Dependent Quantities Research Articles

Discussion of “Measuring and Understanding Contact Area at the Nanoscale: A Review” (Jacobs, T. D. B., and Ashlie Martini, A., 2017, ASME Appl. Mech. Rev., 69(6), p. 060802)

Jacobs and Martini (JM) give a nice review of direct measurement methods (in situ electron microscopy), as well as indirect methods (which are based on contact resistance, contact stiffness, lateral forces, and topography) for measurement of the contact area, mostly at nanoscale. They also discuss simulation techniques and theories from single-contact continuum mechanics, to multicontact continuum mechanics and atomistic accounting. As they recognize, even at very small scales, “multiple-contacts” case occurs, and a returning problem is that the “real contact area” is often an ill-defined, “magnification” dependent quantity. The problem remains to introduce a truncation to the fractal roughness process, what was called in the 1970s “functional filtering.” The truncation can be “atomic roughness” or can be due to adhesion, or could be the resolution of the measuring instrument. Obviously, this also means that the strength (hardness) at the nanoscale is ill-defined. Of course, it is perfectly reasonable to fix the magnification and observe the dependence of contact area, and strength, on any other variable (speed, temperature, time, etc.).

The Non-homogeneous Groshev Convergence theorem for Diophantine Approximation on Manifolds

This paper is based on Khintchine theorem, Groshev theorem and measure and dimension theorems for non-degenerate manifolds. The inhomogeneous Diophantine approximation of Groshev type on manifolds is studied. Major work is to discuss the inhomogeneous convergent theory of Diophantine approximation restricted to non-degenerate manifold in , based on the proof of Barker-Sprindzuk conjecture, the homogeneous theory of Diophantine approximation and inhomogeneous Groshev type theory for Diophantine approximation, by the decomposition of the set in manifold, with the aid of Borel Cantell lemma and transformation of lemma and its properties and the main inhomogeneous conversion principle, we know these two types of set in sense of Lebesgue measure is zero provided that the convergent sum condition is satisfied, from which several conclusions about the inhomogeneous convergent theory of Diophantine approximation is obtained. The main result is that Lebesgue measure is inhomogeneous strongly extremal. At last we use the fact that friendly measure is strongly contracting measure to develop an inhomogeneous strong extreme measure which is restricted to matrices with dependent quantities

Investigation of turbocharger compressor surge inception by means of an acoustic two-port model

The use of centrifugal compressors have increased tremendously in the last decade being implemented in the modern IC engine design as a key component. However, an efficient implementation is restricted by the compression system surge phenomenon. The focus in the investigation of surge inception have mainly been on the aerodynamic field while neglecting the acoustic field. In the present work a new method based on the full acoustic 2-port model is proposed for investigation of centrifugal compressor stall and surge inception. Essentially, the compressor is acoustically decoupled from the compression system, hence enabling the determination of sound generation and the quantification of internal aero-acoustic coupling effects, both independently of the connected pipe system. These frequency dependent quantities are indicating if the compressor is prone to self-sustained oscillations in case of positive feedback when installed in a system. The method is demonstrated on experimentally determined 2-port data of an automotive turbocharger centrifugal compressor under a variety of realistic operating conditions.

Mesh-independent data point finite element method (MDP-FEM) for large deformation elastic-plastic problems - An application to the problems of diffused necking

In this paper, a method to carry out the finite strain elastic-plastic analysis using a remeshing technique is presented. When the remeshing is performed, deformation history dependent physical quantities that are stored at the integration points of finite elements need to be transferred to those of the refined finite elements. Such operations are generally performed based on the shape functions of the finite elements. A typical procedures are that i) the strain history dependent quantities are assigned at the nodal points and ii) interpolations are performed by the shape functions. Such processes assume that the sizes and the arrangements of finite elements change moderately after the remesh. We are aiming at developing a methodology that allows drastic changes in mesh arrangements and sizes and in even kinds of finite elements when the remeshing is carried out. We propose a method that the deformation history dependent physical quantities are stored at points independent of the finite element mesh. They move along with the deformation of the solid. The physical quantities at the points evolve in a Lagrange manner. We name such points to be Mesh-independent Data Points (MDPs). The MDPs take the function to store the physical quantities whereas the finite element mesh takes that of performing the numerical integration. Necessary variables are mapped between the MDPs and the finite element. We call proposed technique to be MDP-Finite Element Method (MDP-FEM). This paper describes the concept of the MDP-FEM and numerical implementations are discussed first. Then, the analyses of diffused necking of tensile bars are presented for a demonstrative purpose.

