Implicit Dependence Research Articles

Ac response of thin-film superconductors at various temperatures and magnetic fields

Abstract A common method for measuring the electromagnetic properties of superconductors is to measure their complex magnetic ac susceptibility χ as a function of freauency ω and amplitude H0 , with the temperature T and applied dc magnetic field Hdc a as parameters. The basic theory of the linear χ(ω)and nonlinear χ(H0 , ω) is outlined for various geometries, for example, discs, rings and strips of thin films or thicker platelets in a perpendicular magnetic field. It is shown how χ (ω) explicitly depends on the linear resistivity p ac(ω) = E/J or penetration depth Λac(ω), and how χ (H 0, ω) depends on the nonlinear current-voltage law E(J, B) where E(r), J(r) and B(r) are the local electric field, current density and induction respectively. The dependences of E(J, B) on T and on various material properties such as pinning forces or pinning energies, structural defects and granularity lead to an implicit dependence of χ on these parameters.

LIBOR market models in practice

In this paper, LIBOR market models with a number of factors ranging from 1 to 10 are studied. The emphasis throughout is on the application for term structure modeling and (exotic) securities pricing rather than on technical issues. The study falls into two parts. In the first part, the models are calibrated to cap and swaption prices for several major markets and it is observed - perhaps contrary to expectations - that the overall market fit is independent of the number of factors. Closer investigation shows that the number of factors affects the implicit calendar time dependence of the volatility function: models with a high number of factors allow a more stationary volatility function than do models with few factors. In the second part of the study, the implications for exotics pricing of the number of factors in the model are investigated. As expected in view of the findings regarding the time dependence of the volatility function, a very strong sensitivity of exotics prices to the number of factors is found. This finding has far-reaching implications for derivatives pricing in practice.

Renormalization of two-dimensional quantum electrodynamics

The Schwinger model, when quantized in a gauge non-invariant way exhibits a dependence on a parameter a (the Jackiw-Rajaraman parameter) in a way which is analogous to the case involving chiral fermions (the chiral Schwinger model). For all values of a 6= 1, there are divergences in the fermionic Green’s functions. We propose a regularization of the generating functional Z[η, η, J ] and we use it to renormalize the theory to one loop level, in a semi-perturbative sense. At the end of the renormalization procedure we find an implicit dependence of a on the renormalization scale μ. ∗casana@cat.cbpf.br †tiao@cat.cbpf.br

The whole-partial derivative

We discuss two types of partial derivatives which occur, e.g., in the Euler–Lagrange equations. To avoid confusion, a different notation (ðF/ðxμ) and a new name (whole-partial derivative) are suggested for what is usually written as ∂F/∂xμ but acts on both the explicit and implicit dependence of F upon the coordinate xμ.

Finite deformation Cosserat-type modelling of dissipative solids and its application to crystal plasticity

Recently, several proposals were made for the enlargement of the classical field equations in order to solve locally inhomogeneous deformation problems (e.g. at shear banding and damage localization or of composites). In the present paper basic issues of this topic will be treated: i) the implicit dependence within the gradient plasticity theory, ii) the more open micromorphic view-point of the gradient of internal variable approach, iii) a derivation of an elastic-plastic decomposition of the Cosserat strain measures, iv) its application to the description of lattice curvature in crystals. Finally, finite element simulations of strain localization in Cosserat single crystals are presented.

Measurements of the relationship between submicron aerosol number and volume concentration

The relationship between aerosol number concentration and volume, or mass, concentration is a key linkage for the impact of aerosols on cloud albedo and thus climate forcing. Furthermore, this relationship is important in interpreting aerosol remote retrievals by satellites. We report here aircraft data, primarily from the TARFOX (Tropospheric Aerosol Radiative Forcing Experiment) study, which suggest a general linear relationship between aerosol number and mass concentration in the effective cloud condensation nucleus (CCN) size range (diameter >0.1 μm) for the locations examined. Limited data on the relationship between aerosol number concentration and chemical composition are also presented, which show a preferential dependence of effective CCN number concentration on sulfate mass. However, an implicit dependence on organic mass is also suggested.

