Intuitive Physical Interpretation Research Articles

Vibrational spectra of ammonia, benzene, and benzene adsorbed onSi(001)byfirst principlescalculations with periodic boundary conditions

We develop an efficient method for the calculation of dynamical dipoles and frequencies of vibrational transitions in the framework of density-functional theory with periodic boundary conditions. It augments previous approaches by accounting for the substrate influence on the vibrations of the adsorbate. It allows one to reproduce and predict optical infrared and electron energy loss spectra including the correct relative oscillator strengths while still staying in the familiar picture of normal modes so that an intuitive physical interpretation of experimental results is possible.

Non-iterative numerical method for laterally superresolving Fourier domain optical coherence tomography

A numerical deconvolution method to cancel lateral defocus in Fourier domain optical coherence tomography (FD-OCT) is presented. This method uses a depth-dependent lateral point spread function and some approximations to design a deconvolution filter for the cancellation of lateral defocus. Improved lateral resolutions are theoretically estimated; consequently, the effect of lateral superresolution in this method is derived. The superresolution is experimentally confirmed by a razor blade test, and an intuitive physical interpretation of this effect is presented. The razor blade test also confirms that this method enhances the signal-to-noise ratio of OCT. This method is applied to OCT images of medical samples, in vivo human anterior eye segments, and exhibits its potential to cancel the defocusing of practical OCT images. The validity and restrictions involved in each approximation employed to design the deconvolution filter are discussed. A chromatic and a two-dimensional extensions of this method are also described.

C15 MEMSジャイロセンサによるはり構造物の損傷モニタリング(OS6-1 建築・都市のモニタリングとリスク制御I)

This paper describes a damage identification method for beam structures based on the local flexibility. A modal flexibility-based damage indices that have simple and intuitive physical interpretation is presented. Since the proposed damage indices are computed using angular mode shapes of the lowest several modes, MEMS gyroscopes are adopted as the sensing device. The bandwidth of the MEMS gyroscope is experimentally investigated to show the feasibility of MEMS gyro-based damage monitoring. Experiments using a bolted beam are conducted to show the applicability of the proposed algorithm to the detection of loose bolt failures.

Inverse and Direct Dynamic Modeling of Gough–Stewart Robots

This paper presents closed-form solutions for the inverse and direct dynamic models of the Gough-Stewart parallel robot. The models are obtained in terms of the Cartesian dynamic model elements of the legs and of the Newton-Euler equation of the platform. The final form has an interesting and intuitive physical interpretation. The base inertial parameters of the robot, which constitute the minimum number of inertial parameters, are explicitly determined. The number of operations to compute the inverse and direct dynamic models are given.

Sum-rule approaches to the elementary excitation spectrum of interacting gases of finite bosons in harmonic potentials

Based on the corrected sum rules and generalized virial identities, we derive an expression for all modes of excitation spectrum of interacting Bose gases at finite atom numbers in axially anisotropic potentials, in terms of the N-body ground state average. Using the variational Gaussian calculation for the ground-state wave function, its explicit analytic formulas are obtained. These results show clearly the dependence of excitation spectrum on the interaction strength parameter $p = \sqrt{2/\pi}({a_{\rm sc}}/{a_{\rm ho}})(N-1)$ and trap geometry parameter $ \lambda $ for the system with N = 1 through $N\rightarrow \infty $ . For $ \lambda = 0$ and 1 the dependences have simple and intuitive physical interpretations. We compare the low-lying excitation spectra with the existing numerical results and make quantitative predications for future experiments and numerical simulation for higher-lying excitation modes.

Area-Average Solar Radiative Transfer in Three-Dimensionally Inhomogeneous Clouds: The Independently Scattering Cloudlet Model