Federer Measures, Good and Nonplanar Functions of Metric Diophantine Approximation

The goal of this paper is to generalize the main results of [1] and subsequent papers on metric Diophantine approximation with dependent quantities to the set-up of systems of linear forms. In particular, we establish “joint strong extremality” of arbitrary finite collection of smooth nondegenerate submani- folds of .The proof was based on quantitative nondivergence estimates for quasi-polynomial flows on the space of lattices.

Bayesian data analysis tools for atomic physics

We present an introduction to some concepts of Bayesian data analysis in the context of atomic physics. Starting from basic rules of probability, we present the Bayes’ theorem and its applications. In particular we discuss about how to calculate simple and joint probability distributions and the Bayesian evidence, a model dependent quantity that allows to assign probabilities to different hypotheses from the analysis of a same data set. To give some practical examples, these methods are applied to two concrete cases. In the first example, the presence or not of a satellite line in an atomic spectrum is investigated. In the second example, we determine the most probable model among a set of possible profiles from the analysis of a statistically poor spectrum. We show also how to calculate the probability distribution of the main spectral component without having to determine uniquely the spectrum modeling. For these two studies, we implement the program Nested_fit to calculate the different probability distributions and other related quantities. Nested_fit is a Fortran90/Python code developed during the last years for analysis of atomic spectra. As indicated by the name, it is based on the nested algorithm, which is presented in details together with the program itself.

Comment on “Fermion production in a magnetic field in a de Sitter universe”

We point out that the transition probabilities used in a recent perturbative calculation of pair creation in an external magnetic field in the expanding de Sitter space with the $in$ and $out$ fermion states defined by the Bunch-Davies modes [C. Crucean et al., Phys. Rev. D 73 044019 (20016)] are gauge dependent quantities. We examine the gauge variations of these amplitudes assuming a decoupling of the interaction at infinite times, which allows to conclude that the source of the problem lies in the nonoscillatory behavior of the fermion current in the infinite future.

Comparison of brief versus extended personalised feedback in an online intervention for cannabis users: Short-term findings of a randomised trial

Previous studies have shown brief online self-help interventions to be a useful method of treating cannabis use and related problems; however, no studies have compared the effects of brief versus extended feedback for online brief intervention programs. ObjectivesThe current study was a two arm randomised trial aimed at testing the short term effectiveness of a brief and extended feedback version of Grassessment, a brief online intervention for cannabis users that provides individualised feedback regarding use, motives, and harms. MethodsParticipants (n=287) reporting at least one symptom of DSM IV cannabis abuse or dependence were recruited using online and offline advertising methods. Participants were randomised to receive either a brief or extended feedback version of the Grassessment program and were required to complete a one month follow up questionnaire. ResultsOne hundred and ninety four participants completed the one month follow up. Wilcoxon analyses showed a significant decrease in past month quantity and frequency of cannabis use (ps<0.001; r=−0.41 and −0.40 respectively) and lower severity of dependence scores (p=0.002; r=−0.31) among those in the brief feedback condition. Participants in the extended feedback group also demonstrated significant decreases in patterns of use (ps<0.002; r=−0.39 and −0.33) but not severity of dependence (p=0.09; r=0.18). A Generalized Estimating Equation (GEE) analysis showed no significant interaction between length of feedback received and past month cannabis use frequency (p=0.78), quantity (p=0.73), or severity of dependence (p=0.47). ConclusionThis study adds support for the use of brief online self-complete interventions to reduce cannabis use and related problems in the short term. The findings suggest that in the case of the brief online screening and feedback program Grassessment, extended feedback does not lead to superior outcomes over brief feedback.

Comparing Labour Laws in the EU Internal Market: A Social Actor Perspective

The discipline of comparative labour law suffers from a dual crisis: comparative law may seem irrelevant if nation states are pushed back by ever accelerating globalization, and labour law may be rendered irrelevant by the digitalized economy. This article argues that, since states are becoming interdependent instead of superfluous, and work remains a dependent quantity, there is a future for comparative labour law. This future requires an even higher degree of interdisciplinarity with a strong recovery of disciplinary (doctrinal) research. This article develops a social actor-centred approach for comparing labour law and policy in the context of economic integration beyond states, as pursued by the European Union. A comparative project relating to collective labour rights in the EU internal market is outlined as an example of this methodology.

Development of an inventory model for two suppliers with random capacity considering supply disruption

Supply disruption occurs for diverse reasons including transportation problem, equipment failure, raw material shortages, natural calamities etc. As a result supplier may become unavailable at random times for random time length. In addition, suppliers may also have random capacities leading to uncertain yield in orders. Again under random supplier capacities, the retailer should order from a number of suppliers in order to diversify the risk associated with shortages. The objective of this paper is to develop an inventory model for two suppliers with random capacities considering supply disruption. A modified (Q, r) model is developed to tackle the problem of future supply uncertainty in response to the demand generated by Poisson process. Two suitable optimisation algorithms are applied to search for the optimal values of the decision variables which are state dependent order quantities and reorder point to minimise the cost per unit time. A hypothetical example and its solution are then provided to have a better understanding about the demonstration of the proposed model. Finally, sensitivity analysis is also carried out to have better insights about the model developed.

