Study of thermal decoherence of harmonic oscillators

The thermal decoherence of harmonic oscillators is investigated here.The quantum system presented here is a one-dimensional oscillator with angular frequency,which is surrounded by a thermal bath of environmental oscillators.There are various environmental oscillators with different angular frequency(below an ultraviolet cutoff).At the beginning,the quantum system is a pure state and the environmental oscillators are in thermodynamic equilibrium with temperature.After a period,the system-environment interactions inspire significant decoherence of the quantum state.Such decoherence is displayed by explicit calculations of the purity and von Neumann entropy of the quantum system.It is worth noting that the decoherence could be significant even in the weak coupling and low temperature case due to the large amount of environmental degrees of freedom.Since the decoherence process is inspired between the quantum system and an ordinary thermal environment here,the thermal decoherence result is quite general.

Chimera states of phase oscillator populations with nonlocal higher-order couplings

The chimera states underlying many realistic dynamical processes have attracted ample attention in the area of dynamical systems.Here, we generalize the Kuramoto model with nonlocal coupling incorporating higher-order interactions encoded with simplicial complexes.Previous works have shown that higher-order interactions promote coherent states.However, we uncover the fact that the introduced higher-order couplings can significantly enhance the emergence of the incoherent state.Remarkably, we identify that the chimera states arise as a result of multi-attractors in dynamic states.Importantly, we review that the increasing higher-order interactions can significantly shape the emergent probability of chimera states.All the observed results can be well described in terms of the dimension reduction method.This study is a step forward in highlighting the importance of nonlocal higher-order couplings, which might provide control strategies for the occurrence of spatial-temporal patterns in networked systems.

Dynamics of a Quantum Dissipative System Coupled with an Oscillator

We study the dynamics of a quantum dissipative system. Besides its linear coupling with a harmonic bath modelling the dissipation, we suppose that it is coupled with an oscillator with an interaction of the form s 2 x 2 . In our study, we integrate over the bath and the oscillator, extract the corresponding influence functionals and then solve the system’s sign problem. We apply the theory to the case of a double well and study the time evolution of the expectation value of the position.

Linearization of Intrinsically Nonlinear Oscillators

We show that an intrinsically nonlinear oscillator can always be transformed into a linear or harmonic oscillator by addition of a constant force, which shifts the equilibrium position of the oscillator.

Experimental and simulation study on shear stress-induced erythrocyte damage based on vortex oscillator

Background:Shear stress-induced erythrocyte damage,namely hemolysis,is an important problem in the development of blood-contacting medical devices such as mechanical circulatory support devices.Computational fluid dynamics simulation combined with hemolysis prediction models have been widely used to predict hemolysis.With the development of hemolysis prediction models,the new hemolysis prediction model requires more experimental data to verify.In addition,the difference of in vitro blood-shearing device also affect the accuracy of hemolysis prediction.Methods:To address these problems,a new in vitro blood-shearing device(vortex oscillator)was used to further verify the accuracy of the hemolysis prediction models,and to guide the optimal design of blood-contacting medical devices such as mechanical circulatory support devices.Firstly,the flow field information such as wall stress and velocity of the vortex oscillator under different speeds was analyzed.Secondly,different hemolysis prediction models were used to calculate hemolysis,and the predicted data was compared with the experimental data.Results and Conclusion:In this study,the flow field information inside the vortex oscillator at high rotational speeds was systematically investigated,and the prediction of hemolysis was carried out.The results showed that the predicted data of hemolysis was significantly different from the experimental data,which indicated that it was urgent to establish a standardized in vitro blood-shearing platform to provide a reference for accurate hemolysis prediction.

An Accurate 1.08GHz CMOS LC Voltage-Controlled Oscillator

An accurate 1.08GHz CMOS LC voltage-controlled oscillator is implemented in a 0.35μm standard 2P4M CMOS process.A new convenient method of calculating oscillator period is presented.With this period calculation technique,the frequency tuning curves agree well with the experiment.At a 3.3V supply,the LC-VCO measures a phase noise of -82.2dBc/Hz at a 10kHz frequency offset while dissipating 3.1mA current.The chip size is 0.86mm×0.82mm.

Oscillatory squeeze flow through an Oldroyd-B fluid-saturated porous layer

This study deals with the analytical investigation of oscillatory squeeze film flow through a Brinkman viscoelastic Oldroyd-B fluid-saturated porous layer subject to two vertically harmonically oscillatory disks.The validity of the present proposed analytical solutions is first demonstrated for the Newtonian fluids when bothΛ_(1)andΛ_(2)tend to zero by comparison with the previous literature.Results demonstrate that an increase in the elasticity parameterΛ_(1)correlates with a rise in axial velocities,indicating that the relaxation timeΛ_(1)facilitates enhanced squeeze flow.In the case of squeeze film flow in porous layers,low oscillating frequencies exert minimal effects on axial velocities,independent of variations in the viscoelasticity parameterΛ_(1).However,at higher oscillating frequencies,axial velocities escalate with increasing the viscoelasticity parameterΛ_(1).Furthermore,the retardation timeΛ_(2)of the viscoelastic fluid shows no significant effect on the axial velocity,regardless of oscillating frequency changes in both pure fluids and porous layers.