A new conceptual and computational basis is described for renormalizing the single-scatter and extinction properties (optical depth, single-scatter albedo, and scattering phase function or asymmetry parameter) of a three-dimensionally inhomogeneous cloud volume or layer so as to describe a radiatively equivalent homogeneous volume or layer. The renormalization may allow area-averaged fluxes and intensities to be efficiently computed for some inhomogeneous cloud fields using standard homogeneous (e.g., plane parallel) radiative transfer codes. In the Independently Scattering Cloudlet (ISC) model, macroscopic “cloudlets” distributed randomly throughout a volume are treated as discrete scatterers, analogous to individual cloud droplets but with modified single-scatter properties due to internal multiple scattering. If a volume encompasses only cloudlets that are optically thin, the renormalized single-scatter properties for the volume revert to the intrinsic values and the homogeneous case is recovered. Although the ISC approach is based on a highly idealized, and therefore unrealistic, geometric model of inhomogeneous cloud structure, comparisons with accurate Monte Carlo flux calculations for more realistic random structures reveal surprising accuracy in its reproduction of the relationship between area-averaged albedo, direct transmittance, diffuse transmittance, and in-cloud absorptance. In particular, it describes the approximate functional dependence of these characteristics on the intrinsic single-scatter albedo when all other parameters are held constant. Moreover, it reproduces the relationship between renormalized single-scatter albedo and renormalized optical thickness derived independently, via a perturbative analysis, by other authors. Finally, the ISC model offers a reasonably intuitive physical interpretation of how cloud inhomogeneities influence area-averaged solar radiative transfer, including the significant enhancement of in-cloud absorption under certain conditions.

Performance bounds for estimating vector systems

We propose a unified framework for the analysis of estimators of geometrical vector quantities and vector systems through a collection of performance measures. Unlike standard performance indicators, these measures have intuitive geometrical and physical interpretations, are independent of the coordinate reference frame, and are applicable to arbitrary parameterizations of the unknown vector or system of vectors. For each measure, we derive both finite-sample and asymptotic lower bounds that hold for large classes of estimators and serve as benchmarks for the assessment of estimation algorithms. Like the performance measures themselves, these bounds are independent of the reference coordinate frame, and we discuss their use as system design criteria.

Understanding System Zeros

An intuitive physical interpretation of a transfer function's poles is easily made: the natural frequencies of the system. A similar physical interpretation of a transfer function's zeros can also be made: the natural frequencies of special subsystems. In this paper, such an interpretation is advanced for certain spring-mass-damper systems using a rigorous and intuitive demonstration. This interpretation may serve as a useful paradigm for understanding the relationship between structural dynamics and transfer functions.

Evidence of different conduction mechanisms in accumulation-mode p-channel SOI MOSFET's at room and liquid-helium temperatures

The threshold voltage for the three different conduction components of an accumulation-mode PMOS SOI were experimentally extracted at room and liquid-helium temperatures. A deep-depletion transient effect was observed to play an important role when one of the interfaces was in inversion, even at room temperature. An intuitive physical interpretation is given for the suppression of some current components at liquid-helium temperatures. In addition, a simple model for calculating the silicon-film thickness and the doping level is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A 3-D finite element for laminated composites with 2-D kinematic constraints

In this paper, a new 3-D element (3DLC) is presented for the analysis of laminated composite shells. The new element expedites the modeling process by presenting the designer with an intuitive physical interpretation for the different components of the model. The element is compatible with conventional 3-D continuum elements. It can represent arbitrarily curved shells with variable number of layers and variable thickness. Each element has a small number of degrees of freedom which facilitates its incorporation in commercial finite element codes. Aspect ratio limitations and shear locking of conventional 3-D continuum elements have been eliminated by using the kinematic constraints of layer-wise constant shear theories. The formulation and simple validation problems are presented.

The accelerated failure time model: A useful alternative to the cox regression model in survival analysis

For the past two decades the Cox proportional hazards model has been used extensively to examine the covariate effects on the hazard function for the failure time variable. On the other hand, the accelerated failure time model, which simply regresses the logarithm of the survival time over the covariates, has seldom been utilized in the analysis of censored survival data. In this article, we review some newly developed linear regression methods for analysing failure time observations. These procedures have sound theoretical justification and can be implemented with an efficient numerical method. The accelerated failure time model has an intuitive physical interpretation and would be a useful alternative to the Cox model in survival analysis.