Improved R-factors for diffraction data analysis in macromolecular crystallography.

The quantity Rsym (also called Rmerge) is almost universally used for describing X-ray diffraction data quality. Here, we prove that Rsym is seriously flawed, because it has an implicit dependence on the redundance of the data. A corrected R-factor, Rmeas, is introduced as the equivalent robust indicator of data consistency. In addition, we introduce Rmrgd an R-factor that reflects the gain in accuracy upon averaging of equivalent reflections, as a useful indicator of the quality of reduced data. These new data quality indicators better reveal the benefits of highly redundant data and should stimulate improvements in data quality through increased merging of data from multiple crystals.

THE KBM DERIVATIVE EXPANSION METHOD IS EQUIVALENT TO THE MULTIPLE-TIME-SCALES METHOD

Several perturbation methods are commonly used to predict the free and forced response of weakly non-linear oscillators. The Krylov-Bogoliubov-Mitropolsky (KBM) and multiple-time-scales (MTS) methods use expansions of dependent variables, ordinary time derivatives, and some system parameters to convert the equations of motion into a set of first order differential equations. Each of these equations represents the slow time modulations of the amplitude and phase of the zeroth order solution(s).In this paper, a simple correspondence between the expansions of ordinary time derivatives employed in these two methods is used to show that, except for notation, these two methods are identical in the sense that to any order of approximation these two methods will provide identical results when they use the same parameter expansions and identical additional constraints. The KBM method attempts to reduce unneeded algebraic calculations by tailoring the derivative expansions to the simplest applicable form. This, however, requires some experience or a trial and error approach to establish the intermediate expansion variables and the implicit and explicit dependence of perturbation solutions on the different time scales. This relation depends not only on the problem at hand but also on the parameter expansions used in the solution procedure. By using the most general expansion for the time derivatives, the MTS method establishes this dependence as a part of the analysis. In this method, the algebraic details are hidden by using a compact derivative operator type notation. However, these operators do not commute in general.

A Newton–Raphson Pseudo-Solid Domain Mapping Technique for Free and Moving Boundary Problems: A Finite Element Implementation

An implicit, pseudo-solid domain mapping technique is described that facilitates finite element analysis of free and moving boundary problems. The technique is based on an implicit, full-Newton strategy, free of restrictions on mesh structure; this leads to many advantages over existing domain mapping techniques. The fully coupled approach using Newton's method is particularly effective for problems with strong coupling between the internal bulk physics and the governing physics at unknown free boundary locations. It is also useful when the distinguishing conditions which constrain the free boundary shape provide only an implicit dependence on the boundary location. Unstructured meshes allow for efficient resolution of internal and boundary layers and other regions of strong local variations in the solution and they also reduce the amount of user interaction required to define a problem since the meshes may be generated automatically. The technique is readily applied to steady or transient problems in complex geometries of two and three dimensions. Examples are shown that include free and moving boundary problems from solidification and capillary hydrodynamics.

Nuclear curvature energy in relativistic models.

The difficulties arising in the calculation of the nuclear curvature energy are analyzed in detail, especially with reference to relativistic models. It is underlined that the implicit dependence on curvature of the quantal wave functions is directly accessible only in a semiclassical framework. It is shown that also in the relativistic models quantal and semiclassical calculations of the curvature energy are in good agreement. \textcopyright{} 1996 The American Physical Society.

