Monte Carlo investigation of an atom laser with a modulated quasi-one-dimensional cavity

Abstract

The dynamics of a recently proposed atom laser scheme based on a modulated quasi-one-dimensional atom cavity are investigated. A three-mode model is developed which includes the effects of dipole–dipole collisions as well as pump and loss mechanisms. It is shown that the Monte Carlo wavefunction simulation technique is superior to a direct solution of the resulting master equation because of the existence of constants of motion which are present in the Monte Carlo wavefunctions but not in the full density operator. Under suitable parameter choices, the solution to the master equation leads to Poissonian atom statistics in the occupation of a single-atomic-cavity mode, analogous to the photon statistics of the optical laser. A threshold behaviour is predicted as the losses are varied relative to the gain for the laser mode.     

Impact of Key Circuit Parameters on Signal-to-Noise Ratio Characteristics for the Radio Frequency Single-Electron Transistors

Hybrid simulation was performed to analyze the response of the real-time reflection-type radio frequency single-electron transistor (RF-SET) measurement system. A compact and physically-based analytical SET model, which was validated with a Monte Carlo simulator, was used to simulate the SET characteristics, while SPICE equivalent circuits were implemented to simulate all other components of the RF-SET measurement system. The impact of various key parameters on the RF-SET response was demonstrated for a carrier frequency much less than I/e ( is the typical current through the SET). It was revealed that an inevitable feed-through loss between the tank circuit and the cryogenic amplifier, and high-frequency parasitics of the inductor degrade the RF-SET performance significantly. As such, they have to be optimized to experimentally realize the shot-noise-limited charge sensitivity.     

Compact analytical model for room-temperature-operating silicon single-electron transistors with discrete quantum energy levels

A compact and analytical model for silicon single-electron transistors (SETs) considering the discrete quantum energy levels and the parabolic tunneling barriers is proposed. The model is based on a steady-state master equation that considers only the three most probable states derived from ground level and the first excited level for each number of electrons in the dot to reduce the complexity while accounting for the quantum-level spacing and multiple peaks in Coulomb oscillation. Negative differential conductance (NDC) characteristics and aperiodic Coulomb oscillations due to nonuniform quantum-level spacings can be reproduced in this model. The model was compared with measurements, and good agreement was obtained. Simulations of some basic circuits that utilize NDC are successfully carried out by applying our model to the HSPICE circuit simulation. Our model can provide suitable environments for designing CMOS-combined room-temperature-operating highly functional SET circuits.     

Analysis of Energy Quantization Effects on Single-Electron Transistor Circuits

In this paper, the effects of energy quantization on different single-electron transistor (SET) circuits (logic inverter, current-biased circuits, and hybrid MOS-SET circuits) are analyzed through analytical modeling and Monte Carlo simulations. It is shown that energy quantization mainly increases the Coulomb blockade area and Coulomb blockade oscillation periodicity, and thus, affects the SET circuit performance. A new model for the noise margin of the SET inverter is proposed, which includes the energy quantization effects. Using the noise margin as a metric, the robustness of the SET inverter is studied against the effects of energy quantization. An analytical expression is developed, which explicitly defines the maximum energy quantization (termed as “ quantization threshold”) that an SET inverter can withstand before its noise margin falls below a specified tolerance level. The effects of energy quantization are further studied for the current-biased negative differential resistance (NDR) circuit and hybrid SETMOS circuit. A new model for the conductance of NDR characteristics is also formulated that explains the energy quantization effects.      

Analog-digital and digital-analog converters using single-electron and MOS transistors

This paper proposes two kinds of novel single-electron analog-digital conversion (ADC) and digital-analog conversion (DAC) circuits that consist of single-electron transistors (SETs) and metal-oxide-semiconductor (MOS) transistors. The SET/MOS hybrid ADC and DAC circuits possess the merits of the SET circuit and the MOS circuit. We obtain the SPICE macro-modeling code of the SET transistor by studying and fitting the characteristics of the SET with SPICE simulation and Monte Carlo simulation methods. The SPICE macro-modeling code is used for the simulation of the SET/MOS hybrid ADC and DAC circuits. We simulate the performances of the SET/MOS hybrid 3-b ADC and 2-b DAC circuits by using the H-SPICE simulator. The simulation results demonstrate that the hybrid circuits can perform analog-digital and digital-analog data conversion well at room temperature. The hybrid ADC and DAC circuits have advantages as follows: 1) compared with conventional circuits, the architectures of the circuits are simpler; 2) compared with single electron transistor circuits, the circuits have much larger load capability; 3) the power dissipation of the circuits are lower than /spl omega/W; 4) the data conversion rate of the circuits can exceed 100 MHz; and 5) the resolution of the ADC and DAC circuits can be increased by the pipeline architectures.     

