Dynamic Response Function Research Articles

Spectral intensity distribution of trapped fermions

To calculate static response properties of a many body system, local density approximation (LDA) can be safely applied. But applicability of LDA is limited for the case of dynamical response functions since dynamics of the system needs to be considered as well. To examine this in the context of cold atoms, we consider a system of non-interacting spin-$1/2$ fermions confined by a harmonic trapping potential. We have calculated a very important response function, the spectral intensity distribution function (SIDF), both exactly and using LDA at zero temperature and compared with each other for different dimensions, trap frequencies and momenta. The behavior of the SIDF at a particular momentum can be explained by noting the behavior of the density of states (DOS) of the free system (without trap) in that particular dimension. The agreement between exact and LDA SIDFs becomes better with increase in dimensions and number of particles.

Transient response of stochastic finite element systems using Dynamic Variability Response Functions

In this study a methodology is presented for effective analysis of dynamic systems with stochastic material properties. The concept of dynamic mean and variability response functions, recently established for linear stochastic single degree of freedom oscillators, is extended to general finite element systems such as statically indeterminate beam/frame structures and plane stress problems, leading to closed form integral expressions for their dynamic mean and variability response. The integrand of these integral expressions involves the spectral density function of the uncertain material properties and the so called dynamic mean and variability response functions respectively, which are assumed to be deterministic, i.e. independent of the power spectrum as well as the marginal pdf of the uncertain parameters. A finite element method-based fast Monte Carlo simulation procedure is used for the accurate and efficient numerical evaluation of these functions. In order to demonstrate the validity of the proposed procedure, the results obtained using the aforementioned integral expressions are compared to brute-force Monte Carlo simulation. As a further validation of the assumption of independence of the variability response function to the stochastic parameters of the problem, the concept of the generalized variability response function was applied and compared to the steady state dynamic variability response function. The methodology is applied in a dynamically loaded statically indeterminate beam/frame structure and a plane stress problem. The dynamic mean and variability response functions, once established, can be used to perform sensitivity/parametric analyses with respect to various probabilistic characteristics involved in the problem (i.e., correlation distance, standard deviation) and to establish realizable upper bounds on the dynamic mean and variance of the response, at practically no additional computational cost.

Quantum impurity in a Tomonaga-Luttinger liquid: Continuous-time quantum Monte Carlo approach

We develop a continuous-time quantum Monte Carlo (CTQMC) method for quantum impurities coupled to interacting quantum wires described by a Tomonaga-Luttinger liquid. The method is negative-sign free for any values of the Tomonaga-Luttinger parameter, which is rigorously proved, and thus, efficient low-temperature calculations are possible. Duality between electrons and bosons in one dimensional systems allows us to construct a simple formula for the CTQMC algorithm in these systems. We show that the CTQMC for Tomonaga-Luttinger liquids can be implemented with only minor modifications of previous CTQMC codes developed for impurities coupled to non-interacting fermions. We apply this method to the Kane-Fisher model of a potential scatterer in a spin-less quantum wire and to a single spin coupled with the edge state of a two-dimensional topological insulator assuming an anisotropic XXZ coupling. Various dynamical response functions such as the electron Green's function and spin-spin correlation functions are calculated numerically and their scaling properties are discussed.

Modelling the spindle–holder taper joint in machine tools: A tapered zero-thickness finite element method

This study presents a tapered zero-thickness finite element model together with its parameter identification method for modelling the spindle–holder taper joint in machine tools. In the presented model, the spindle and the holder are modelled as solid elements and the taper joint is modelled as a tapered zero-thickness finite element with stiffness and damping but without mass or thickness. The proposed model considers not only the coupling of adjacent degrees of freedom but also the radial, tangential and axial effects of the spindle–holder taper joint. Based on the inverse relationship between the dynamic matrix and frequency response function matrix of a multi-degree-of-freedom system, this study proposes a combined analytical–experimental method to identify the stiffness matrix and damping coefficient of the proposed tapered zero-thickness finite element. The method extracts those parameters from FRFs of an entire specimen that contains only the spindle–holder taper joint. The simulated FRF obtained from the proposed model matches the experimental FRF quite well, which indicates that the presented method provides high accuracy and is easy to implement in modelling the spindle–holder taper joint.