Development of an inventory model for two suppliers with random capacity considering supply disruption

Supply disruption occurs for diverse reasons including transportation problem, equipment failure, raw material shortages, natural calamities etc. As a result supplier may become unavailable at random times for random time length. In addition, suppliers may also have random capacities leading to uncertain yield in orders. Again under random supplier capacities, the retailer should order from a number of suppliers in order to diversify the risk associated with shortages. The objective of this paper is to develop an inventory model for two suppliers with random capacities considering supply disruption. A modified (Q, r) model is developed to tackle the problem of future supply uncertainty in response to the demand generated by Poisson process. Two suitable optimisation algorithms are applied to search for the optimal values of the decision variables which are state dependent order quantities and reorder point to minimise the cost per unit time. A hypothetical example and its solution are then provided to have a better understanding about the demonstration of the proposed model. Finally, sensitivity analysis is also carried out to have better insights about the model developed.

A dynamic strategy for wavelength sensing using the diffracted orders of a grating.

We propose a strategy for real time multicolour detection of light emitting particles under flow conditions, using the diffracted orders of a grating. The method relies on the fact that the spatial (angular/linear) separation between the orders of a diffraction grating is a wavelength dependent quantity. Thus, the difference in arrival times at a fixed detector for neighbouring orders produced by a moving, light-emitting particle can be used as a wavelength sensing mechanism. We demonstrate this functionality using a prototype PDMS microfluidic device that incorporates a focusing transmission grating. A key attribute of this approach is that it requires only a single sensitive detector, such as a photomultiplier tube, in contrast to many conventional approaches which require multiple sensitive detectors or a detector array.

On large deformation analysis method using mesh-independent data points to store the strain history dependent quantities

On large deformation analysis method using mesh-independent data points to store the strain history dependent quantities

サイクルジャンプ法を用いた繰返し荷重問題解析の高精度化に関する研究

In this paper, formulations and some computational results of cycle jump method based on the nonlinear finite element method are presented. Problems, involving nonlinear cyclic deformation, such as low cycle fatigue problems can be solved by the proposed cycle jump method. To solve the problems of nonlinear cyclic deformation of structure by the nonlinear finite element method with a cycle-by-cycle approach, a large amount of computational time is generally required. Thus a cycle jump method is presented from a view point of temporal multi-scale analysis. Then, an alternative analytical procedure consisting of three steps is proposed. They are a few cycles of nonlinear analysis in a cycle-by-cycle fashion, computations of jumps of strain history dependent quantities (extrapolations) based on the results of the cycle-by-cycle analysis and a cycle jump for several dozen to several hundred cycles using the results of the extrapolations. The results of cycle jump analyses are presented and their accuracies are critically examined. It was found that the results of several load cycles at the beginning of each cycle-by-cycle analysis step should be excluded from the computations of the extrapolation step.

Radiation budget of vegetation canopies with reflective surface: A generalization using the Markovian approach

Empirical and theoretical evidence has shown that the scattering and absorptance of a homogeneous leaf canopy with black soil can be modeled using simple algebraic combinations of two spectrally invariant parameters (the recollision probability and the canopy interceptance) and one spectrally dependent quantity (the single scattering albedo of an average phytoelement). This study generalizes such results for vegetation canopies composed of one or more types of phytoelements and with a reflective background surface also composed of one or more materials, all of which are treated as endmembers of a nonlinear spectral mixture. The conservative radiation field of a canopy is represented by a finite state Markov chain, such that for a vegetation-surface medium composed of m endmembers, the model is thereby parameterized in terms of an m-length vector of endmember interceptances and an mth-order square matrix containing probabilities of photon recollision amongst the endmembers. Comparisons of some instances of the model with radiative transfer based approximations showed how the latter may overestimate canopy reflectance and transmittance. The two-endmembers model was also compared with Monte Carlo simulations for spherically-oriented leaf canopies with reflective soil. Results indicated that the analytical model accurately describes the radiation field for a wide range of soil reflectance and LAI values. Simulations also showed that while the zenith angle of the illumination source has a small influence on the recollision probabilities, the LAI value mainly determines these through distinct functional relationships. The application of the model to estimate the canopy radiation field of two coniferous species located on the Mexico City Conservation Land is also demonstrated using airborne hyperspectral measurements.