Stability of the entry flow rate of pulsating liquid in a tapered leaking elastic tube

Summary The two gas-kinetical simulation methods, the molecular dynamics method and the direct simulation Monte Carlo method, are used to calculate the Oseen vortex decay. The simulation solutions are compared with the analytical solution of the Navier-Stokes equation, this allowing examination of the influence of method-specific parameters on the simulation solution, particularly in relation to the conservation of angular momentum.The results obtained with the molecular dynamics method near the limit of the continuum-mechanical regime correlate very well with the analytical solution, the angular momentum being conserved exactly, due to the nature of the method. The direct simulation Monte Carlo method can also be used to simulate the vortex decay, provided that suitable parameters are selected. In this case, however, the angular momentum is not conserved exactly, due to the statistical assumptions. One of the objectives of this work is to optimize the Monte Carlo simulation method in relation to the conservation of angular momentum.With 10 Figures     

Accurate and computer efficient modelling of single event transients in CMOS circuits

A new analytical modelling approach to evaluate the impact of single event transients (SETs) on CMOS circuits has been developed. The model allows evaluation of transient pulse amplitude and width (duration) at the logic level, without the need to run circuit level (Spice-like) simulations. The SET mechanism in MOS circuits is normally investigated by Spice-like circuit simulation. The problem is that electrical simulation is time-consuming and must be performed for each different circuit topology, incident particle and track. The availability of a simple model at the logic gate level may greatly improve circuit sensitivity analysis. The electrical response of a circuit to an ionising particle hit depends on many parameters, such as circuit topology, circuit geometry and waveform shape of the charge injection mechanism. The proposed analytical model, which is accurate and computer efficient, captures these transistor-level effects of ionising particle hits and models them to the logic level of abstraction. The key idea is to exploit a model that allows the rapid determination of the sensitivity of any logic gate in a CMOS circuit, without the need to run circuit simulations. The model predicts whether or not a particle hit generates a SET, which may propagate to the next logic gate or memory element, making possible to analyse the sensitivity of each node in a complex circuit. Model derivation is strongly related to circuit electrical behaviour, being consistent with technology scaling. The model is suitable for integration into CAD tools, intending to make automated evaluation of circuit sensitivity to SET possible, as well as automated estimation of soft error rate     

Binary adders of multigate single-electron transistors: specific design using pass-transistor logic

We describe how to construct area-efficient adders using single-electron transistors (SETs). The design is based on pass-transistor logic and multigate SETs are used as pass transistors. The proposed design enables us to construct a full adder using only six SETs. We also show that multibit binary adders can be built using cascaded SET structures without any long wires. The small number of transistors and no-metal-interconnection configuration significantly reduces the circuit area and capacitance to be charged. A Monte Carlo simulation shows that even when the inter-SET-node capacitances are reduced and consequently the carry signal level terribly fluctuates in its path due to single-electron charging effects, the carry can correctly propagate as long as the final output node capacitance is sufficiently large. This proves that the area reduction and speed improvement are compatible in our design. We also discuss the possibility of large-scale integration, touching on the random-offset-charge issue.     

First passage failure of quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations

The first passage failure of multi-degree-of-freedom (MDOF) quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations in the case of external resonance is studied. First, a stochastic averaging method for quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations using generalized harmonic functions is reviewed briefly. Then, a backward Kolmogorov equation governing the conditional reliability function and a Pontryagin equation governing the conditional mean of the first passage time are established from the averaged Itô equations, respectively. The conditional reliability function, and the conditional probability density and conditional mean of the first passage time are obtained from solving these equations together with suitable initial condition and boundary conditions. The comparison between the analytical results and those from Monte Carlo simulation for an example shows that the proposed method works very well. It is also shown by using Monte Carlo simulation that the reliability of the system in the case of external resonance is much lower than that in the non-resonant case.     