The Additive Ep-Condition and the Critical Scuffing Limit for Rolling-Sliding

Abstract This paper introduces a new model for the scuffing load capacity in heavily loaded contacts, concerned specifically with the effects of EP-additive oils. The scuffing limit for the additive condition will be closely related to the initial additive-free case, using the calculation method of Blok, solely on a referential level. The process thermodynamics involved at a friction contact will be related to a phenomenological integral relation, containing the necessary internal coordinate to describe the implicit dependence of the friction coefficient with time. The experimental response of the friction contact depends on a relaxant friction coefficient due to the additive effect. The simple calculation method requires only three input parameters for the prediction of the scuffing limit, and these can be obtained from a few experimental scuffing tests. All the tribology of the present scuffing model can be considered to be contained in a simple linear relationship, with the sliding speed as the dominant variable. The calculation criterion has shown to have predictive capability which agrees well with experiments.

State space boundary element–finite element coupling for fluid–structure interaction analysis

State space coupling is a new approach for handling computational fluid–structure interaction problems in the low to medium frequency range. The method is based on standard boundary element (BEM) and finite element (FEM) discretizations of the acoustic and structural domains, respectively. The implicit frequency dependence of a traditional acoustic impedance matrix is made explicit through a power series expansion on circular frequency and considering time harmonic motion. Once expanded, the acoustic energy of the fluid is directly coupled to that of the structure via Hamilton’s principle. The coupled system is then recast in a canonical state space form which is also in the form of a standard eigenvalue problem. Solution of this system produces a series of complex eigenvalues and eigenvectors which represent a modal decomposition of the fluid-loaded structure. Biorthogonality properties of the state space eigensystem allow for an uncoupled, modal solution of the forced problem. Results for a submerged spherical shell and a finite plate in an infinite ridged baffle are given to illustrate the state space approach.

Two-loop calculations with vertex corrections in the Walecka model.

Two-loop corrections with scalar and vector form factors are calculated for nuclear matter in the Walecka model. The on-shell form factors are derived from vertex corrections within the framework of the model and are highly damped at large spacelike momenta. The two-loop corrections are evaluated first by using the one-loop parameters and mean fields and then by refitting the total energy/baryon to empirical nuclear matter saturation properties. The modified two-loop corrections are significantly smaller than those computed with bare vertices. Contributions from the anomalous isoscalar form factor of the nucleon are included for the first time. The effects of the implicit density dependence of the form factors, which arise from the shift in the baryon mass, are also considered. Finally, necessary extensions of these calculations are discussed.

Source, path and site effects on dominant frequency and spatial variation of strong ground motion recorded by smart1 and smart2 arrays in Taiwan

AbstractThe reduction in spatial variance of strong ground motion with increasing earthquake magnitude has been reported recently. However, we show that the observed dependence of spatial variance on magnitude is its implicit dependence on the frequency content (dominant frequency) of the wave field. Time‐domain cross‐correlations of pairs of accelerograms are used to quantify the spatial variations in this paper. Magnitude is one of the factors contributing to the dominant frequency. We attempt to study separately the effects of magnitude, hypocentral distance, peak ground acceleration and focal depth on the dominant frequency in order to find the most significant one. The data base consists of 1965 records of horizontal acceleration from 148 local earthquakes in Taiwan. The analysis shows the overwhelming effect of the source magnitude on the formation of the dominant frequency with an empirical relationship: No significant effect of hypocentral distance, local acceleration amplitude or depth is detected for all their values available (up to 170 km, 250 cm/s2, and 100 km, respectively). The prevailing effect of magnitude on the dominant frequency is a real cause of the consistently observed reduction of spatial variance of ground motion with increasing magnitude of earthquakes.

Resonant energy dependence of the hyperpolarizability β: On the possibility of double resonance enhancement

The dependence of the first molecular hyperpolarizability on the energy of the transition to the first excited state is examined under the assumptions of the two-level model of Oudar and Chemla. It is found that the resonance enhancement term is not maximized when λmax lies between the fundamental wavelength and its harmonic, contrary to frequency assertion. It is also found that the explicit λmax dependence of β is much smaller than the implicit dependence. These two facts imply that it is indeed desirable for a nonlinear chromophore’s λmax to lie to the red of a laser’s second harmonic, but not because of double resonance enhancement.