Determination of effective properties for CFRP curing coupled to viscoleasticity based on a three‐scale framework

AbstractOur work presents a three‐scale model for temperature‐dependent visco‐elastic effects accompanied by curing, which are important phenomena in a resin transfer molding (RTM) process. The effective bulk quantities in dependence on the degree of cure are obtained by homogenization for a representative unit cell (micro‐RVE) on the heterogeneous microscale. To this end, an analytic solution is derived by extension of the composite spheres model [1]. Voigt and Reuss bounds resulting from the assumption of a homogeneous matrix proposed in [2] are compared to the effective quantities. During curing, the periodic mesostructure defined by a visco‐elastic polymeric matrix and linear‐thermo‐elastic fibres is taken into account as a representative unit cell (meso‐RVE) subjected to thermo‐mechanical loading on the mesoscale. (© 2016 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Improved Reissner–Nordström–(A)dS black hole in asymptotic safety

This paper studies the quantum modifications of the Reissner–Nordström–(A)dS black hole within Quantum Einstein Gravity, coupled to an electromagnetic sector. Quantum effects are introduced on the level of the improvements of the classical solution, where the originally constant couplings ([Formula: see text], [Formula: see text] and [Formula: see text]) are promoted to scale dependent quantities ([Formula: see text], [Formula: see text] and [Formula: see text]). Those running couplings are calculated in the functional renormalization group approach. A crucial point of this so-called “improving solutions” procedure is the scale setting where the arbitrary scale [Formula: see text] acquires physical meaning due to a relation to the coordinate scale [Formula: see text]. It is proposed to use such scale settings which are stable after iterative improvements. Using this method one finds that for those improved solutions, there is no stable remnant and due to the appearance of a new internal horizon, there is also no necessity to impose a minimal black hole mass for charged black holes, in order to avoid the cosmic censorship hypothesis.

Nonclassicality in an atom–molecule Bose–Einstein condensate: Higher-order squeezing, antibunching and entanglement

Abstract The transient quantum statistical properties of the atoms and molecules in an atom–molecule BEC system are investigated by obtaining a third-order perturbative solution of the Heisenberg’s equations of motion corresponding to the Hamiltonian of the system, where two atoms can collide to form a molecule. Time dependent quantities, like two boson correlation, entanglement, squeezing, antibunching, etc., are computed, and their properties are compared. It is established that the atom–molecule BEC system is highly nonclassical as lower-order and higher-order squeezing and antibunching in pure (atomic and molecular) modes, squeezing and antibunching in compound mode, and lower-order and higher-order entanglement in compound mode can be observed in the atom–molecule BEC system. Exact numerical results are also reported and the analytic results obtained using the perturbative technique are shown to agree with the exact numerical results.

Off-shell amplitudes as boundary integrals of analytically continued Wilson line slope

One of the methods to calculate tree-level multi-gluon scattering amplitudes is to use the Berends-Giele recursion relation involving off-shell currents or off-shell amplitudes, if working in the light cone gauge. As shown in recent works using the light-front perturbation theory, solutions to these recursions naturally collapse into gauge invariant and gauge-dependent components, at least for some helicity configurations. In this work, we show that such structure is helicity independent and emerges from analytic properties of matrix elements of Wilson line operators, where the slope of the straight gauge path is shifted in a certain complex direction. This is similar to the procedure leading to the Britto-Cachazo-Feng-Witten (BCFW) recursion, however we apply a complex shift to the Wilson line slope instead of the external momenta. While in the original BCFW procedure the boundary integrals over the complex shift vanish for certain deformations, here they are non-zero and are equal to the off-shell amplitudes. The main result can thus be summarized as follows: we derive a decomposition of a helicity-fixed off-shell current into gauge invariant component given by a matrix element of a straight Wilson line plus a reminder given by a sum of products of gauge invariant and gauge dependent quantities. We give several examples realizing this relation, including the five-point next-to-MHV helicity configuration.

A uniaxial stress capacitive dilatometer for high-resolution thermal expansion and magnetostriction under multiextreme conditions.

Thermal expansion and magnetostriction are directional dependent thermodynamic quantities. For the characterization of novel quantum phases of matter, it is required to study materials under multi-extreme conditions, in particular, down to very low temperatures, in very high magnetic fields or under high pressure. We developed a miniaturized capacitive dilatometer suitable for temperatures down to 20 mK and usage in high magnetic fields, which exerts a large spring force between 40 to 75 N on the sample. This corresponds to a uniaxial stress up to 3 kbar for a sample with cross section of (0.5 mm)(2). We describe design and performance test of the dilatometer which resolves length changes with high resolution of 0.02 Å at low temperatures. The miniaturized device can be utilized in any standard cryostat, including dilution refrigerators or the commercial physical property measurement system.