Uncertainty propagation for deterministic models of biochemical networks using moment equations and the extended Kalman filter

Differential equation models of biochemical networks are frequently associated with a large degree of uncertainty in parameters and/or initial conditions. However, estimating the impact of this uncertainty on model predictions via Monte Carlo simulation is computationally demanding. A more efficient approach could be to track a system of low-order statistical moments of the state. Unfortunately, when the underlying model is nonlinear, the system of moment equations is infinite-dimensional and cannot be solved without a moment closure approximation which may introduce bias in the moment dynamics. Here, we present a new method to study the time evolution of the desired moments for nonlinear systems with polynomial rate laws. Our approach is based on solving a system of low-order moment equations by substituting the higher-order moments with Monte Carlo-based estimates from a small number of simulations, and using an extended Kalman filter to counteract Monte Carlo noise. Our algorithm provides more accurate and robust results compared to traditional Monte Carlo and moment closure techniques, and we expect that it will be widely useful for the quantification of uncertainty in biochemical model predictions.     

Modeling anisotropic light propagation in a realistic model of the human head

A Monte Carlo model capable of describing photon migration in arbitrary three-dimensional geometry with spatially varying optical properties and tissue anisotropy is presented. We use the model to explore the effects of anisotropy for optical measurements of the human head. An anisotropic diffusion equation that corresponds to our Monte Carlo model is derived, and a comparison between the Monte Carlo model and the diffusion equation solution with finite elements is given.     

Estimation of Uncertainty in the Calibration of Industrial Platinum Resistance Thermometers (IPRT) Using Monte Carlo Method

Monte Carlo method has been implemented for uncertainty estimation in IPRT calibration. The work is based on the Callendar van Dusen equation for 0–500 °C calibration range. Derivation of the mathematics model for running the simulation is also described. Results are compared with output from the traditional GUM method and we find close agreement between two methods.     

A practical SPICE model based on the physics and characteristics of realistic single-electron transistors

A practical model for a single-electron transistor (SET) was developed based on the physical phenomena in realistic Si SETs, and implemented into a conventional circuit simulator. In the proposed model, the SET current calculated by the analytic model is combined with the parasitic MOSFET characteristics, which have been observed in many recently reported SETs formed on Si nanostructures. The SPICE simulation results were compared with the measured characteristics of the Si SETs. In terms of the bias, temperature, and size dependence of the realistic SET characteristics, an extensive comparison leads to good agreement within a reasonable level of accuracy. This result is noticeable in that a single set of model parameters was used, while considering divergent physical phenomena such as the parasitic MOSFET, the Coulomb oscillation phase shift, and the tunneling resistance modulated by the gate bias. When compared to the measured data, the accuracy of the voltage transfer characteristics of a single-electron inverter obtained from the SPICE simulation was within 15%. This new SPICE model can be applied to estimating the realistic performance of a CMOS/SET hybrid circuit or various SET logic architectures.     

Influence of index table accuracy on roundness calibration in the multi-step method using monte carlo simulation

The precise and accurate roundness measurement is required year by year. The multi-step method is commonly used in the high-accuracy measurement for the roundness. The multi-step method is the self-calibration of the roundness capable of performing highly-advanced precise measurement. It depends on the reason that is able to separate measurement wave from the spindle rotation component and the form component of hemispherical master. But the mathematical models of the roundness measurement using that method are very complicated, describing numerous parameters and processes. So, recently, the Monte Carlo technique has attracted increasing attention as a very useful method for uncertainty estimation. This paper describes influences of the indexing angle accuracy and the noises generated by the roundness measuring machine, on the roundness measurements, both of which were analyzed by the Monte Carlo simulation. Furthermore, an example of hemispherical master is compared with the actual measurement data between when a reference guide plate is used utilizing the magnetic rotary encoder.     

Coupled Mechanical and 3-D Monte Carlo Simulation of Silicon Nanowire MOSFETs

In this paper we report on a general methodology to investigate nanowire MOSFETs based on the coupling of mechanical simulation with 3-D real-space Monte Carlo simulation. The Monte Carlo transport model accounts for both strain silicon and quantum mechanical effects. Mechanical strain effects are accounted for through an appropriate change of the anisotropic band structure computed with the empirical pseudopotential method. Quantum effects are instead included by means of a quantum mechanical correction of the potential coming from the self-consistent solution of the Schrodinger equation. This methodology has been then applied to the simulation of a test case silicon nanowire n-MOSFET. Impact of mechanical strain and quantum effects on the drive current is investigated. It is shown that only the inclusion of strain and quantum mechanical effects allows a good agreement with experimental data, demonstrating the validity of the proposed methodology for ultimate devices.     