Ageing and non-equilibrium critical phenomena in Monte Carlo simulations

It is considered the non-equilibrium critical evolution of statistical systems which displays some features, such as ageing and violation of the fluctuation-dissipation theorem. We review here some theoretical results of computations that have been obtained in recent years for universal quantities, such as the exponents determining the scaling behaviour of dynamic response and correlation functions and the fluctuation-dissipation ratio, associated with the non-equilibrium critical dynamics, with particular focus on the 3D pure and diluted Ising models with Glauber dynamics. We analyse an influence of critical fluctuations, different non-equilibrium initial states and presence of nonmagnetic impurities in spin systems on two-time dependence of correlation and response functions on characteristic time variables as waiting time tw and time of observation t – tw with t > tw. We discuss the obtained values of non-equilibrium exponents for autocorrelation and response functions and values of the universal long-time limit of the fluctuation-dissipation ratio X∞. Analysis of simulation results show that the insertion of disorder leads to new values of X∞ with X∞diluted > X∞pure.

Dynamic Model of Spindle-Holder Taper Joint of BT40 Holder

The dynamic characteristics of spindle-holder taper joint greatly influencethe performance of machine tools. This paper proposed a 24-DOFs spring-damper model to deal with the dynamic model of spindle-holder taper joint. To identify the stiffness of springs and damping coefficient of damper, a parameter identification method was developed based on the inverse relationship of dynamic matrix and frequency response function matrix. Using modal test and the proposed dynamic model, the taper joint of BT40 holder was studied. At the end of this paper, a case was presented to validate the dynamic model. Because the radial, tangential and axial effects of the taper joint were all taken into considerations, the proposed model provided a higher accurate model of spindle-holder taper joint.

A derivation and discussion of a mutual information lower bound for dynamic acoustic response functions under a Gauss Markov law

A derivation and discussion of a mutual information lower bound for broadband acoustic channels under a Gauss-Markov assumption is provided. This lower bound is associated with dynamic broadband acoustic response functions that obey a Gauss Markov law. Considered here is the difference of the mutual information between source and receive signals given the acoustic response and the mutual information between acoustic response and receive signal given the source signal. The derivation illuminates the features of this mutual information and permits identifying two key information loss mechanisms. The first is an added self noise term proportional to signal power that is only associated with the innovation variance of the Gauss Markov response. The second term also increases with the innovation variance but is associated with the uncertainty in the state of the channel operator at the initial time of signaling. This later variance is identified as a forward-backward channel estimation error. Platform motion effects and their impact on these two loss mechanisms are discussed and the structure of an effective signal to noise ratio (eSNR) ceiling at high SNR are identified.

Systematic study of isovector and isoscalar giant quadrupole resonances in normal and superfluid deformed nuclei

The systematic study of isoscalar (IS) and isovector (IV) giant quadrupole responses (GQR) in normal and superfluid nuclei presented in [G. Scamps and D. Lacroix, Phys. Rev. 88, 044310 (2013)] is extended to the case of axially deformed and triaxial nuclei. The static and dynamical energy density functional based on Skyrme effective interaction are used to study static properties and dynamical response functions over the whole nuclear chart. Among the 749 nuclei that are considered, 301 and 65 are respectively found to be prolate and oblate while 54 do not present any symmetry axis. For these nuclei, the IS- and IV-GQR response functions are systematically obtained. In these nuclei, different aspects related to the interplay between deformation and collective motion are studied. We show that some aspects like the fragmentation of the response induced by deformation effects in axially symmetric and triaxial nuclei can be rather well understood using simple arguments. Besides this simplicity, more complex effects show up like the appearance of non-trivial deformation effects on the collective motion damping or the influence of hexadecapole or higher-orders effects. A specific study is made on the triaxial nuclei where the absence of symmetry axis adds further complexity to the nuclear response. The relative importance of geometric deformation effects and coupling to other vibrational modes are discussed.

On the transient response of viscoelastic beams and plates on viscoelastic medium

In the present study, free vibration of isotropic viscoelastic beams and plates on viscoelastic medium is investigated. The Boltzmann superposition integral model with Dynamic Mechanical Analysis (DMA) results is considered for viscoelastic material of the beam and plate to describe more accurately the behavior of material rather than simple complex constants model. The viscoelastic beam and plate on viscoelastic medium modeling are used in railroad vibration with the damping layer on the lateral surface of the rail and the polymeric flooring on the floor as a viscoelastic medium for the beam and the plate, respectively. Weighted residual method and QZ algorithm are applied to obtain beam and plate natural frequency. In addition, medium properties׳ effects on the natural frequencies of the beam and plate are discussed. For the first time, critical damping of viscoelastic beam is presented due to the greater effect of medium viscosity at all boundary conditions. The unknown coefficients of dynamic response function are calculated by Fourier transform. Closed form expressions are obtained for lateral displacement of the beam and plate with various boundary conditions in terms of complex natural frequency, mode numbers, geometry parameters, initial conditions, material and medium properties. Results show excellent agreement with relative studies.