Measurement of threshold voltages of thin-film accumulation-mode PMOS/SOI transistors

Accumulation-mode PMOS transistors on SOI (silicon on insulator) are characterized by several conduction mechanisms. Measurements of the threshold voltage corresponding to each of them are presented for the first time. An intuitive physical interpretation of their dependence on the front- and back-gate voltages is also given. >

Nuclear Collective Motion from a Group Theoretical Standpoint

6'are classified using the method of the induced representations and the imprimitivity theorem. The wave function and the wave equation are obtained by this method. We introduce a Hamiltonian and give a formula for calculating the energy spectrum that depends on. deformations and rotations. basis, has developed primarily from symmetry concepts since the very beginning of nuclear physics. Hence one strongly relies on group theory in building new models which describe the nuclear collective motion by either introducing groups or exploit­ ing techniques based on group theory which are not customary in nuclear physics. The present paper exploits a fundamental technique well-known to mathematical physicists but not often used in nuclear physics. This technique is that of induced representations and imprimitivity theorem, originated by Wignei for the Poincare group, and is very well adapted to the collective motion group CM(3), since both the same intrinsic structure (semi-direct product). The use of this technique allows us to obtain several results, the most important one being the classification of all unitary irreducible representations of CM(3). The Hilbert space that carries an irreducible representation of CM(3) is to be regarded as the space of collective nuclear wave functions. Such a Hilbert space, for each irreducible representation, is characterized by an equation which assumes the role of a wave equation. The wave functions are defined on the space of mass quadrupole tensors, which allows an intuitive physical interpretation of the model. Using physical intuition and the symmetry of the model we define a Hamiltonian which yields a concise and easily interpreted formula for the energy spectrum. The latter depends on both deforma­ tions and rotations and is a continuum spectrum. One could add a potential, depend­ ing also on the mass quadrupole coordinates, in order to have a discrete energy sp~ctrum. This possibility remains open, since we have not pursued it further here. The outline of the paper is the following. In § 2 we present a survey on the subject of nuclear collective motions aimed at singling out CM(3) as nuclear collective motion group. Section 3 is very technical and yields the classification of the unitary irreducible representations of CM(3). In § 4 we introduce a possible Hamiltonian for , our model and derive the energy spectrum.

Tipología axiomática de las teorías empíricas

The author analyses, within a framework of the structuralist conception of science, different types of axioms that may occur in empirical theories, set-theoretically axiomatized ; in the process, he states six theses, offering formal definítions to characterize each type of axiom, except for the last one. The following set-theoretieal axiomatization of classical collision mechanies (CM) is used as ilIustration: CM (x) iff there exists P, S, T, e, v, m, t1, t2 such that: (0) x= ≺P, S, T, /R, c, v, m≻ (1) P is a finite non-empty set (2) S is a non-empty set (3) T = {t1 , t2} (4) c maps S onto /R3 (5) v maps P X T into S (6) m is a function from Pinto /R such that for all p ∈ P, m(p) &gt; O (7) Σ m(p) . c ° v(p, t1,) = P ∈ P Σ m(p) . c ° v(p, t2) p ∈ P (where '/R' designa the real numbers and '°', the composition of functions). This axiomatization is completed with a set of informal statements that offers the intuitive physical interpretation of the basic concepts ; e.g., "The elements of P are particles" and "m is the mass of each particle". First thesis: Among the axioms of an empirical theory at least one typification occurs. Through the "constructive echelons" of the projection (π), power set (P) and cartesian product (X) operations, the typifications make explicit and precise the type of the set-theoretical entities that corresponds to some of the basic concepts: relations and functions. E.g., for m, we have: m ∈ P (π1 ≺P, /R≻ X π2 ≺P, /R≻. The typifications have no empirical meaning at all; they can be stated by means of pure conceptual analysis. Second thesis: Among the axioms of an empirical theory at least one characterization occurs. Obviously, the typifications do not exhaust all that can be said in set-theoretical terms about the basic concepts. The characterizations supply additional information which contains, although in a minimal degree, certain factual meaning, as we can see in the characterization of m: Func (m) &amp; ∀ p ∈ P(m(p) &gt; O), where 'Func' is a term for the general concept of function. Third thesis: Among the axioms of an empirical theory al least one sinoptic law occurs. What type of axiom is (7), the momentum conservation law? Evidenttly, it is neither a typification nor a characterization; it is just a scientific law. Laws are the kind of essential statements in a theory (without a law a theory is not a theory); they contain the maximum amount and most important empirical meaning of a theory among all the axioms. It would seem that the three types of axioms listed are sufficient to describe an axiomatization of an empirical theory. However, there are other components that contribute to the identification, which are necessary for the empirical applications of theories. Fourth thesis: Among the axioms of an empirical theory at least one interpretation axiom occurs. An interpretation axiom is a statement that asserts a link between the potential models of a theory and the (actual) models of another. These links, as inter-theoretic relations, are vital for the empirical applications of theories; without them we do not know, e.g., to what kind of things the concepts of mass or speed are applicable. In CM we need interpretation axioms for the existing links between itself and, e.g., the chassical kinematics, (physical) euclidean geometry and chronometry. Fifth thesis: Among the axioms of many empirical theories at least one constraint occurs. This type of axioms states a relation among models of the same theory such that it allows to export data of a model in order to make e.g., a calculation or a measurement for a further model. In CM we have constraints for the invariation of both mass and speed and for the extensivity of mass. Sixth thesis: Among the axioms of many empirical theories at least one special law occurs. Is (7) the only law of CM? Certainly not. In some kind of applications of CM, e.g., the conservation of kinematics energy law is used. However, this law does not hold in all applications of CM and, thus, it is not a general law hut rather a special one. The same situation occurs in many empirical theories, in particular, in the complexes. But due to the open character of the set of the special laws, they can hardly be captured in a formal fashion. [J.L. Rolleri]