Novel Hybrid Voltage Controlled Ring Oscillators Using Single Electron and MOS Transistors

This paper proposes two kinds of novel hybrid voltage controlled ring oscillators (VCO) using a single electron transistor (SET) and metal-oxide-semiconductor (MOS) transistor. The novel SET/MOS hybrid VCO circuits possess the merits of both the SET circuit and the MOS circuit. The novel VCO circuits have several advantages: wide frequency tuning range, low power dissipation, and large load capability. We use the SPICE compact macro model to describe the SET and simulate the performances of the SET/MOS hybrid VCO circuits by HSPICE simulator. Simulation results demonstrate that the hybrid circuits can operate well as a VCO at room temperature. The oscillation frequency of the VCO circuits could be as high as 1 GHz, with a -71 dBc/Hz phase noise at 1 MHz offset frequency. The power dissipations are lower than 2 uW. We studied the effect of fabrication tolerance, background charge, and operating temperature on the performances of the circuits     

Crossover Behavior of Linear and Star Polymers in Good Solvents

Monte Carlo simulation calculations for the mean-square end-to-end distance and second virial coefficient for model linear and star polymers composed of hard spheres with square-well attractions are presented. For these polymers, two types of crossover behavior are observed: (i) crossover from the Gaussian chain to the Kuhnian chain limits and (ii) crossover from the semiflexible chain to the Kuhnian chain limits. A crossover theory for the properties of dilute linear and star polymers under good solvent conditions is presented. This model directly relates the properties of the monomer–monomer interaction to the renormalized parameters of the theory. The predictions of the crossover theory are in good agreement with simulation data. A new equation of state for linear and star polymers in good solvents is presented. The equation of state captures the scaling behavior of polymer solutions in the dilute/semidilute regimes and also performs well in the concentrated regimes, where the details of the monomer–monomer interactions become important. This theory is compared to Monte Carlo simulation data for the volumetric behavior of tangent hard-sphere polymers.     

Analysis of one-dimensional stochastic finite elements using neural networks

This paper explores the applicability of neural networks for analyzing the uncertainty spread of structural responses under the presence of one-dimensional random fields. Specifically, the neural network is intended to be a partial surrogate of the structural model needed in a Monte Carlo simulation, due to its associative memory properties. The network is trained with some pairs of input and output data obtained by some Monte Carlo simulations and then used in substitution of the finite element solver. In order to minimize the size of the networks, and hence the number of training pairs, the Karhunen–Loéve decomposition is applied as an optimal feature extraction tool. The Monte Carlo samples for training and validation are also generated using this decomposition. The Nyström technique is employed for the numerical solution of the Fredholm integral equation. The radial basis function (RBF) network was selected as the neural device for learning the input/output relationship due to its high accuracy and fast training speed. The analysis shows that this approach constitutes a promising method for stochastic finite element analysis inasmuch as the error with respect to the Monte Carlo simulation is negligible.     

Novel single-electron logic circuits using charge-induced signal transmission (CIST) structures

In this paper, on the basis of the Monte Carlo simulation, we demonstrate a method to realize logical operations by the use of the single-electron charge-induced signal transmission (CIST) circuit which we have proposed previously. First, we propose three new-type signal transmission circuits. Then, we demonstrate through construction of a NAND circuit and a full-adder circuit on the basis of the Monte Carlo simulation that we can construct any logic circuit by the use of these circuits. Since the CIST circuit can perform any logical operation and can transmit the state of the presence or absence of an electron and a hole as a binary signal over long distance during one clock cycle bidirectionally, these CIST circuits are expected to be applied to integrated circuit devices as a new circuit construction method.     

Hybrid radiative-transfer-diffusion model for optical tomography

A hybrid radiative-transfer-diffusion model for optical tomography is proposed. The light propagation is modeled with the radiative-transfer equation in the vicinity of the laser sources, and the diffusion approximation is used elsewhere in the domain. The solution of the radiative-transfer equation is used to construct a Dirichlet boundary condition for the diffusion approximation on a fictitious interface within the object. This boundary condition constitutes an approximative distributed source model for the diffusion approximation in the remaining area. The results from the proposed approach are compared with finite-element solutions of the radiative-transfer equation and the diffusion approximation and Monte Carlo simulation. The results show that the method improves the accuracy of the forward model compared with the conventional diffusion model.