Excitations and quasi-one-dimensionality in field-induced nematic and spin density wave states

We study the excitation spectrum and dynamical response functions for several quasi-one-dimensional spin systems in magnetic fields without dipolar spin order transverse to the field. This includes both nematic phases, which harbor "hidden" breaking of spin-rotation symmetry about the field and have been argued to occur in high fields in certain frustrated chain systems with competing ferromagnetic and antiferromagnetic interactions, and spin density wave states, in which spin-rotation symmetry is truly unbroken. Using bosonization, field theory, and exact results on the integrable sine-Gordon model, we establish the collective mode structure of these states, and show how they can be distinguished experimentally.

패션제품의 동태적 구매반응함수에 관한 연구

In cases of fashion businesses operating by consignment, base estimate on quantity of sales is the most essential part of merchandising. This study classified factors influential to sales into factors with systematic influence and factors with unsystematic influence. In order to find out influence of each factor on sales, non-linear regression was used with SPSS package on the basis of actual data on sales for 5 years for sport shoes brand. Major findings of this study are as follows. First, price level had significant negative(-) influence on sales. Second, price expectation effects had significant negative(-) influence on sales. Third, competitor's price effect showed significant negative(-) value. Fourth, day-of-the-week effect showed significant positive(+) effect. The theoretical marketing implications of this study are as follows. First, study on price leads to expansion of the researches from apparels to sport shoes. Field of study on price was enlarged through expansion of variable of study from price level and price expectation effect to promotion, day-of-the-week effect and rainfall effect. Second, quantitative scale of day-of-the-week effect was found and it could be confirmed that there was seasonal differences with day-of-the-week effect. Implications of above findings on marketing managers are as follows. First, it was found that an increase in competitiveness of brand power and a decline in absolute value of competitor's price effect can be realized when new product groups are developed to meet the unsatisfied needs in the market. Second, it was possible to find out the parameters scales of the price response function, making it possible to estimate sales for the next season, and in turn realize increase in rate of sales and profit rate. This research is based on the dynamic price response function, which is rare to find in the apparel business and it academic significance due to its expanding response model which was focused on price in conventional researches to non-systematic variables.

Calculation of the fluctuation-dissipation ratio for the nonequilibrium critical behavior of disordered systems

The values of a new universal parameter characterizing a nonequilibrium critical behavior, namely, the fluctuation-dissipation ratio specifying a fundamental relation between the dynamic response function and the correlation function, are calculated for the disordered three-dimensional Ising model. The analysis of the two-time dependence for autocorrelation functions and the ac susceptibility for the systems with spin densities p = 1.0, 0.8, and 0.6 shows the aging effects characterized by the anomalous slowing of relaxation in the system with the growth of the waiting time and the violation of the fluctuation-dissipation theorem. To improve the accuracy of the ac susceptibility calculations, the “thermal bath” technique has been used without introducing the applied magnetic field in the simulation. It has been shown that the structural defects lead to the pronounced enhancement of the aging effects.

Delamination Detection of Composite Cantilever Beam Coupled With Piezoelectric Transducer Using Natural Frequency Deviation

Delaminations are common damages in laminated composites, which can significantly reduce the structural stiffness, which changes the dynamic response of the structures and therefore changes modal parameters such as natural frequency mode shape and damping. This paper presents effect of delamination lengths and locations on the natural frequencies of an electromechanical system consisting of a piezoelectric transducer glued on part of the upper surface of a laminated composite cantilever beam. To obtain dynamic responses of the structure transient analysis is carried out using ANSYS 13 software. From the dynamic responses frequency response functions (FRF) are obtained by using MATLAB code. Effectiveness of the proposed methodology is evaluated by numerical simulation of three delamination scenarios, i.e. delamination near fixed end, at center and at free end. It is observed that natural frequency decrease when length of delamination increases.

Dynamic structure factors of Cu, Ag, and Au: Comparative study from first principles

We present a comparative theoretical and experimental study of dynamic structure factors (momentum-dependent loss functions) of the noble metals Cu, Ag, and Au in the energy range of 0$-$60 eV. The emphasis is on theoretical results that are compared with new as well as available experimental data. Dynamic structure factors are calculated within the linear-response formalism of time-dependent density-functional theory, using the full-potential linearized augmented plane-wave (FP-LAPW) method. For the studied energy range, local-field effects are found to be very important for Ag and Au and only marginally relevant for Cu. We present an explanation for this surprising behavior. Loss functions of all three metals possess a complex multi-peak structure. We classify the features in the loss function as being related to collective excitations, interband transitions, or mixed modes. The impact of short-range correlations on the dynamic response functions are evaluated by comparing the results of the random-phase approximation to those of the time-dependent local-density approximation. Exchange correlation effects are found to be weak for small momentum transfers, but increasingly important for larger momenta. The calculated structure factors agree well with experiments.

