Dynamic analysis for a pair of spur gears with translational motion due to bearing deformation

In this study, the dynamic response of a pair of spur gears is analyzed when the gear set has translational motion due to bearing deformation. A new dynamic model for the gear set, considering translational motion, is proposed, in which the distance between the centers of a pinion and a gear varies with time. Therefore, the proposed model regards the pressure angle and the contact ratio as time-varying variables, while the previous model regards them as constants. After deriving nonlinear equations of motion for the gear set, the dynamic responses are computed by applying the Newmark time integration method. This paper claims that the new model produces more accurate dynamic responses in comparison to those of the previous model. Some dynamic response differences between the new and previous models are demonstrated, and the effects of damping and stiffness upon the dynamic responses are also investigated.     

Density Matrix of a Finite Sub-chain of the Heisenberg Anti-ferromagnet

We consider a finite sub-chain on an interval of the infinite XXX model in the ground state. The density matrix for such a subsystem was described in our previous works for the model with inhomogeneous spectral parameters. In the present letter, we give a compact formula for the physically interesting case of the homogeneous model.     

Holographic coupler for GRIN lenses: Analysis of coupling conditions and phase profile of the coupled signal

Based on a previous model describing the behavior of a holocoupler/fiber optic device, we develop a new model for a holocoupler/GRIN lens system and analyze the conditions for the coupling to hold and the requirements of the coupled signal.     

Direct laser pumping of adatom-surface vibrational modes

A classical model for direct-laser-induced vibrational excitation of an adatom-lattice bond is investigated in order to resolve discrepancies between previous treatments. We also give a critical discussion on the applicability of the model to real systems.     

A stochastic study of the non-stationary non-negative random process based on two models of time series: multiplication and addition

As is well-known, there are two contrasting and fundamental models for simulating actual random processes with time series: a multiplication model and an addition model. In this letter, two explicit expressions of the probability density function for a non-stationary non-negative random process (a statistical Laguerre expansion type and a statistical Hermite expansion type) are derived from the above two fundamental viewpoints of modeling a time series, in relation to the statistical method described in a previous paper by the authors, in which the analysis was based on the use of a Hankel transform type characteristic function. The unified theory introduced in this previous paper can be obtained by a very simplified calculation as compared with that of the previous study, by the natural introduction of a random time series multiplication model.     

Holographic coupler for GRIN lenses: Analysis of coupling conditions and phase profile of the coupled signal

Abstract

Based on a previous model describing the behavior of a holocoupler/fiber optic device, we develop a new model for a holocoupler/GRIN lens system and analyze the conditions for the coupling to hold and the requirements of the coupled signal.     

On the mass distribution in Time-Dependent Hartree-Fock calculations of heavy-ion collisions

In previous papers we have introduced a simple model for backbending nuclei which satisfactorily describes the essential experimental features of those nuclei. In this paper we show that the basic assumptions of this model can be deduced by a more microscopic treatment.     

Offline estimation of decay time for an optical cavity with a low pass filter cavity model

This Letter presents offline estimation results for the decay-time constant for an experimental Fabry-Perot optical cavity for cavity ring-down spectroscopy (CRDS). The cavity dynamics are modeled in terms of a low pass filter (LPF) with unity DC gain. This model is used by an extended Kalman filter (EKF) along with the recorded light intensity at the output of the cavity in order to estimate the decay-time constant. The estimation results using the LPF cavity model are compared to those obtained using the quadrature model for the cavity presented in previous work by Kallapur et?al. The estimation process derived using the LPF model comprises two states as opposed to three states in the quadrature model. When considering the EKF, this means propagating two states and a (2×2) covariance matrix using the LPF model, as opposed to propagating three states and a (3×3) covariance matrix using the quadrature model. This gives the former model a computational advantage over the latter and leads to faster execution times for the corresponding EKF. It is shown in this Letter that the LPF model for the cavity with two filter states is computationally more efficient, converges faster, and is hence a more suitable method than the three-state quadrature model presented in previous work for real-time estimation of the decay-time constant for the cavity.     

