959 resultados para Newtonian equations


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We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

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In the presence of inhomogeneities, defects and currents, the equations describing a Bose-condensed ensemble of alkali atoms have to be solved numerically. By combining both linear and nonlinear equations within a Discrete Variable Representation framework, we describe a computational scheme for the solution of the coupled Bogoliubov-de Gennes (BdG) and nonlinear Schrodinger (NLS) equations for fields in a 3D spheroidal potential. We use the method to calculate the collective excitation spectrum and quasiparticle mode densities for excitations of a Bose condensed gas in a spheroidal trap. The method is compared against finite-difference and spectral methods, and we find the DVR computational scheme to be superior in accuracy and efficiency for the cases we consider. (C) 2004 Elsevier B.V. All rights reserved.

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Predicting the velocity within the ship’s propeller jet is the initial step to investigate the scouring made by the propeller jet. Albertson et al. (1950) suggested the investigation of a submerged jet can be undertaken through observation of the plain water jet from an orifice. The plain water jet investigation of Albertson et al. (1950) was based on the axial momentum theory. This has been the basis of all subsequent work with propeller jets. In reality, the velocity characteristic of a ship’s propeller jet is more complicated than a plain water jet. Fuehrer and Römisch (1977), Blaauw and van de Kaa (1978), Berger et al. (1981), Verhey (1983) and Hamill (1987) have carried out investigations using physical model. This paper reviews the state-of-art of the equations used to predict the time-averaged axial, tangential and radial components of velocity within the zone of flow establishment and the zone of established flow of a ship’s propeller jet.

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New protic ionic liquids (PILs) based on the diisopropyl-ethylammonium cation have been synthesized through a simple and atom-economic neutralization reaction between the diisopropyl-ethylamine and selected carboxylic acid. Densities and rheological properties were then measured for two original diisopropyl-ethylammonium-based protic ionic liquids (heptanoate and octanoate) at 298.15 K and atmospheric pressure. The effect of the presence of water or acetonitrile on the measured values was also examined over the whole composition range at 298.15 K and atmospheric pressure. From these values, excess properties were calculated and correlated by using a Redlich-Kister-type equation. Finally, a qualitative analysis of the evolution of studied properties with the alkyl chain length of the anion and with the presence or not of water (or acetonitrile) was performed. From this analysis, it appears that selected PILs and their mixtures with water or acetonitrile have a non-Newtonian shear thickening behavior, and the addition of water or acetonitrile on these PILs increases this phenomena by the formation of aggregates in these media.

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A post-Markovian master equation has been recently proposed as a tool to describe the evolution of a system coupled to a memory-keeping environment [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101 ( R) ( 2005)]. For a single qubit affected by appropriately chosen environmental conditions, the corresponding dynamics is always legitimate and physical. Here we extend such a situation to the case of two qubits, only one of which experiences the environmental effects. We show how, despite the innocence of such an extension, the introduction of the second qubit should be done cum grano salis to avoid consequences such as the breaking of the positivity of the associated dynamical map. This hints at the necessity of using care when adopting phenomenologically derived models for evolutions occurring outside the Markovian framework.

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A parametric study of cold-formed steel sections with web openings subjected to web crippling was undertaken using finite element analysis, to investigate the effects of web holes and cross-section sizes on the web crippling strengths of channel sections subjected to web crippling under both interior-two-flange (ITF) and end-two-flange (ETF) loading conditions. In both loading conditions, the hole was centred beneath the bearing plate. It was demonstrated that the main factors influencing the web crippling strength are the ratio of the hole depth to the flat depth of the web, and the ratio of the length of bearing plates to the flat depth of the web. In this paper, design recommendations in the form of web crippling strength reduction factors are proposed, that are conservative to both the experimental and finite element results.

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A new linear equations method for calculating the R-matrix, which arises in the R-matrix-Floquet theory of multiphoton processes, is introduced. This method replaces the diagonalization of the Floquet Hamiltonian matrix by the solution of a set of linear simultaneous equations which are solved, in the present work, by the conjugate gradient method. This approach uses considerably less computer memory and can be readily ported onto parallel computers. It will thus enable much larger problems of current interest to be treated. This new method is tested by applying it to three-photon ionization of helium at frequencies where double resonances with a bound state and autoionizing states are important. Finally, an alternative linear equations method, which avoids the explicit calculation of the R-matrix by incorporating the boundary conditions directly, is described in an appendix.

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Physical modelling of musical instruments involves studying nonlinear interactions between parts of the instrument. These can pose several difficulties concerning the accuracy and stability of numerical algorithms. In particular, when the underlying forces are non-analytic functions of the phase-space variables, a stability proof can only be obtained in limited cases. An approach has been recently presented by the authors, leading to unconditionally stable simulations for lumped collision models. In that study, discretisation of Hamilton’s equations instead of the usual Newton’s equation of motion yields a numerical scheme that can be proven to be energy conserving. In this paper, the above approach is extended to collisions of distributed objects. Namely, the interaction of an ideal string with a flat barrier is considered. The problem is formulated within the Hamiltonian framework and subsequently discretised. The resulting nonlinearmatrix equation can be shown to possess a unique solution, that enables the update of the algorithm. Energy conservation and thus numerical stability follows in a way similar to the lumped collision model. The existence of an analytic description of this interaction allows the validation of the model’s accuracy. The proposed methodology can be used in sound synthesis applications involving musical instruments where collisions occur either in a confined (e.g. hammer-string interaction, mallet impact) or in a distributed region (e.g. string-bridge or reed-mouthpiece interaction).