Trouble withξscaling?

We review our analysis of inclusive lepton-hadron scattering, which is based on the use of the variable ξ that incorporates target- and constituent-mass effects in a color-gauge theory [quantum chromodynamics (QCD)]. We show that the apparent recently encountered by several groups in connection with ξ scaling are not at all, but rather are based on misunderstanding of our analysis. Paradoxes arise when the ξ-scaling analysis is applied for all ξ, but, as we stated in earlier work, QCD predicts that corrections (due to twist-greater-than-2 operators) are negligible only for W well above the proton mass. We restate our previous analysis in which we introduced a smooth function Fs that ξ-scales up to explicit logarithmic corrections. Fs has no thresholds (it is nonzero for 0<ξ<1). QCD predicts that Fs describes the data in the sense of Bloom-Gilman local duality. More constructively, we use the parton-model language to interpret the field-theoretic operator-product expansion in successive twists and develop an intuitive physical interpretation of twist. We reanalyze the paradoxes in parton language. We resolve (to our satisfaction) the question of nonperturbative effects in the analysis of electroproduction.

X-ray scattering from liquids with nearly spherical molecules

For fluids with molecules in which the electron density can be represented by a rapidly converging expansion in spherical harmonics, the intensity of the X-ray scattering can be obtained from a theory by Steele and Pecora. We have re-expanded their result using a different reference frame. This allows us to give a more intuitive physical interpretation of the coefficients of the expansion of the binary correlation function. For any type of molecules, the small angle scattering is given by the compressibility term plus pure orientational contributions. For molecules that are closely spherical, the orientational contribution is of second order in the coefficients of the higher spherical form factors, and therefore small. We have calculated the form factors for NH 3, HF, and H 2O. In all of these molecules, the coefficient of the spherical part is much larger than all the others. This simplifies the interpretation of the experimental data since only three parameters are needed, instead of the six necessary if the orientational part were important.

Sur la fréquence fondamentale d'une membrane vibrante: évaluations par défaut et principe de maximum

The starting point of the present paper is a simple method ofPayne-Weinberger to obtain lower bounds for the first eigenvalue of a membrane through comparison with the Rayleigh principle for homogeneous strings. A generalization of this idea to auxiliary non-homogeneous strings leads to a maximum principle (7) (of which an inequality ofBarta-Polya is a special case) or (7′); in its form (8), it was essentially known (although with some unnecessary restrictive hypotheses) toM. H. Protter in 1958. — This principle is closely related to theThomson principle of boundary value problems; in particular, the allowed discontinuities of the concurrent vector fields (in the formulation (7′)) are the same as inThomson's principle.—Someapplications of the principle to the calculation of rather sharp lower bounds are indicated, as well as an intuitivephysical interpretation (in terms of variation of masses and constraints). It is valid inthree dimensions as well; we indicate its extension toSchrodinger's equation.