Cole-Hopf Transformation Based Lattice Boltzmann Model for One-dimensional Burgers' Equation

In this paper,we present a Cole-Hopf transformation based lattice Boltzmann(LB) model for solving one-dimensional Burgers' equation,and compared to available LB models,the effect of nonlinear convection term can be eliminated.Through Chapman-Enskog analysis,it can be found that the converted diffusion equation based on the Cole-Hopf transformation can be recovered correctly from present LB model.Some numerical tests are also performed to validate the present LB model,and the numerical results show that,similar to previous LB models,the present model also has a second-order convergence rate in space,but it is more accurate than the previous ones.     

A synapse memristor model with forgetting effect

In this Letter we improved the ion diffusion term proposed in literature [13] and redesigned the previous model as a dynamical model with two more internal state variables ‘forgetting rate’ and ‘retention’ besides the original variable ‘conductance’. The new model can not only describe the basic memory ability of memristor but also be able to capture the new finding forgetting behavior in memristor. And different from the previous model, the transition from short term memory to long term memory is also defined by the new model. Besides, the new model is better matched with the physical memristor (Pd/WOx/W) than the previous one.     

Modeling of light coupling effect using tunneling theory based on particle properties of light

Based on the wave-particle duality of light, the Schrödinger equation for a photon as a particle is established to treat the light coupling effect by introducing concepts of the virtual mass and potential for a photon, which is different from the previous method that uses the analogy with quantum mechanics. The virtual mass is physically correlated to the kinetic energy according to Einstein’s energy–momentum relation. As a consequence, this new model has merits of physical simplicity and analytic nature. This new model can well explain the exponential dependence of the light coupling effect on the physical parameters in coupled waveguides on, which can be observed in the experimental and simulation data reported in the literature. Moreover, an explicit expression for the coupling length (coefficient) on the effects of physical parameters can be obtained by virtue of this new model, whereas the previous modal approach and the coupled-wave model resulted in implicit expressions. This new model does not only give a better physical understanding but also offers a possibility to design and fabricate optic devices based on the light coupling effect by optimizing the physical parameters.     

Multiple car-following model of traffic flow and numerical simulation

On the basis of the full velocity difference (FVD) model, an improved multiple car-following (MCF) model is proposed by taking into account multiple information inputs from preceding vehicles. The linear stability condition of the model is obtained by using the linear stability theory. Through nonlinear analysis, a modified Korteweg-de Vries equation is constructed and solved. The traffic jam can thus be described by the kink--antikink soliton solution for the mKdV equation. The improvement of this new model over the previous ones lies in the fact that it not only theoretically retains many strong points of the previous ones, but also performs more realistically than others in the dynamical evolution of congestion. Furthermore, numerical simulation of traffic dynamics shows that the proposed model can avoid the disadvantage of negative velocity that occurs at small sensitivity coefficients λ in the FVD model by adjusting the information on the multiple leading vehicles. No collision occurs and no unrealistic deceleration appears in the improved model.     

Accounting for delay of energy transfer between coupled rooms in statistical-acoustics models of reverberant-energy decay

A statistical-acoustics model for energy decay in systems of two or more coupled rooms is introduced, which accounts for the distribution of delay in the transfer of energy between subrooms that results from the finite speed of sound. The method extends previous models based on systems of coupled ordinary differential equations by using functional differential equations to explicitly model dependence on prior values of energy in adjacent subrooms. Predictions of the model are illustrated for a two-room coupled system and compared with the predictions of a benchmark computational geometrical-acoustics model.     

Theory of optical scintillation: Gaussian-beam wave model

Abstract

A scintillation model previously developed by the authors is extended in this paper to the case of a propagating Gaussian-beam wave. As in the previous model, we account for the loss of spatial coherence as the optical wave propagates through atmospheric turbulence by eliminating effects of certain turbulent scale sizes that exist between the scale size of the spatial coherence radius of the beam and that of the scattering disc. These mid-range scale-size effects are eliminated through the formal introduction of spatial frequency filters that continually adjust spatial cut-off frequencies as the optical wave propagates. Unlike the previous model, in this paper we include the effect of a finite outer scale in addition to the inner scale. With a finite outer scale, the scintillation index can be substantially lower in strong turbulence than that predicted by a model with an infinite outer scale. This particular behaviour of scintillation in strong turbulence, mostly associated with horizontal paths near the ground, cannot be explained on the basis of previous expressions deduced from the asymptotic theory. Comparisons of the scintillation models with published experimental and simulation data through weak and strong irradiance fluctuations show excellent fits.     