Bayesian quality control using multivariate normal distributions

AbstractAn expression for the probability density of any distribution of observed values (given background values of known accuracy) is derived from the properties of multivariate normal distributions. This is used in the quality control of observations—‘good’ and ‘bad’ observations are assumed to have errors from a normal distribution and from a distribution giving no useful information respectively.Three Methods of quality control are presented and compared; two of these are based on the probability density derived above, and the third is based on a related maximum probability analysis. They differ in the optimality principal used: Individual Quality Control finds the most likely quality (i.e. good or bad) for each observation, given information from all the others; Simultaneous quality Control finds the most likely combination of qualities; while Variational Quality Control is based on a variational analysis which finds the most likely true values. The quality control should be considered as part of the ‘analysis’ process of using the observations; these approaches to quality control are considered as approximations to a system giving the ‘best’ analysis, based on minimizing a Bayesian loss function. Approximation are also necessary in their practical implementations; the effect of these on various operational schemes is discussed.The multi‐observation framework used includes the ‘background’ check as a special case, and it is extended to deal with observations with common sources of gross error. Applications to multi‐level checks, bias checks and checks for known error patterns are sketched.As a by‐product the standard statistical interpolation formulae are derived from the properties of normal distributions, thus demonstrating the implicit dependence of statistical interpolation on the normal distribution.

A relationship between NMR cross‐polarization rates and dynamic storage modulae of polymers

AbstractA relationship between dynamic storage modulus (E′) and the mean cross‐polarization time constants 〈TCH〉 for 16 polymer data sets has been established by using a standard linear solid model. This model is used in an attempt to equate the process of cross‐polarization with mechanical rigidity by virtue of the implicit dependence of each phenomenon on molecular motion. The apparent validity of the relationship between these parameters indicates that cross‐polarization in polymers can be a function of molecular motion in addition to microscopic spin dynamics. The limitations as well as practical applications of this relationship are discussed. © 1993 John Wiley & Sons, Inc.

Systems models for infrastructures

Abstract The paper analyzes the equations which model the growth of human populations and the accompanying infrastructure developments which are required to support the corresponding societies because of their direct or implicit dependence upon human needs. Systems methods are employed to treat the coupled non-linear phenomena, and numerical examples are displayed. The fundamental nature of the models is found to be logistic, and there is switching at critical points between regimes or phases of growth.

Functional-integral approach to strongly correlated Fermi systems: Quantum fluctuations beyond the Gutzwiller approximation.

A systematic extension of the model of almost localized fermions to finite temperatures is presented. It consists in accounting for the quantum fluctuations beyond the Gutzwiller approximation (GA). We use the slave-boson formulation of the Hubbard model which has been proved to be equivalent at the saddle-point level to the GA. We determine the values of the Lagrange multipliers introduced to enforce the constraints, and show how they involve a Mott gap at nearly half filling for {ital U}{gt}{ital U}{sub {ital c}} (localization edge). The results of the GA for the correlation functions are reproduced at the saddle point when taking into account the implicit dependence of the boson fields with the external excitation. The Gaussian fluctuations are then considered in a renormalized basis of the boson fields which brings out two distinct channels (symmetric {ital s} and antisymmetric {ital a}). We show how the free energy and the correlation functions can be simply expressed as a function of the same Landau parameters {ital F}{sub 0}{sup {ital s}} and {ital F}{sub 0}{sup {ital a}} defined in the GA.

Infall patterns around rich clusters of galaxies

The pattern of infall velocities induced by a rich cluster of galaxies is considered, using an infall model based on the Friedmann solution to determine the exact implicit dependence of the peculiar velocity on the density enhancment and the mean cosmological mass density, Omega(0). An analytic model for the distribution of galaxies around a cluster core in redshift space is developed. The high-density caustics in redshift space are shown to appear as envelopes around rich clusters. Assuming that the galaxies trace the matter distribution, low Omega(0) models can explain observational data obtained for four clusters. The present results support the prediction that light traces mass in the infall region. 26 refs.