Tone-mapping and dynamic range compression using dynamic cone response

Over the last several decades, the tone-mapping and color correction methods have been incorporated into the display device such as LCD/LED display device or the photographic print. However, conventional methods are based on Gray-World Assumption using spatial smoothing filter to estimate the local illumination component. For this reason, most of these methods have several problems like visual perception problem, scale the contrast, gray-out, color distortion (dominate color, halo-artifact) and so on. Accordingly, this paper presents a color correction method using the dynamic cone response function based on human visual perception. The proposed method consists of tone-mapping and dynamic cone response. The tone-mapped image is obtained by using chromatic and achromatic colors. Thereafter, the resultant image is processed through the dynamic cone response function, and it is to estimate the dynamic response of human eye as well as to deal with mismatch between a real scene and the rendered image. The experimental results show that the proposed method yields better performance of color correction over the conventional methods.

Structural Vibration Analysis under Fuzzy Excitations Due to Passing Heavy Vehicles

This paper presents a new method to predict the dynamic response of buildings due to passing heavy vehicles in the context of multi-source fuzzy dynamic finite element analysis. The uncertain parameters considered as fuzzy variables include structural mass, stiffness, damping matrix and magnitude of excitation applied at the ground or base level. The implementation of the proposed method consists of the following steps: 1) acquisition of the ground acceleration data through in-situ measurements, 2) analysis of the one-third octave band power spectrum density of the measured data, 3) construction of the fuzzy source membership functions of favorite center frequencies of the one-third octave band, 4) construction of the fuzzy dynamic finite element model of the building structure, 5) analysis of the fuzzy membership function of model responses, and 6) calculation of the overall weighted root-mean-square acceleration in α-sublevel of fuzzy number by ISO2631 standards, from which the effect of ground excitation on building response is assessed. A case study is provided to demonstrate the evaluation of the fuzzy dynamic characteristics and frequency response function in terms of multi-source fuzzy numbers.

Dynamical density and spin response functions of two-dimensional correlated fermion systems: Self-consistent second-order perturbation theory

Dynamical density and spin responses of a two-dimensional fermion system are studied with the self-consistent second-order perturbation theory using a model Hamiltonian. Special attention is paid to the density response at a large wave vector, where it was reported that a sharp mode develops below the particle-hole continuum in two-dimensional liquid ${}^{3}$He. We find that at a large wave vector, a peak in the dynamical density structure factor shifts to lower energy as interaction sets in, but it is not sharp enough to represent a well-defined mode because of the strong damping effect of the quasiparticles. We point out that it is necessary to treat the large damping effect properly in explaining the propagating mode found in two-dimensional liquid ${}^{3}$He.

Effect of magnetic field on dynamic response function in Ising systems

As a continuation of our previously published work, we use the Nelsonʼs method to study the effect of the magnetic field on the temperature-, frequency-, and momentum-dependent response function and dynamic correlation function in the Ising-type systems with relaxational dynamics. The scaling function is given within the renormalization group formalism at one-loop order for nonzero field. We show how the typical two-peak structure of the real part of response function changes with magnetic field. We discuss the deviations of the correlation function from the Gaussian expression. The Fisher–Langer maximum is also considered. • We study the effect of magnetic field on dynamic response and correlation function. • Crossover in magnetic dispersion factor from two peaks to a single peak is shown. • We discuss the deviations of the correlation function from the Gaussian expression. • The Fisher–Langer maximum in the correlation function is shifted.

Optimal design of Base Isolation System considering uncertain bounded system parameters

The optimum design of base isolation system considering model parameter uncertainty is usually performed by using the unconditional response of structure obtained by the total probability theory, as the performance index. Though, the probabilistic approach is powerful, it cannot be applied when the maximum possible ranges of variations are known and can be only modelled as uncertain but bounded type. In such cases, the interval analysis method is a viable alternative. The present study focuses on the bounded optimization of base isolation system to mitigate the seismic vibration effect of structures characterized by bounded type system parameters. With this intention in view, the conditional stochastic response quantities are obtained in random vibration framework using the state space formulation. Subsequently, with the aid of matrix perturbation theory using first order Taylor series expansion of dynamic response function and its interval extension, the vibration control problem is transformed to appropriate deterministic optimization problems correspond to a lower bound and upper bound optimum solutions. A lead rubber bearing isolating a multi-storeyed building frame is considered for numerical study to elucidate the proposed bounded optimization procedure and the optimum performance of the isolation system.

Adilet Imambekov

Adilet Imambekov