Oscillatory Dynamics of a Spherical Solid in a Liquid in an Axisymmetric Variable Cross Section Channel

The dynamics of a solid spherical body in an oscillating liquid flow in a vertical axisymmetric channel of variable cross section is experimentally studied.It is shown that the oscillating liquid leads to the generation of intense averaged flows in each of the channel segments.The intensity and direction of these flows depend on the dimensionless oscillating frequency.In the region of studied frequencies,the dynamics of the considered body is examined when the primary vortices emerging in the flow occupy the whole region in each segment.For a fixed frequency,an increase in the oscillation amplitude leads to a phase-inclusion holding effect,i.e.,the body occupies a quasi-stationary position in one of the cells of the vertical channel,while oscillating around its average position.It is also shown that the oscillating motion of a liquid column generates an averaged force acting on the body,the magnitude of which depends on the properties of the body and its position in the channel.The quasi-stationary position is determined by the relative density and size of the body,as well as the dimensionless frequency.The behavior of the body as a function of the amplitude and frequency of fluid oscillation and relative size is discussed in detail.Such findings may be used in the future to control the position of a phase inclusion and/or to strengthen mass transfer effects in a channel of variable cross section by means of fluid oscillations.

A low-phase-noise and low-power crystal oscillator for RF tuner

A 37. 5 MHz differential complementary metal oxide semiconductor （CMOS） crystal oscillator with low power and low phase noise for the radio frequency tuner of digital radio broadcasting digital radio mondiale （DRAM） and digital audio broadcasting （DAB） systems is realized and characterized. The conventional cross-coupled n-type metal oxide semiconductor （NMOS） transistors are replaced by p-type metal oxide semiconductor （PMOS） transistors to decrease the phase noise in the core part of the crystal oscillator. A symmetry structure of the current mirror is adopted to increase the stability of direct current. The amplitude detecting circuit made up of a single- stage CMOS operational transconductance amplifier （OTA） and a simple amplitude detector is used to improve the current accuracy of the output signals. The chip is fabricated in a 0. 18- pxn CMOS process, and the total chip size is 0. 35 mm x 0. 3 mm. Under a supply voltage of 1.8 V, the measured power consumption is 3.6 mW including the output buffer for 50 testing loads. The proposed crystal oscillator exhibits a low phase noise of - 134. 7 dBc/Hz at 1-kHz offset from the center frequency of 37. 5 MHz.

Perturbed Solving Method for Interdecadal Sea-air Oscillator Model

A coupled system of the interdecadal sea-air oscillator model is studied. The E1 Nifio-southem oscillation （ENSO） atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The oscillator model is involved with the variations of both the eastern and western Pacific anomaly pat- terns. This paper proposes an ENSO atmospheric physics model using a method of the perturbation theory. The aim is to create an asymptotic solving method for the ENSO model. Employing the perturbed method, the asymptotic solution of corresponding problem is obtained, and the asymptotic behaviour of the solution is studied. Thus we can obtain the prognoses of the sea surface temperature anomaly and related physical quantities.

The homotopic method of travelling wave solution for El Nio tropic sea-air coupled oscillator

The EI Nimo and Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific sea-air interactions. In this paper, an asymptotic method of solving nonlinear equations for the ENSO model is proposed. And based on a class of oscillator of the ENSO model and by employing the method of homotopic mapping, the approximate solution of equations for the corresponding ENSO model is studied. It is proved from the results that homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial Pacific of the sea-air oscillator for the ENSO model.

A 10GHz LC Voltage-Controlled Oscillator in 0.25μm CMOS

A monolithic 10GHz LC voltage-controlled oscillator （VCO） is implemented in standard 0.25μm CMOS technology. The VCO adopts an optimized symmetric circular inductor with center-tap, an accumulation-mode MOS （A-MOS） varactor in series with a passive metal-isolator-metal capacitor （MIM-CAP） and a tail current source with an LC filter to operate with high-frequency and low-noise resulting in - 103.2dBc/Hz at 1MHz offset from carrier frequency of 10.2GHz and approximately 11.5% tuning range. With a 3.3V supply voltage, the core circuit consumes 9.9mW. The chip area is 0.67mm × 0.58mm.

Low Phase Noise Quadrature Oscillators Using New Injection Locked Technique

A low phase noise quadrature oscillator using the new injection locked technique is proposed. The incident signal is directly injected into the common-source connection of the sub-harmonic oscillator. In principle, the phase noise performance of the quadrature output is better than the sub-harmonic oscillator itself. The quadrature oscillator is implemented in a 0. 25μm CMOS process. Measurements show the proposed oscillator could achieve a phase noise of --130dBc/Hz at 1MHz offset from 1. 13GHz carrier while only drawing an 8.0mA current from the 2.5V power supply.