The gap survival probability and diffractive dissociation

We study the survival probability for rapidity gaps in a model which includes diffractive dissociation. A Good-Walker model implementation of the minijet model, which consistently includes inelastic diffraction, predicts a much larger survival probability than previous calculations.     

Hamiltonian of a Slightly Asymmetric Molecules with a Three Fold Internal Rotor and Its Applications to Optically Pumped FIR Lasers: Theoretical Aspects

In this paper, a Model of the Hamiltonian function is reviewed for the slightly asymmetric class of molecules, which is the most successful so far, according to our present knowledge. This model does not have the redundancy problem suffered by previous models. The observed frequencies are calculated to within experimental accuracy. In our subsequent papers we will show the application of this model for the prediction and quantum number assignments of optically pumped far infrared lasers and thereby increasing the possibility of new lines in the region of the spectrum which severely lacks enough monochromatic sources. We will also show that this model is capable of calculating even MMW transitions for the second excited state of methanol. All the previous models consider transitions up to the first excited torsional state.     

Evaluation of decay times in coupled spaces: Bayesian decay model selection

This paper applies Bayesian probability theory to determination of the decay times in coupled spaces. A previous paper [N. Xiang and P. M. Goggans, J. Acoust. Soc. Am. 110, 1415-1424 (2001)] discussed determination of the decay times in coupled spaces from Schroeder's decay functions using Bayesian parameter estimation. To this end, the previous paper described the extension of an existing decay model [N. Xiang, I. Acoust. Soc. Am. 98, 2112-2121 (1995)] to incorporate one or more decay modes for use with Bayesian inference. Bayesian decay time estimation will obtain reasonable results only when it employs an appropriate decay model with the correct number of decay modes. However, in architectural acoustics practice, the number of decay modes may not be known when evaluating Schroeder's decay functions. The present paper continues the endeavor of the previous paper to apply Bayesian probability inference for comparison and selection of an appropriate decay model based upon measured data. Following a summary of Bayesian model comparison and selection, it discusses selection of a decay model in terms of experimentally measured Schroeder's decay functions. The present paper, along with the Bayesian decay time estimation described previously, suggests that Bayesian probability inference presents a suitable approach to the evaluation of decay times in coupled spaces.     

Exact solution of the mean spherical model for fluids of non-spherical molecules

The mean spherical model is solved in closed form for a fluid of molecules represented by hard spheres together with short-range angle-dependent repulsion and long-range multipole attraction, with no restriction placed on the parity of the angular functions. This constitutes an extension of a previous report which presented a solution for the same model but with the restriction that the angular terms had even parity.     

Variational solution of a superfluidity model

We derive, using the variational principle for the free energy, the solution of a model for superfluidity proposed in a previous paper. The solution has the phase diagram and the excitation spectrum expected from a superfluid. We draw the attention to the fact that the model is obtained, as compared with the Bogoliubov model, by a milder suppressing of interactions with the zero mode fluctuations, leading to the good spectral properties of superfluidity.     

Effective carrying capacity and analytical solution of a particular case of the Richards-like two-species population dynamics model

We consider a generalized two-species population dynamic model and analytically solve it for the amensalism and commensalism ecological interactions. These two-species models can be simplified to a one-species model with a time dependent extrinsic growth factor. With a one-species model with an effective carrying capacity one is able to retrieve the steady state solutions of the previous one-species model. The equivalence obtained between the effective carrying capacity and the extrinsic growth factor is complete only for a particular case, the Gompertz model. Here we unveil important aspects of sigmoid growth curves, which are relevant to growth processes and population dynamics.