 (1992)]. Along with pioneering work by Batchelor, these are the touchstone for low-Reynolds-number hydrodynamic interactions and have been applied directly in the solution of many important problems related to the dynamics of dilute colloidal dispersions [G. K. Batchelor and J. T. Green, J. Fluid Mech. 56, 375-400 (1972) and G. K. Batchelor, J. Fluid Mech. 74, 1-29 (1976)]. Toward extension of these functions to concentrated systems, here we present a new stochastic sampling technique to rapidly calculate an analogous set of mobility functions describing the hydrodynamic interactions between two hard spheres immersed in a suspension of arbitrary concentration, utilizing accelerated Stokesian dynamics simulations. These mobility functions provide precise, radially dependent couplings of hydrodynamic force and torque to particle translation and rotation, for arbitrary colloid volume fraction ϕ. The pair mobilities (describing entrainment of one particle by the disturbance flow created by another) decay slowly with separation distance: as 1/r, for volume fractions 0.05 ≤ ϕ ≤ 0.5. For the relative mobility, we find an initially rapid growth as a pair separates, followed by a slow, 1/r growth. Up to ϕ ≤ 0.4, the relative mobility does not reached the far-field value even beyond separations of many particle sizes. In the case of ϕ = 0.5, the far-field asymptote is reached but only at a separation of eight radii and after a slow 1/r growth. At these higher concentrations, the coefficients also reveal liquid-like structural effects on pair mobility at close separations. These results confirm that long-range many-body hydrodynamic interactions are an essential part of the dynamics of concentrated systems and that care must be taken when applying renormalization schemes.

Numerical studies of ductile failure including the third stress invariant

This work addresses an extended version of the well known GTN isotropic hardening model and its numerical integration within a finite element code. The pre-existing yield function of the proposed constitutive model possesses the distinctiveness to be more accurate for arbitrary void volume fraction and especially to explicitly depend upon the third stress invariant. A fully implicit stress integration procedure, based on the return-mapping algorithm, with calculation of the consistent tangent operator is developed for the proposed model. In order to demonstrate the global accuracy and stability of the numerical solution, finite element damage simulations accounting for finite strain and using both the proposed model and, for the purpose of comparison, the GTN isotropic hardening model are performed for the traditional ductile solid problem of necking of a round tensile bar and the two-dimensional simple dynamic shearing problem. The numerical results highlight similarities, good agreement as long as softening initiation of specimen is not reached, and discrepancy as soon as failure of specimen starts, between the proposed model and the GTN model.