Joint MAP channel estimation and data detection for OFDM in presence of phase noise from free running and phase locked loop oscillator

This paper addresses a computationally compact and statistically optimal joint Maximum a Posteriori(MAP)algorithm for channel estimation and data detection in the presence of Phase Noise(PHN)in iterative Orthogonal Frequency Division Multiplexing(OFDM)receivers used for high speed and high spectral efficient wireless communication systems.The MAP cost function for joint estimation and detection is derived and optimized further with the proposed cyclic gradient descent optimization algorithm.The proposed joint estimation and detection algorithm relaxes the restriction of small PHN assumptions and utilizes the prior statistical knowledge of PHN spectral components to produce a statistically optimal solution.The frequency-domain estimation of Channel Transfer Function(CTF)in frequency selective fading makes the method simpler,compared with the estimation of Channel Impulse Response(CIR)in the time domain.Two different time-varying PHN models,produced by Free Running Oscillator(FRO)and Phase-Locked Loop(PLL)oscillator,are presented and compared for performance difference with proposed OFDM receiver.Simulation results for joint MAP channel estimation are compared with Cramer-Rao Lower Bound(CRLB),and the simulation results for joint MAP data detection are compared with“NO PHN"performance to demonstrate that the proposed joint MAP estimation and detection algorithm achieve near-optimum performance even under multipath channel fading.

非对易相空间Dirac oscillator的研究(英文)

在极坐标系中研究了非对易相空间中的Dirac oscillator问题.研究显示:系统的波函数可以表示为合流超几何函数,而非对易相空间Dirac oscillator的量子行为类似于朗道问题.最后,对μ=0和对易极限两种特殊情况进行了简单讨论.

CALCULATING ACCURATE PERIODIC MOTIONS OF HARMONICALLY FORCED PIECEWISE LINEAR OSCILLATORS

This paper presents an efficient numerical scheme for calculating the periodic motion of a harmonically forced piecewise linear oscillator very accurately. The scheme is based on the shooting technique with the traditional numerical Poincare mapping and its Jacobian replaced by the piecewise analytic ones. Thus, the scheme gets rid of the requirement of the current schemes for an assumed order of the oscillator trajectory passing through different linear regions. The numerical examples in the paper demonstrate that the new scheme, compared with the current schemes, enables one to cope with more complicated dynamics of harmonically forced piecewise linear oscillators.

Dissipative Travelling Wave Solution for El Nio Tropic Sea-air Coupled Oscillator

El Nifio and Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific sea-air interactions. An asymptotic method of solving equations for the ENSO model is proposed. Based on a class of oscillator of ENSO model and by employing a simple and valid method of the variational iteration, the coupled system for a sea-air oscillator model of interdecadal climate fluctuations is studied. Firstly, by introducing a set of functionals and computing the variationals, the Lagrange multipliers are obtained. And then, the generalized variational iteration expressions are constructed. Finally, by selecting appropriate initial iteration, and from the iterations expressions, the approximations of solution for the sea-air oscillator ENSO model are solved successively. The approximate dissipative travelling wave solution of equations for corresponding ENSO model is studied. It is proved from the results that the method of the variational iteration can be used for analyzing the sea surface temperature anomaly in the equatorial Pacific of the sea-air oscillator for ENSO model.

Cu^(2+)-Catalyzed Oscillatory Oxidation of Ascorbic Acid by O_2 Flow

A novel heterogeneous oscillator, the Cu2+-catalyzed oscillatory oxidation of ascorbic acid (Vitamin C) in aqueous solution by O-2 flow was reported. Both the potential oscillations on Pt-electrode corresponding to [Cu2+] and the absorbance oscillations at lambda =260 nm corresponding to [ascorbic acid] were observed. Oscillations in the completely homogeneous system were also observed. Effects of several factors on the oscillations were investigated.

Application of the Homotopy Perturbation Method to Nonlinear Heat Conduction and Fractional Van der Pol Damped Nonlinear Oscillator

In this paper, a powerful analytical method, called He’s homotopy perturbation method is applied to obtaining the approximate periodic solutions for some nonlinear differential equations in mathematical physics via Van der Pol damped non-linear oscillators and heat transfer. Illustrative examples reveal that this method is very effective and convenient for solving nonlinear differential equations. Comparison of the obtained results with those of the exact solution, reveals that homotopy perturbation method leads to accurate solutions.

Straightforward Method for Nonlinear Oscillators

It is challenging to predict the frequency property of a nonlinear vibration system conveniently and efficiently.Especially,an invalid or physically irrelevant result might be obtained by some advanced methods.Therefore,predicting the frequency lacks an expedient and efficient method.This challenge is addressed by developing a straightforward and effective frequency formulation that reliably predicts the frequency-amplitude relationship.This study provides a one-step approach which can fast determine the periodic properties of any conservative oscillators and also provides a reference for other similar studies.