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From the early 1900s, some psychologists have attempted to establish their discipline as a quantitative science. In using quantitative methods to investigate their theories, they adopted their own special definition of measurement of attributes such as cognitive abilities, as though they were quantities of the type encountered in Newtonian science. Joel Michell has presented a carefully reasoned argument that psychological attributes lack additivity, and therefore cannot be quantities in the same way as the attributes of classical Newtonian physics. In the early decades of the 20th century, quantum theory superseded Newtonian mechanics as the best model of physical reality. This paper gives a brief, critical overview of the evolution of current measurement practices in psychology, and suggests the need for a transition from a Newtonian to a quantum theoretical paradigm for psychological measurement. Finally, a case study is presented that considers the implications of a quantum theoretical model for educational measurement. In particular, it is argued that, since the OECD’s Programme for International Student Assessment (PISA) is predicated on a Newtonian conception of measurement, this may constrain the extent to which it can make accurate comparisons of the achievements of different education systems.

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As a comparative newly-invented PKM with over-constraints in kinematic chains, the Exechon has attracted extensive attention from the research society. Different from the well-recognized kinematics analysis, the research on the stiffness characteristics of the Exechon still remains as a challenge due to the structural complexity. In order to achieve a thorough understanding of the stiffness characteristics of the Exechon PKM, this paper proposed an analytical kinetostatic model by using the substructure synthesis technique. The whole PKM system is decomposed into a moving platform subsystem, three limb subsystems and a fixed base subsystem, which are connected to each other sequentially through corresponding joints. Each limb body is modeled as a spatial beam with a uniform cross-section constrained by two sets of lumped springs. The equilibrium equation of each individual limb assemblage is derived through finite element formulation and combined with that of the moving platform derived with Newtonian method to construct the governing kinetostatic equations of the system after introducing the deformation compatibility conditions between the moving platform and the limbs. By extracting the 6 x 6 block matrix from the inversion of the governing compliance matrix, the stiffness of the moving platform is formulated. The computation for the stiffness of the Exechon PKM at a typical configuration as well as throughout the workspace is carried out in a quick manner with a piece-by-piece partition algorithm. The numerical simulations reveal a strong position-dependency of the PKM's stiffness in that it is symmetric relative to a work plane due to structural features. At the last stage, the effects of some design variables such as structural, dimensional and stiffness parameters on system rigidity are investigated with the purpose of providing useful information for the structural optimization and performance enhancement of the Exechon PKM. It is worthy mentioning that the proposed methodology of stiffness modeling in this paper can also be applied to other overconstrained PKMs and can evaluate the global rigidity over workplace efficiently with minor revisions.

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Collisions are an innate part of the function of many musical instruments. Due to the nonlinear nature of contact forces, special care has to be taken in the construction of numerical schemes for simulation and sound synthesis. Finite difference schemes and other time-stepping algorithms used for musical instrument modelling purposes are normally arrived at by discretising a Newtonian description of the system. However because impact forces are non-analytic functions of the phase space variables, algorithm stability can rarely be established this way. This paper presents a systematic approach to deriving energy conserving schemes for frictionless impact modelling. The proposed numerical formulations follow from discretising Hamilton׳s equations of motion, generally leading to an implicit system of nonlinear equations that can be solved with Newton׳s method. The approach is first outlined for point mass collisions and then extended to distributed settings, such as vibrating strings and beams colliding with rigid obstacles. Stability and other relevant properties of the proposed approach are discussed and further demonstrated with simulation examples. The methodology is exemplified through a case study on tanpura string vibration, with the results confirming the main findings of previous studies on the role of the bridge in sound generation with this type of string instrument.

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We introduce the equations of magneto-quantum-radiative hydrodynamics. By rewriting them in a dimensionless form, we obtain a set of parameters that describe scale-dependent ratios of characteristic hydrodynamic quantities. We discuss how these dimensionless parameters relate to the scaling between astrophysical observations and laboratory experiments.

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We extend the generalized Langevin equation (GLE) method [L. Stella, C. D. Lorenz, and L. Kantorovich, Phys. Rev. B 89, 134303 (2014)] to model a central classical region connected to two realistic thermal baths at two different temperatures. In such nonequilibrium conditions a heat flow is established, via the central system, in between the two baths. The GLE-2B (GLE two baths) scheme permits us to have a realistic description of both the dissipative central system and its surrounding baths. Following the original GLE approach, the extended Langevin dynamics scheme is modified to take into account two sets of auxiliary degrees of freedom corresponding to the mapping of the vibrational properties of each bath. These auxiliary variables are then used to solve the non-Markovian dissipative dynamics of the central region. The resulting algorithm is used to study a model of a short Al nanowire connected to two baths. The results of the simulations using the GLE-2B approach are compared to the results of other simulations that were carried out using standard thermostatting approaches (based on Markovian Langevin and Nosé-Hoover thermostats). We concentrate on the steady-state regime and study the establishment of a local temperature profile within the system. The conditions for obtaining a flat profile or a temperature gradient are examined in detail, in agreement with earlier studies. The results show that the GLE-2B approach is able to treat, within a single scheme, two widely different thermal transport regimes, i.e., ballistic systems, with no temperature gradient, and diffusive systems with a temperature gradient.